Daily Papers

Linear Attention (LA) offers a promising paradigm for scaling large language models (LLMs) to long sequences by avoiding the quadratic complexity of self-attention. Recent LA models such as Mamba2 and GDN interpret linear recurrences as closed-form online stochastic gradient descent (SGD), but naive SGD updates suffer from rapid information decay and suboptimal convergence in optimization. While momentum-based optimizers provide a natural remedy, they pose challenges in simultaneously achieving training efficiency and effectiveness. To address this, we develop a chunkwise parallel algorithm for LA with a stepwise momentum rule by geometrically reordering the update coefficients. Further, from a dynamical systems perspective, we analyze the momentum-based recurrence as a second-order system that introduces complex conjugate eigenvalues. This analysis guides the design of stable gating constraints. The resulting model, Momentum DeltaNet (MDN), leverages Triton kernels to achieve comparable training throughput with competitive linear models such as Mamba2 and KDA. Extensive experiments on the 400M and 1.3B parameter models demonstrate consistent performance improvements over strong baselines, including Transformers, Mamba2 and GDN, across diverse downstream evaluation benchmarks. Code: https://github.com/HuuYuLong/MomentumDeltaNet .

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network. Additionally, we find that sparse momentum is insensitive to the choice of its hyperparameters suggesting that sparse momentum is robust and easy to use.

Deep neural networks conventionally employ end-to-end backpropagation for their training process, which lacks biological credibility and triggers a locking dilemma during network parameter updates, leading to significant GPU memory use. Supervised local learning, which segments the network into multiple local blocks updated by independent auxiliary networks. However, these methods cannot replace end-to-end training due to lower accuracy, as gradients only propagate within their local block, creating a lack of information exchange between blocks. To address this issue and establish information transfer across blocks, we propose a Momentum Auxiliary Network (MAN) that establishes a dynamic interaction mechanism. The MAN leverages an exponential moving average (EMA) of the parameters from adjacent local blocks to enhance information flow. This auxiliary network, updated through EMA, helps bridge the informational gap between blocks. Nevertheless, we observe that directly applying EMA parameters has certain limitations due to feature discrepancies among local blocks. To overcome this, we introduce learnable biases, further boosting performance. We have validated our method on four image classification datasets (CIFAR-10, STL-10, SVHN, ImageNet), attaining superior performance and substantial memory savings. Notably, our method can reduce GPU memory usage by more than 45\% on the ImageNet dataset compared to end-to-end training, while achieving higher performance. The Momentum Auxiliary Network thus offers a new perspective for supervised local learning. Our code is available at: https://github.com/JunhaoSu0/MAN.

Linear Recurrent Neural Networks (linear RNNs) have emerged as competitive alternatives to Transformers for sequence modeling, offering efficient training and linear-time inference. However, existing architectures face a fundamental trade-off between expressivity and efficiency, dictated by the structure of their state-transition matrices. Diagonal matrices, used in models such as Mamba, GLA, or mLSTM, yield fast runtime but have limited expressivity. To address this, recent architectures such as DeltaNet and RWKV-7 adopted a diagonal plus rank-1 structure, which allows simultaneous token and channel mixing, improving associative recall and, as recently shown, state-tracking when allowing negative eigenvalues in the state-transition matrices. Building on the interpretation of DeltaNet's recurrence as performing one step of online gradient descent per token on an associative recall loss, we introduce DeltaProduct, which instead takes multiple (n_h) steps per token. This naturally leads to diagonal plus rank-n_h state-transition matrices, formed as products of n_h generalized Householder transformations, providing a tunable mechanism to balance expressivity and efficiency. We provide a detailed theoretical characterization of the state-tracking capability of DeltaProduct in finite precision, showing how it improves by increasing n_h. Our extensive experiments demonstrate that DeltaProduct outperforms DeltaNet in both state-tracking and language modeling, while also showing significantly improved length extrapolation capabilities.

Transformers with linear attention (i.e., linear transformers) and state-space models have recently been suggested as a viable linear-time alternative to transformers with softmax attention. However, these models still underperform transformers especially on tasks that require in-context retrieval. While more expressive variants of linear transformers which replace the additive outer-product update in linear transformers with the delta rule have been found to be more effective at associative recall, existing algorithms for training such models do not parallelize over sequence length and are thus inefficient to train on modern hardware. This work describes a hardware-efficient algorithm for training linear transformers with the delta rule, which exploits a memory-efficient representation for computing products of Householder matrices. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B model for 100B tokens and find that it outperforms recent linear-time baselines such as Mamba and GLA in terms of perplexity and zero-shot performance on downstream tasks (including on tasks that focus on recall). We also experiment with two hybrid models which combine DeltaNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrid models outperform strong transformer baselines.

Momentum is known to accelerate the convergence of gradient descent in strongly convex settings without stochastic gradient noise. In stochastic optimization, such as training neural networks, folklore suggests that momentum may help deep learning optimization by reducing the variance of the stochastic gradient update, but previous theoretical analyses do not find momentum to offer any provable acceleration. Theoretical results in this paper clarify the role of momentum in stochastic settings where the learning rate is small and gradient noise is the dominant source of instability, suggesting that SGD with and without momentum behave similarly in the short and long time horizons. Experiments show that momentum indeed has limited benefits for both optimization and generalization in practical training regimes where the optimal learning rate is not very large, including small- to medium-batch training from scratch on ImageNet and fine-tuning language models on downstream tasks.

Accurately segmenting different organs from medical images is a critical prerequisite for computer-assisted diagnosis and intervention planning. This study proposes a deep learning-based approach for segmenting various organs from CT and MRI scans and classifying diseases. Our study introduces a novel technique integrating momentum within residual blocks for enhanced training dynamics in medical image analysis. We applied our method in two distinct tasks: segmenting liver, lung, & colon data and classifying abdominal pelvic CT and MRI scans. The proposed approach has shown promising results, outperforming state-of-the-art methods on publicly available benchmarking datasets. For instance, in the lung segmentation dataset, our approach yielded significant enhancements over the TransNetR model, including a 5.72% increase in dice score, a 5.04% improvement in mean Intersection over Union (mIoU), an 8.02% improvement in recall, and a 4.42% improvement in precision. Hence, incorporating momentum led to state-of-the-art performance in both segmentation and classification tasks, representing a significant advancement in the field of medical imaging.

The efficacy of deep residual networks is fundamentally predicated on the identity shortcut connection. While this mechanism effectively mitigates the vanishing gradient problem, it imposes a strictly additive inductive bias on feature transformations, thereby limiting the network's capacity to model complex state transitions. In this paper, we introduce Deep Delta Learning (DDL), a novel architecture that generalizes the standard residual connection by modulating the identity shortcut with a learnable, data-dependent geometric transformation. This transformation, termed the Delta Operator, constitutes a rank-1 perturbation of the identity matrix, parameterized by a reflection direction vector k(X) and a gating scalar β(X). We provide a spectral analysis of this operator, demonstrating that the gate β(X) enables dynamic interpolation between identity mapping, orthogonal projection, and geometric reflection. Furthermore, we restructure the residual update as a synchronous rank-1 injection, where the gate acts as a dynamic step size governing both the erasure of old information and the writing of new features. This unification empowers the network to explicitly control the spectrum of its layer-wise transition operator, enabling the modeling of complex, non-monotonic dynamics while preserving the stable training characteristics of gated residual architectures.

Federated learning is a powerful paradigm for large-scale machine learning, but it faces significant challenges due to unreliable network connections, slow communication, and substantial data heterogeneity across clients. FedAvg and SCAFFOLD are two prominent algorithms to address these challenges. In particular, FedAvg employs multiple local updates before communicating with a central server, while SCAFFOLD maintains a control variable on each client to compensate for ``client drift'' in its local updates. Various methods have been proposed to enhance the convergence of these two algorithms, but they either make impractical adjustments to the algorithmic structure or rely on the assumption of bounded data heterogeneity. This paper explores the utilization of momentum to enhance the performance of FedAvg and SCAFFOLD. When all clients participate in the training process, we demonstrate that incorporating momentum allows FedAvg to converge without relying on the assumption of bounded data heterogeneity even using a constant local learning rate. This is novel and fairly surprising as existing analyses for FedAvg require bounded data heterogeneity even with diminishing local learning rates. In partial client participation, we show that momentum enables SCAFFOLD to converge provably faster without imposing any additional assumptions. Furthermore, we use momentum to develop new variance-reduced extensions of FedAvg and SCAFFOLD, which exhibit state-of-the-art convergence rates. Our experimental results support all theoretical findings.

Flow-based generative models have become a strong framework for high-quality generative modeling, yet pretrained models are rarely used in their vanilla conditional form: conditional samples without guidance often appear diffuse and lack fine-grained detail due to the smoothing effects of neural networks. Existing guidance techniques such as classifier-free guidance (CFG) improve fidelity but double the inference cost and typically reduce sample diversity. We introduce Momentum Guidance (MG), a new dimension of guidance that leverages the ODE trajectory itself. MG extrapolates the current velocity using an exponential moving average of past velocities and preserves the standard one-evaluation-per-step cost. It matches the effect of standard guidance without extra computation and can further improve quality when combined with CFG. Experiments demonstrate MG's effectiveness across benchmarks. Specifically, on ImageNet-256, MG achieves average improvements in FID of 36.68% without CFG and 25.52% with CFG across various sampling settings, attaining an FID of 1.597 at 64 sampling steps. Evaluations on large flow-based models like Stable Diffusion 3 and FLUX.1-dev further confirm consistent quality enhancements across standard metrics.

We propose a novel framework, Stable Diffusion-based Momentum Integrated Adversarial Examples (SD-MIAE), for generating adversarial examples that can effectively mislead neural network classifiers while maintaining visual imperceptibility and preserving the semantic similarity to the original class label. Our method leverages the text-to-image generation capabilities of the Stable Diffusion model by manipulating token embeddings corresponding to the specified class in its latent space. These token embeddings guide the generation of adversarial images that maintain high visual fidelity. The SD-MIAE framework consists of two phases: (1) an initial adversarial optimization phase that modifies token embeddings to produce misclassified yet natural-looking images and (2) a momentum-based optimization phase that refines the adversarial perturbations. By introducing momentum, our approach stabilizes the optimization of perturbations across iterations, enhancing both the misclassification rate and visual fidelity of the generated adversarial examples. Experimental results demonstrate that SD-MIAE achieves a high misclassification rate of 79%, improving by 35% over the state-of-the-art method while preserving the imperceptibility of adversarial perturbations and the semantic similarity to the original class label, making it a practical method for robust adversarial evaluation.

Knowledge distillation (KD) is a widely adopted approach for compressing large neural networks by transferring knowledge from a large teacher model to a smaller student model. In the context of large language models, token level KD, typically minimizing the KL divergence between student output distribution and teacher output distribution, has shown strong empirical performance. However, prior work assumes student output distribution and teacher output distribution share the same optimal representation space, a premise that may not hold in many cases. To solve this problem, we propose Delta Knowledge Distillation (Delta-KD), a novel extension of token level KD that encourages the student to approximate an optimal representation space by explicitly preserving the distributional shift Delta introduced during the teacher's supervised finetuning (SFT). Empirical results on ROUGE metrics demonstrate that Delta KD substantially improves student performance while preserving more of the teacher's knowledge.

In the training of large language models, momentum is widely used and often demonstrated to achieve significant acceleration. However, storing momentum typically presents memory challenges. In this paper, we propose AdaPM, an adaptive training strategy that leverages partial momentum to implement a memory-efficient optimizer. To this end, AdaPM utilizes a non-uniform momentum design: for most blocks, full momentum is not necessary to preserve the performance of the optimization. In the momentum design of AdaPM, to mitigate the bias and performance loss caused by partial momentum, we enhance the partial momentum by a bias correction technique. Empirically, we verify that our approach reduces memory by over 90% in momentum while maintaining both efficiency and performance for pretraining various language models ranging from 60M to 1.5B, as well as for supervised fine-tuning and RLHF. AdaPM can further reduce memory by up to 95% in optimizer states by combining the memory-efficient technique on the second-order statistic, saving over 30% GPU hours for pretraining GPT-2 1.5B.

In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model training speed across deep networks, we propose the ADAptive Nesterov momentum algorithm, Adan for short. Adan first reformulates the vanilla Nesterov acceleration to develop a new Nesterov momentum estimation (NME) method, which avoids the extra overhead of computing gradient at the extrapolation point. Then Adan adopts NME to estimate the gradient's first- and second-order moments in adaptive gradient algorithms for convergence acceleration. Besides, we prove that Adan finds an epsilon-approximate first-order stationary point within O(epsilon^{-3.5}) stochastic gradient complexity on the non-convex stochastic problems (e.g., deep learning problems), matching the best-known lower bound. Extensive experimental results show that Adan consistently surpasses the corresponding SoTA optimizers on vision, language, and RL tasks and sets new SoTAs for many popular networks and frameworks, e.g., ResNet, ConvNext, ViT, Swin, MAE, DETR, GPT-2, Transformer-XL, and BERT. More surprisingly, Adan can use half of the training cost (epochs) of SoTA optimizers to achieve higher or comparable performance on ViT, GPT-2, MAE, e.t.c., and also shows great tolerance to a large range of minibatch size, e.g., from 1k to 32k. Code is released at https://github.com/sail-sg/Adan, and has been used in multiple popular deep learning frameworks or projects.

Linear Transformers have gained attention as efficient alternatives to standard Transformers, but their performance in retrieval and long-context tasks has been limited. To address these limitations, recent work has explored two distinct mechanisms: gating for adaptive memory control and the delta update rule for precise memory modifications. We observe that these mechanisms are complementary: gating enables rapid memory erasure while the delta rule facilitates targeted updates. Building on this insight, we introduce the gated delta rule and develop a parallel training algorithm optimized for modern hardware. Our proposed architecture, Gated DeltaNet, consistently surpasses existing models like Mamba2 and DeltaNet across multiple benchmarks, including language modeling, common-sense reasoning, in-context retrieval, length extrapolation, and long-context understanding. We further enhance performance by developing hybrid architectures that combine Gated DeltaNet layers with sliding window attention or Mamba2 layers, achieving both improved training efficiency and superior task performance.

Anticipating diverse future states is a central challenge in video world modeling. Discriminative world models produce a deterministic prediction that implicitly averages over possible futures, while existing generative world models remain computationally expensive. Recent work demonstrates that predicting the future in the feature space of a vision foundation model (VFM), rather than a latent space optimized for pixel reconstruction, requires significantly fewer world model parameters. However, most such approaches remain discriminative. In this work, we introduce DeltaTok, a tokenizer that encodes the VFM feature difference between consecutive frames into a single continuous "delta" token, and DeltaWorld, a generative world model operating on these tokens to efficiently generate diverse plausible futures. Delta tokens reduce video from a three-dimensional spatio-temporal representation to a one-dimensional temporal sequence, for example yielding a 1,024x token reduction with 512x512 frames. This compact representation enables tractable multi-hypothesis training, where many futures are generated in parallel and only the best is supervised. At inference, this leads to diverse predictions in a single forward pass. Experiments on dense forecasting tasks demonstrate that DeltaWorld forecasts futures that more closely align with real-world outcomes, while having over 35x fewer parameters and using 2,000x fewer FLOPs than existing generative world models. Code and weights: https://deltatok.github.io.

The vast majority of modern deep learning models are trained with momentum-based first-order optimizers. The momentum term governs the optimizer's memory by determining how much each past gradient contributes to the current convergence direction. Fundamental momentum methods, such as Nesterov Accelerated Gradient and the Heavy Ball method, as well as more recent optimizers such as AdamW and Lion, all rely on the momentum coefficient that is customarily set to β= 0.9 and kept constant during model training, a strategy widely used by practitioners, yet suboptimal. In this paper, we introduce an adaptive memory mechanism that replaces constant momentum with a dynamic momentum coefficient that is adjusted online during optimization. We derive our method by approximating the objective function using two planes: one derived from the gradient at the current iterate and the other obtained from the accumulated memory of the past gradients. To the best of our knowledge, such a proximal framework was never used for momentum-based optimization. Our proposed approach is novel, extremely simple to use, and does not rely on extra assumptions or hyperparameter tuning. We implement adaptive memory variants of both SGD and AdamW across a wide range of learning tasks, from simple convex problems to large-scale deep learning scenarios, demonstrating that our approach can outperform standard SGD and Adam with hand-tuned momentum coefficients. Finally, our work opens doors for new ways of inducing adaptivity in optimization.

We propose a lightweight CPU network based on the MKLDNN acceleration strategy, named PP-LCNet, which improves the performance of lightweight models on multiple tasks. This paper lists technologies which can improve network accuracy while the latency is almost constant. With these improvements, the accuracy of PP-LCNet can greatly surpass the previous network structure with the same inference time for classification. As shown in Figure 1, it outperforms the most state-of-the-art models. And for downstream tasks of computer vision, it also performs very well, such as object detection, semantic segmentation, etc. All our experiments are implemented based on PaddlePaddle. Code and pretrained models are available at PaddleClas.

Training large neural networks typically requires sharing gradients between accelerators through specialized high-speed interconnects. Drawing from the signal processing principles of frequency decomposition and energy compaction, we demonstrate that synchronizing full optimizer states and model parameters during training is unnecessary. By decoupling momentum updates and allowing controlled divergence in optimizer states across accelerators, we achieve improved convergence compared to state-of-the-art optimizers. We introduce {De}coupled {Mo}mentum (DeMo), a fused optimizer and data parallel algorithm that reduces inter-accelerator communication requirements by several orders of magnitude. This enables training of large neural networks even with limited network bandwidth and heterogeneous hardware. Our method is topology-agnostic and architecture-independent and supports scalable clock-synchronous distributed training with negligible compute and memory overhead. Empirical results show that models trained with DeMo match or exceed the performance of equivalent models trained with AdamW, while eliminating the need for high-speed interconnects when pre-training large scale foundation models. An open source reference PyTorch implementation is published on GitHub at https://github.com/bloc97/DeMo

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

Data-driven surrogate models are increasingly adopted to accelerate vehicle design. However, open-source multi-fidelity datasets and empirical guidelines linking dataset size to model performance remain limited. This study investigates the relationship between training data size and prediction accuracy for a graph neural network (GNN) based surrogate model for aerodynamic field prediction. We release an open-source, multi-fidelity aerodynamic dataset for double-delta wings, comprising 2448 flow snapshots across 272 geometries evaluated at angles of attack from 11 (degree) to 19 (degree) at Ma=0.3 using both Vortex Lattice Method (VLM) and Reynolds-Averaged Navier-Stokes (RANS) solvers. The geometries are generated using a nested Saltelli sampling scheme to support future dataset expansion and variance-based sensitivity analysis. Using this dataset, we conduct a preliminary empirical scaling study of the MF-VortexNet surrogate by constructing six training datasets with sizes ranging from 40 to 1280 snapshots and training models with 0.1 to 2.4 million parameters under a fixed training budget. We find that the test error decreases with data size with a power-law exponent of -0.6122, indicating efficient data utilization. Based on this scaling law, we estimate that the optimal sampling density is approximately eight samples per dimension in a d-dimensional design space. The results also suggest improved data utilization efficiency for larger surrogate models, implying a potential trade-off between dataset generation cost and model training budget.

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.

3D Gaussian Splatting has demonstrated notable success in large-scale scene reconstruction, but challenges persist due to high training memory consumption and storage overhead. Hybrid representations that integrate implicit and explicit features offer a way to mitigate these limitations. However, when applied in parallelized block-wise training, two critical issues arise since reconstruction accuracy deteriorates due to reduced data diversity when training each block independently, and parallel training restricts the number of divided blocks to the available number of GPUs. To address these issues, we propose Momentum-GS, a novel approach that leverages momentum-based self-distillation to promote consistency and accuracy across the blocks while decoupling the number of blocks from the physical GPU count. Our method maintains a teacher Gaussian decoder updated with momentum, ensuring a stable reference during training. This teacher provides each block with global guidance in a self-distillation manner, promoting spatial consistency in reconstruction. To further ensure consistency across the blocks, we incorporate block weighting, dynamically adjusting each block's weight according to its reconstruction accuracy. Extensive experiments on large-scale scenes show that our method consistently outperforms existing techniques, achieving a 12.8% improvement in LPIPS over CityGaussian with much fewer divided blocks and establishing a new state of the art. Project page: https://jixuan-fan.github.io/Momentum-GS_Page/

We present PolyKV, a system in which multiple concurrent inference agents share a single, asymmetrically compressed KV cache pool. Rather than allocating a separate KV cache per agent -- the standard paradigm -- PolyKV writes a compressed cache once and injects it into N independent agent contexts via HuggingFace DynamicCache objects. Compression is asymmetric: Keys are quantized at int8 (q8_0) to preserve softmax stability, while Values are compressed using TurboQuant MSE -- a Fast Walsh-Hadamard Transform (FWHT) rotation followed by 3-bit Lloyd-Max quantization with centroids tuned to N(0,1). We evaluate across two model scales (SmolLM2-1.7B-Instruct and Llama-3-8B-Instruct), three context lengths (600-7,194 tokens), and up to 15 concurrent agents. PolyKV achieves a stable 2.91x compression ratio across all configurations. On Llama-3-8B with 15 agents sharing a 4K-token context, PolyKV reduces KV cache memory from 19.8 GB to 0.45 GB -- a 97.7% reduction -- while maintaining only +0.57% perplexity degradation and a mean BERTScore F1 of 0.928. PPL delta does not grow with agent count and improves as context length increases, inverting to -0.26% at 1,851 coherent tokens. To our knowledge, no prior work combines a single shared, lossy-compressed KV pool with multi-reader concurrent agent access.

Communication costs within Federated learning hinder the system scalability for reaching more data from more clients. The proposed FL adopts a hub-and-spoke network topology. All clients communicate through the central server. Hence, reducing communication overheads via techniques such as data compression has been proposed to mitigate this issue. Another challenge of federated learning is unbalanced data distribution, data on each client are not independent and identically distributed (non-IID) in a typical federated learning setting. In this paper, we proposed a new compression compensation scheme called Global Momentum Fusion (GMF) which reduces communication overheads between FL clients and the server and maintains comparable model accuracy in the presence of non-IID data. GitHub repository: https://github.com/tony92151/global-momentum-fusion-fl

Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and behaviour. Moreover, these hidden features can be directly manipulated to steer model behaviour. However, it remains an open question whether this phenomenon is unique to models trained on inherently structured data (ie. language, images) or if it is a general property of foundation models. In this work, we investigate the internal representations of a large physics-focused foundation model. Inspired by recent work identifying single directions in activation space for complex behaviours in LLMs, we extract activation vectors from the model during forward passes over simulation datasets for different physical regimes. We then compute "delta" representations between the two regimes. These delta tensors act as concept directions in activation space, encoding specific physical features. By injecting these concept directions back into the model during inference, we can steer its predictions, demonstrating causal control over physical behaviours, such as inducing or removing some particular physical feature from a simulation. These results suggest that scientific foundation models learn generalised representations of physical principles. They do not merely rely on superficial correlations and patterns in the simulations. Our findings open new avenues for understanding and controlling scientific foundation models and has implications for AI-enabled scientific discovery.

We introduce Leap+Verify, a framework that applies speculative execution -- predicting future model weights and validating predictions before acceptance -- to accelerate neural network training. Inspired by speculative decoding in language model inference and by the Automatically Scalable Computation (ASC) architecture for program execution, Leap+Verify decomposes training into three dynamically detected regimes (chaotic, transition, stable) using activation-space cosine similarity as a real-time Lyapunov proxy signal. Within each regime, analytic weight predictors (momentum, linear, quadratic extrapolation) attempt to forecast model parameters K training steps ahead; predictions are accepted only when validated against a held-out loss criterion. We evaluate Leap+Verify on GPT-2 124M and Qwen 2.5-1.5B trained on WikiText-103 across five random seeds, sweeping prediction depth K in {5, 10, 25, 50, 75, 100}. Momentum-based prediction (Adam moment extrapolation) fails catastrophically at both scales, with predicted losses exceeding actuals by 100-10,000x -- a universal norm explosion in optimizer-state extrapolation. Finite-difference predictors (linear, quadratic) succeed where momentum fails: at 124M, they achieve 24% strict acceptance at K=5 in stable regimes; at 1.5B, they achieve 37% strict acceptance in transition regimes. The scale-dependent finding is in regime distribution: GPT-2 124M spends 34% of training in stable regime, while Qwen 1.5B spends 64% in chaotic regime and reaches stable in only 0-2 of 40 checkpoints. Larger models are more predictable when predictable, but less often predictable -- the practical bottleneck shifts from predictor accuracy to regime availability. Cross-seed results are highly consistent (less than 1% validation loss variance), and the three-regime framework produces identical phase boundaries (plus or minus 50 steps) across seeds.

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling to endow the invariant properties. ConCerNet consists of two steps: (i) a contrastive learning method to automatically capture the system invariants (i.e. conservation properties) along the trajectory observations; (ii) a neural projection layer to guarantee that the learned dynamics models preserve the learned invariants. We theoretically prove the functional relationship between the learned latent representation and the unknown system invariant function. Experiments show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics by a large margin. With neural network based parameterization and no dependence on prior knowledge, our method can be extended to complex and large-scale dynamics by leveraging an autoencoder.

In this paper, we propose Scene Splatter, a momentum-based paradigm for video diffusion to generate generic scenes from single image. Existing methods, which employ video generation models to synthesize novel views, suffer from limited video length and scene inconsistency, leading to artifacts and distortions during further reconstruction. To address this issue, we construct noisy samples from original features as momentum to enhance video details and maintain scene consistency. However, for latent features with the perception field that spans both known and unknown regions, such latent-level momentum restricts the generative ability of video diffusion in unknown regions. Therefore, we further introduce the aforementioned consistent video as a pixel-level momentum to a directly generated video without momentum for better recovery of unseen regions. Our cascaded momentum enables video diffusion models to generate both high-fidelity and consistent novel views. We further finetune the global Gaussian representations with enhanced frames and render new frames for momentum update in the next step. In this manner, we can iteratively recover a 3D scene, avoiding the limitation of video length. Extensive experiments demonstrate the generalization capability and superior performance of our method in high-fidelity and consistent scene generation.

Efficiently exploring complex loss landscapes is key to the performance of deep neural networks. While momentum-based optimizers are widely used in state-of-the-art setups, classical momentum can still struggle with large, misaligned gradients, leading to oscillations. To address this, we propose Torque-Aware Momentum (TAM), which introduces a damping factor based on the angle between the new gradients and previous momentum, stabilizing the update direction during training. Empirical results show that TAM, which can be combined with both SGD and Adam, enhances exploration, handles distribution shifts more effectively, and improves generalization performance across various tasks, including image classification and large language model fine-tuning, when compared to classical momentum-based optimizers.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

Federated learning (FL) is a distributed machine learning framework where the global model of a central server is trained via multiple collaborative steps by participating clients without sharing their data. While being a flexible framework, where the distribution of local data, participation rate, and computing power of each client can greatly vary, such flexibility gives rise to many new challenges, especially in the hyperparameter tuning on the client side. We propose Delta-SGD, a simple step size rule for SGD that enables each client to use its own step size by adapting to the local smoothness of the function each client is optimizing. We provide theoretical and empirical results where the benefit of the client adaptivity is shown in various FL scenarios.

We introduce novel variants of momentum by incorporating the variance of the stochastic loss function. The variance characterizes the confidence or uncertainty of the local features of the averaged loss surface across the i.i.d. subsets of the training data defined by the mini-batches. We show two applications of the gradient of the variance of the loss function. First, as a bias to the conventional momentum update to encourage conformity of the local features of the loss function (e.g. local minima) across mini-batches to improve generalization and the cumulative training progress made per epoch. Second, as an alternative direction for "exploration" in the parameter space, especially, for non-convex objectives, that exploits both the optimistic and pessimistic views of the loss function in the face of uncertainty. We also introduce a novel data-driven stochastic regularization technique through the parameter update rule that is model-agnostic and compatible with arbitrary architectures. We further establish connections to probability distributions over loss functions and the REINFORCE policy gradient update with baseline in RL. Finally, we incorporate the new variants of momentum proposed into Adam, and empirically show that our methods improve the rate of convergence of training based on our experiments on the MNIST and CIFAR-10 datasets.

Activation sparsity improves compute efficiency and resource utilization in sparsity-aware neural network accelerators. As the predominant operation in DNNs is multiply-accumulate (MAC) of activations with weights to compute inner products, skipping operations where (at least) one of the two operands is zero can make inference more efficient in terms of latency and power. Spatial sparsification of activations is a popular topic in DNN literature and several methods have already been established to bias a DNN for it. On the other hand, temporal sparsity is an inherent feature of bio-inspired spiking neural networks (SNNs), which neuromorphic processing exploits for hardware efficiency. Introducing and exploiting spatio-temporal sparsity, is a topic much less explored in DNN literature, but in perfect resonance with the trend in DNN, to shift from static signal processing to more streaming signal processing. Towards this goal, in this paper we introduce a new DNN layer (called Delta Activation Layer), whose sole purpose is to promote temporal sparsity of activations during training. A Delta Activation Layer casts temporal sparsity into spatial activation sparsity to be exploited when performing sparse tensor multiplications in hardware. By employing delta inference and ``the usual'' spatial sparsification heuristics during training, the resulting model learns to exploit not only spatial but also temporal activation sparsity (for a given input data distribution). One may use the Delta Activation Layer either during vanilla training or during a refinement phase. We have implemented Delta Activation Layer as an extension of the standard Tensoflow-Keras library, and applied it to train deep neural networks on the Human Action Recognition (UCF101) dataset. We report an almost 3x improvement of activation sparsity, with recoverable loss of model accuracy after longer training.

Open-ended text generation with autoregressive language models (LMs) is one of the core tasks in natural language processing. However, maximization-based decoding methods (e.g., greedy/beam search) often lead to the degeneration problem, i.e., the generated text is unnatural and contains undesirable repetitions. Existing solutions to this problem either introduce randomness prone to incoherence or require a look-ahead mechanism that demands extra computational overhead. In this study, we formulate open-ended text generation from a new perspective, i.e., we view it as an exploration process within a directed graph. Thereby, we understand the phenomenon of degeneration as circular loops within the directed graph. Based on our formulation, we propose a novel decoding method -- momentum decoding -- which encourages the LM to greedily explore new nodes outside the current graph. Meanwhile, it also allows the LM to return to the existing nodes with a momentum downgraded by a pre-defined resistance function. We extensively test our approach on three benchmarks from different domains through automatic and human evaluations. The results show that momentum decoding performs comparably with the current state of the art while enjoying notably improved inference speed and computation FLOPs. Furthermore, we conduct a detailed analysis to reveal the merits and inner workings of our approach. Our codes and other related resources are publicly available at https://github.com/gmftbyGMFTBY/MomentumDecoding.

In deep learning, mini-batch training is commonly used to optimize network parameters. However, the traditional mini-batch method may not learn the under-represented samples and complex patterns in the data, leading to a longer time for generalization. To address this problem, a variant of the traditional algorithm has been proposed, which trains the network focusing on mini-batches with high loss. The study evaluates the effectiveness of the proposed training using various deep neural networks trained on three benchmark datasets (CIFAR-10, CIFAR-100, and STL-10). The deep neural networks used in the study are ResNet-18, ResNet-50, Efficient Net B4, EfficientNetV2-S, and MobilenetV3-S. The experimental results showed that the proposed method can significantly improve the test accuracy and speed up the convergence compared to the traditional mini-batch training method. Furthermore, we introduce a hyper-parameter delta ({\delta}) that decides how many mini-batches are considered for training. Experiments on various values of {\delta} found that the performance of the proposed method for smaller {\delta} values generally results in similar test accuracy and faster generalization. We show that the proposed method generalizes in 26.47% less number of epochs than the traditional mini-batch method in EfficientNet-B4 on STL-10. The proposed method also improves the test top-1 accuracy by 7.26% in ResNet-18 on CIFAR-100.

This work is devoted to unresolved problems of Artificial General Intelligence - the inefficiency of transfer learning. One of the mechanisms that are used to solve this problem in the area of reinforcement learning is a model-based approach. In the paper we are expanding the schema networks method which allows to extract the logical relationships between objects and actions from the environment data. We present algorithms for training a Delta Schema Network (DSN), predicting future states of the environment and planning actions that will lead to positive reward. DSN shows strong performance of transfer learning on the classic Atari game environment.

This technical report introduces PIXART-{\delta}, a text-to-image synthesis framework that integrates the Latent Consistency Model (LCM) and ControlNet into the advanced PIXART-{\alpha} model. PIXART-{\alpha} is recognized for its ability to generate high-quality images of 1024px resolution through a remarkably efficient training process. The integration of LCM in PIXART-{\delta} significantly accelerates the inference speed, enabling the production of high-quality images in just 2-4 steps. Notably, PIXART-{\delta} achieves a breakthrough 0.5 seconds for generating 1024x1024 pixel images, marking a 7x improvement over the PIXART-{\alpha}. Additionally, PIXART-{\delta} is designed to be efficiently trainable on 32GB V100 GPUs within a single day. With its 8-bit inference capability (von Platen et al., 2023), PIXART-{\delta} can synthesize 1024px images within 8GB GPU memory constraints, greatly enhancing its usability and accessibility. Furthermore, incorporating a ControlNet-like module enables fine-grained control over text-to-image diffusion models. We introduce a novel ControlNet-Transformer architecture, specifically tailored for Transformers, achieving explicit controllability alongside high-quality image generation. As a state-of-the-art, open-source image generation model, PIXART-{\delta} offers a promising alternative to the Stable Diffusion family of models, contributing significantly to text-to-image synthesis.

In medical healthcare, obtaining detailed annotations is challenging, highlighting the need for robust Vision-Language Models (VLMs). Pretrained VLMs enable fine-tuning on small datasets or zero-shot inference, achieving performance comparable to task-specific models. Contrastive learning (CL) is a key paradigm for training VLMs but inherently requires large batch sizes for effective learning, making it computationally demanding and often limited to well-resourced institutions. Moreover, with limited data in healthcare, it is important to prioritize knowledge extraction from both data and models during training to improve performance. Therefore, we focus on leveraging the momentum method combined with distillation to simultaneously address computational efficiency and knowledge exploitation. Our contributions can be summarized as follows: (1) leveraging momentum self-distillation to enhance multimodal learning, and (2) integrating momentum mechanisms with gradient accumulation to enlarge the effective batch size without increasing resource consumption. Our method attains competitive performance with state-of-the-art (SOTA) approaches in zero-shot classification, while providing a substantial boost in the few-shot adaption, achieving over 90% AUC-ROC and improving retrieval tasks by 2-3%. Importantly, our method achieves high training efficiency with a single GPU while maintaining reasonable training time. Our approach aims to advance efficient multimodal learning by reducing resource requirements while improving performance over SOTA methods. The implementation of our method is available at https://github.com/phphuc612/MSD .

We present Momentum Contrast (MoCo) for unsupervised visual representation learning. From a perspective on contrastive learning as dictionary look-up, we build a dynamic dictionary with a queue and a moving-averaged encoder. This enables building a large and consistent dictionary on-the-fly that facilitates contrastive unsupervised learning. MoCo provides competitive results under the common linear protocol on ImageNet classification. More importantly, the representations learned by MoCo transfer well to downstream tasks. MoCo can outperform its supervised pre-training counterpart in 7 detection/segmentation tasks on PASCAL VOC, COCO, and other datasets, sometimes surpassing it by large margins. This suggests that the gap between unsupervised and supervised representation learning has been largely closed in many vision tasks.

Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This accounts for gradients being local linear approximations which lose their relevance as the iterate moves along the loss landscape. This work questions the use of a single EMA to accumulate past gradients and empirically demonstrates how this choice can be sub-optimal: a single EMA cannot simultaneously give a high weight to the immediate past, and a non-negligible weight to older gradients. Building on this observation, we propose AdEMAMix, a simple modification of the Adam optimizer with a mixture of two EMAs to better take advantage of past gradients. Our experiments on language modeling and image classification show -- quite surprisingly -- that gradients can stay relevant for tens of thousands of steps. They help to converge faster, and often to lower minima: e.g., a 1.3B parameter AdEMAMix LLM trained on 101B tokens performs comparably to an AdamW model trained on 197B tokens (+95%). Moreover, our method significantly slows-down model forgetting during training. Our work motivates further exploration of different types of functions to leverage past gradients, beyond EMAs.

We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization. MVN-Grad scales each coordinate by an exponential moving average of gradient uncertainty and applies momentum to the resulting normalized gradients, eliminating the cross-time coupling between stale momentum and a stochastic normalizer present in standard Adam-type updates. We prove that this decoupling yields strictly smaller one-step conditional update variance than momentum-then-normalize variance methods under standard noise assumptions, and that MVN-Grad is robust to outliers: it has a uniformly bounded response to single gradient spikes. In low-variance regimes, we further show variance normalization avoids sign-type collapse associated with second-moment scaling and can yield accelerated convergence. Across CIFAR-100 image classification and GPT-style language modeling benchmarks, MVN-Grad matches or outperforms Adam, AdaBelief, and LaProp, delivering smoother training and improved generalization with no added overhead.

In recent advancements in high-fidelity image generation, Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a key player. However, their application at high resolutions presents significant computational challenges. Current methods, such as patchifying, expedite processes in UNet and Transformer architectures but at the expense of representational capacity. Addressing this, we introduce the Diffusion State Space Model (DiffuSSM), an architecture that supplants attention mechanisms with a more scalable state space model backbone. This approach effectively handles higher resolutions without resorting to global compression, thus preserving detailed image representation throughout the diffusion process. Our focus on FLOP-efficient architectures in diffusion training marks a significant step forward. Comprehensive evaluations on both ImageNet and LSUN datasets at two resolutions demonstrate that DiffuSSMs are on par or even outperform existing diffusion models with attention modules in FID and Inception Score metrics while significantly reducing total FLOP usage.

These handouts are designed for people who is just starting involved with the topic artificial neural networks. We show how it works a single artificial neuron (McCulloch & Pitt model), mathematically and graphically. We do explain the delta rule, a learning algorithm to find the neuron weights. We also present some examples in MATLAB/Octave. There are examples for classification task for lineal and non-lineal problems. At the end, we present an artificial neural network, a feed-forward neural network along its learning algorithm backpropagation. ----- Estos apuntes est\'an dise\~nados para personas que por primera vez se introducen en el tema de las redes neuronales artificiales. Se muestra el funcionamiento b\'asico de una neurona, matem\'aticamente y gr\'aficamente. Se explica la Regla Delta, algoritmo deaprendizaje para encontrar los pesos de una neurona. Tambi\'en se muestran ejemplos en MATLAB/Octave. Hay ejemplos para problemas de clasificaci\'on, para problemas lineales y no-lineales. En la parte final se muestra la arquitectura de red neuronal artificial conocida como backpropagation.

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of introducing gradient delay, which impedes optimization and can lead to lower final model performance. We introduce Adaptive Braking (AB), a modification for momentum-based optimizers that mitigates the effects of gradient delay. AB dynamically scales the gradient based on the alignment of the gradient and the velocity. This can dampen oscillations along high curvature directions of the loss surface, stabilizing and accelerating asynchronous training. We show that applying AB on top of SGD with momentum enables training ResNets on CIFAR-10 and ImageNet-1k with delays D geq 32 update steps with minimal drop in final test accuracy.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine learning. While the gradient flow in the task at hand is a parabolic partial differential equation, the momentum-method corresponds to a damped hyperbolic PDE, leading to qualitatively and quantitatively different trajectories. Using a convex-concave splitting-based FISTA-type time discretization, we demonstrate empirically that momentum can lead to faster convergence if the time step size is large but not too large. With large time steps, the PDE analysis offers only limited insight into the geometric behavior of solutions and typical hyperbolic phenomena like loss of regularity are not be observed in sample simulations.

Large reasoning models (LRMs) achieve state-of-the-art performance on challenging benchmarks by generating long chains of intermediate steps, but their inference cost is dominated by decoding, where each new token must attend to the entire growing sequence. Existing sparse attention methods reduce computation by pruning the key-value (KV) cache, yet they suffer from severe accuracy degradation on reasoning tasks due to cumulative selection errors and the dynamic importance of tokens over long derivations. We present DELTA, a training-free sparse attention mechanism that achieves computational efficiency without sacrificing model accuracy. DELTA partitions transformer layers into three groups: initial layers that use full attention, a small set of selection layers that identify salient tokens via aggregated head-level attention scores, and subsequent sparse-attention layers that attend only to the selected subset. This design preserves the full KV cache in GPU memory for accuracy, while avoiding expensive full-attention computation over many layers. On reasoning benchmarks such as AIME and GPQA-Diamond, DELTA matches or surpasses full attention in accuracy, while reducing the number of attended tokens by up to 5times and delivering 1.5times end-to-end speedup. Our results show that selective reuse of intermediate attention maps offers a robust path toward efficient long-context reasoning.

In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, existing ICONs process each spatial point as an individual token, severely limiting computational efficiency when handling dense data in higher spatial dimensions. We propose Vision In-Context Operator Networks (VICON), which integrates vision transformer architectures to efficiently process 2D data through patch-wise operations while preserving ICON's adaptability to multiphysics systems and varying timesteps. Evaluated across three fluid dynamics benchmarks, VICON significantly outperforms state-of-the-art baselines: DPOT and MPP, reducing the averaged last-step rollout error by 37.9% compared to DPOT and 44.7% compared to MPP, while requiring only 72.5% and 34.8% of their respective inference times. VICON naturally supports flexible rollout strategies with varying timestep strides, enabling immediate deployment in imperfect measurement systems where sampling frequencies may differ or frames might be dropped - common challenges in real-world settings - without requiring retraining or interpolation. In these realistic scenarios, VICON exhibits remarkable robustness, experiencing only 24.41% relative performance degradation compared to 71.37%-74.49% degradation in baseline methods, demonstrating its versatility for deploying in realistic applications. Our scripts for processing datasets and code are publicly available at https://github.com/Eydcao/VICON.

Neural architecture search (NAS) has shown encouraging results in automating the architecture design. Recently, DARTS relaxes the search process with a differentiable formulation that leverages weight-sharing and SGD where all candidate operations are trained simultaneously. Our empirical results show that such procedure results in the co-adaption problem and Matthew Effect: operations with fewer parameters would be trained maturely earlier. This causes two problems: firstly, the operations with more parameters may never have the chance to express the desired function since those with less have already done the job; secondly, the system will punish those underperforming operations by lowering their architecture parameter, and they will get smaller loss gradients, which causes the Matthew Effect. In this paper, we systematically study these problems and propose a novel grouped operation dropout algorithm named DropNAS to fix the problems with DARTS. Extensive experiments demonstrate that DropNAS solves the above issues and achieves promising performance. Specifically, DropNAS achieves 2.26% test error on CIFAR-10, 16.39% on CIFAR-100 and 23.4% on ImageNet (with the same training hyperparameters as DARTS for a fair comparison). It is also observed that DropNAS is robust across variants of the DARTS search space. Code is available at https://github.com/wiljohnhong/DropNAS.

Scaling up deep Reinforcement Learning (RL) methods presents a significant challenge. Following developments in generative modelling, model-based RL positions itself as a strong contender. Recent advances in sequence modelling have led to effective transformer-based world models, albeit at the price of heavy computations due to the long sequences of tokens required to accurately simulate environments. In this work, we propose Delta-IRIS, a new agent with a world model architecture composed of a discrete autoencoder that encodes stochastic deltas between time steps and an autoregressive transformer that predicts future deltas by summarizing the current state of the world with continuous tokens. In the Crafter benchmark, Delta-IRIS sets a new state of the art at multiple frame budgets, while being an order of magnitude faster to train than previous attention-based approaches. We release our code and models at https://github.com/vmicheli/delta-iris.

The success of powerful open source Large Language Models (LLMs) has enabled the community to create a vast collection of post-trained models adapted to specific tasks and domains. However, navigating and understanding these models remains challenging due to inconsistent metadata and unstructured repositories. We introduce Delta Activations, a method to represent finetuned models as vector embeddings by measuring shifts in their internal activations relative to a base model. This representation allows for effective clustering by domain and task, revealing structure in the model landscape. Delta Activations also demonstrate desirable properties: it is robust across finetuning settings and exhibits an additive property when finetuning datasets are mixed. In addition, we show that Delta Activations can embed tasks via few-shot finetuning, and further explore its use for model selection and merging. We hope Delta Activations can facilitate the practice of reusing publicly available models. Code is available at https://github.com/OscarXZQ/delta_activations.

Deploying Large Language Models (LLMs) on edge devices remains challenging due to their quadratically increasing computations with the sequence length. Existing studies for dynamic attention pruning are designed for hardware with massively parallel computation capabilities, such as GPUs or TPUs, and aim at long context lengths (e.g., 64K), making them unsuitable for edge scenarios. We present DeltaLLM, a training-free framework that exploits temporal sparsity in attention patterns to enable efficient LLM inference across both the prefilling and decoding stages, on resource-constrained edge devices. DeltaLLM introduces an accuracy- and memory-aware delta matrix construction strategy that introduces temporal sparsity, and a context-aware hybrid attention mechanism that combines full attention in a local context window with delta approximation outside it to increase accuracy. We evaluate our framework on the edge-device-friendly BitNet-b1.58-2B-4T model and Llama3.2-1B-Instruct model across diverse language tasks. The results show that on BitNet, our framework increases the attention sparsity from 0% to 60% during the prefilling stage with slight accuracy improvement on the WG task, and 0% to 57% across both the prefilling and decoding stages, with even higher F1 score from 29.63 to 30.97 on SQuAD-v2 task. On the Llama model, it can also achieve up to 60% sparsity during the prefilling stage and around 57% across both stages with negligible accuracy drop. These results demonstrate that DeltaLLM offers a promising solution for efficient edge deployment, requiring no fine-tuning and seamlessly integrating with existing inference pipelines.

Air quality prediction and modelling plays a pivotal role in public health and environment management, for individuals and authorities to make informed decisions. Although traditional data-driven models have shown promise in this domain, their long-term prediction accuracy can be limited, especially in scenarios with sparse or incomplete data and they often rely on black-box deep learning structures that lack solid physical foundation leading to reduced transparency and interpretability in predictions. To address these limitations, this paper presents a novel approach named Physics guided Neural Network for Air Quality Prediction (AirPhyNet). Specifically, we leverage two well-established physics principles of air particle movement (diffusion and advection) by representing them as differential equation networks. Then, we utilize a graph structure to integrate physics knowledge into a neural network architecture and exploit latent representations to capture spatio-temporal relationships within the air quality data. Experiments on two real-world benchmark datasets demonstrate that AirPhyNet outperforms state-of-the-art models for different testing scenarios including different lead time (24h, 48h, 72h), sparse data and sudden change prediction, achieving reduction in prediction errors up to 10%. Moreover, a case study further validates that our model captures underlying physical processes of particle movement and generates accurate predictions with real physical meaning.

The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equations are particularly interesting as they are well-established as highly difficult tasks. To improve learning the challenging multi-objective task posed by PINNs, we propose the ConFIG method, which provides conflict-free updates by ensuring a positive dot product between the final update and each loss-specific gradient. It also maintains consistent optimization rates for all loss terms and dynamically adjusts gradient magnitudes based on conflict levels. We additionally leverage momentum to accelerate optimizations by alternating the back-propagation of different loss terms. We provide a mathematical proof showing the convergence of the ConFIG method, and it is evaluated across a range of challenging PINN scenarios. ConFIG consistently shows superior performance and runtime compared to baseline methods. We also test the proposed method in a classic multi-task benchmark, where the ConFIG method likewise exhibits a highly promising performance. Source code is available at https://tum-pbs.github.io/ConFIG

Recent work has shown that orthonormal matrix updates speed up neural network optimization, improve training stability, and offer better hyperparameter transfer across model sizes. Applying these updates efficiently when model weights and optimizer states are sharded across a large-scale distributed LLM training system remains a major challenge. We introduce Dion (DIstributed OrthoNormalization), a scalable and communication-efficient orthonormalizing optimizer. Dion leverages low-rank approximation and decoupled momentum buffers, eliminating the need for full gradient synchronization while producing numerically equivalent results. It is compatible with simultaneous DDP, FSDP, and TP parallelism, and it computes an orthonormalized update without unsharding a full parameter matrix on any single device. We evaluate Dion on language models from 120M to 3B parameters and find that its benefits improve with increasing model size and batch size.

With the proliferation of task-specific large language models, delta compression has emerged as a method to mitigate the resource challenges of deploying numerous such models by effectively compressing the delta model parameters. Previous delta-sparsification methods either remove parameters randomly or truncate singular vectors directly after singular value decomposition (SVD). However, these methods either disregard parameter importance entirely or evaluate it with too coarse a granularity. In this work, we introduce ImPart, a novel importance-aware delta sparsification approach. Leveraging SVD, it dynamically adjusts sparsity ratios of different singular vectors based on their importance, effectively retaining crucial task-specific knowledge even at high sparsity ratios. Experiments show that ImPart achieves state-of-the-art delta sparsification performance, demonstrating 2times higher compression ratio than baselines at the same performance level. When integrated with existing methods, ImPart sets a new state-of-the-art on delta quantization and model merging.

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which classical analysis applies only if the loss is either convex or smooth. We show that a very small modification to SGDM closes this gap: simply scale the update at each time point by an exponentially distributed random scalar. The resulting algorithm achieves optimal convergence guarantees. Intriguingly, this result is not derived by a specific analysis of SGDM: instead, it falls naturally out of a more general framework for converting online convex optimization algorithms to non-convex optimization algorithms.

While Diffusion Models excel in text-to-image synthesis, they often suffer from concept omission when synthesizing complex multi-instance scenes. Existing training-free methods attempt to resolve this by rescaling attention maps, which merely exacerbates unstructured noise without establishing coherent semantic representations. To address this, we propose Delta-K, a backbone-agnostic and plug-and-play inference framework that tackles omission by operating directly in the shared cross-attention Key space. Specifically, with Vision-language model, we extract a differential key ΔK that encodes the semantic signature of missing concepts. This signal is then injected during the early semantic planning stage of the diffusion process. Governed by a dynamically optimized scheduling mechanism, Delta-K grounds diffuse noise into stable structural anchors while preserving existing concepts. Extensive experiments demonstrate the generality of our approach: Delta-K consistently improves compositional alignment across both modern DiT models and classical U-Net architectures, without requiring spatial masks, additional training, or architectural modifications.

Fluid-structure interaction is common in engineering and natural systems, where floating-body motion is governed by added mass, drag, and background flows. Modeling these dissipative dynamics is difficult: black-box neural models regress state derivatives with limited interpretability and unstable long-horizon predictions. We propose Floating-Body Hydrodynamic Neural Networks (FHNN), a physics-structured framework that predicts interpretable hydrodynamic parameters such as directional added masses, drag coefficients, and a streamfunction-based flow, and couples them with analytic equations of motion. This design constrains the hypothesis space, enhances interpretability, and stabilizes integration. On synthetic vortex datasets, FHNN achieves up to an order-of-magnitude lower error than Neural ODEs, recovers physically consistent flow fields. Compared with Hamiltonian and Lagrangian neural networks, FHNN more effectively handles dissipative dynamics while preserving interpretability, which bridges the gap between black-box learning and transparent system identification.

Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. While Adam uses adaptive moment estimates to promote stability, Muon utilizes the weight layers' matrix structure via orthogonalized momentum, showing superior performance in large language model training. We propose a new optimizer and a diagonal extension, NAMO and NAMO-D, providing the first principled integration of orthogonalized momentum with norm-based Adam-type noise adaptation. NAMO scales orthogonalized momentum using a single adaptive stepsize, preserving orthogonality while improving upon Muon at negligible additional cost. NAMO-D instead right-multiplies orthogonalized momentum by a diagonal matrix with clamped entries. This design enables neuron-wise noise adaptation and aligns with the common near block-diagonal Hessian structure. Under standard assumptions, we establish optimal convergence rates for both algorithms in the deterministic setting and show that, in the stochastic setting, their convergence guarantees adapt to the noise level of stochastic gradients. Experiments on pretraining GPT-2 models demonstrate improved performance of both NAMO and NAMO-D compared to the AdamW and Muon baselines, with NAMO-D achieving further gains over NAMO via an additional clamping hyperparameter that balances the competing goals of maintaining a well-conditioned update direction and leveraging fine-grained noise adaptation.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

Training a modern machine learning architecture on a new task requires extensive learning-rate tuning, which comes at a high computational cost. Here we develop new adaptive learning rates that can be used with any momentum method, and require less tuning to perform well. We first develop MoMo, a Momentum Model based adaptive learning rate for SGD-M (Stochastic gradient descent with momentum). MoMo uses momentum estimates of the batch losses and gradients sampled at each iteration to build a model of the loss function. Our model also makes use of any known lower bound of the loss function by using truncation, e.g. most losses are lower-bounded by zero. We then approximately minimize this model at each iteration to compute the next step. We show how MoMo can be used in combination with any momentum-based method, and showcase this by developing MoMo-Adam - which is Adam with our new model-based adaptive learning rate. Additionally, for losses with unknown lower bounds, we develop on-the-fly estimates of a lower bound, that are incorporated in our model. Through extensive numerical experiments, we demonstrate that MoMo and MoMo-Adam improve over SGD-M and Adam in terms of accuracy and robustness to hyperparameter tuning for training image classifiers on MNIST, CIFAR10, CIFAR100, Imagenet, recommender systems on the Criteo dataset, and a transformer model on the translation task IWSLT14.

Modern diffusion/flow-based models for image generation typically exhibit two core characteristics: (i) using multi-step sampling, and (ii) operating in a latent space. Recent advances have made encouraging progress on each aspect individually, paving the way toward one-step diffusion/flow without latents. In this work, we take a further step towards this goal and propose "pixel MeanFlow" (pMF). Our core guideline is to formulate the network output space and the loss space separately. The network target is designed to be on a presumed low-dimensional image manifold (i.e., x-prediction), while the loss is defined via MeanFlow in the velocity space. We introduce a simple transformation between the image manifold and the average velocity field. In experiments, pMF achieves strong results for one-step latent-free generation on ImageNet at 256x256 resolution (2.22 FID) and 512x512 resolution (2.48 FID), filling a key missing piece in this regime. We hope that our study will further advance the boundaries of diffusion/flow-based generative models.

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 33.2% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.

Deep Neural Network (DNN) is powerful but computationally expensive and memory intensive, thus impeding its practical usage on resource-constrained front-end devices. DNN pruning is an approach for deep model compression, which aims at eliminating some parameters with tolerable performance degradation. In this paper, we propose a novel momentum-SGD-based optimization method to reduce the network complexity by on-the-fly pruning. Concretely, given a global compression ratio, we categorize all the parameters into two parts at each training iteration which are updated using different rules. In this way, we gradually zero out the redundant parameters, as we update them using only the ordinary weight decay but no gradients derived from the objective function. As a departure from prior methods that require heavy human works to tune the layer-wise sparsity ratios, prune by solving complicated non-differentiable problems or finetune the model after pruning, our method is characterized by 1) global compression that automatically finds the appropriate per-layer sparsity ratios; 2) end-to-end training; 3) no need for a time-consuming re-training process after pruning; and 4) superior capability to find better winning tickets which have won the initialization lottery.

Training large neural network models requires extensive computational resources, often distributed across several nodes and accelerators. Recent findings suggest that it may be sufficient to only exchange the fast moving components of the gradients, while accumulating momentum locally (Decoupled Momentum, or DeMo). However, DeMo assumes that models fit on a single accelerator. We relax this assumption and introduce FlexDeMo, whereby nodes fully shard model parameters locally between different accelerators, while inter-node communication is reduced by synchronizing only fast-moving components instead of the full gradients -- resulting in a hybrid sharded data parallel training strategy. We further introduce a framework, denoted as DeToNATION, that generalizes DeMo, FlexDeMo, and other popular distributed training schemes such as DiLoCo -- introducing new variations of replication schemes and challenging choices made in DeMo. Our results across language and vision domains show that FlexDeMo attains similar validation loss as hybrid sharded data parallel training employing AdamW and full gradient synchronization, while being substantially faster. FlexDeMo is thus a promising distributed training scheme for the largest machine learning models.

Large-scale vision and language representation learning has shown promising improvements on various vision-language tasks. Most existing methods employ a transformer-based multimodal encoder to jointly model visual tokens (region-based image features) and word tokens. Because the visual tokens and word tokens are unaligned, it is challenging for the multimodal encoder to learn image-text interactions. In this paper, we introduce a contrastive loss to ALign the image and text representations BEfore Fusing (ALBEF) them through cross-modal attention, which enables more grounded vision and language representation learning. Unlike most existing methods, our method does not require bounding box annotations nor high-resolution images. In order to improve learning from noisy web data, we propose momentum distillation, a self-training method which learns from pseudo-targets produced by a momentum model. We provide a theoretical analysis of ALBEF from a mutual information maximization perspective, showing that different training tasks can be interpreted as different ways to generate views for an image-text pair. ALBEF achieves state-of-the-art performance on multiple downstream vision-language tasks. On image-text retrieval, ALBEF outperforms methods that are pre-trained on orders of magnitude larger datasets. On VQA and NLVR^2, ALBEF achieves absolute improvements of 2.37% and 3.84% compared to the state-of-the-art, while enjoying faster inference speed. Code and pre-trained models are available at https://github.com/salesforce/ALBEF/.

The Mechanistic Interpretability (MI) program has mapped the Transformer as a precise computational graph. We extend this graph with a conservation law and time-varying AC dynamics, viewing it as a physical circuit. We introduce Momentum Attention, a symplectic augmentation embedding physical priors via the kinematic difference operator p_t = q_t - q_{t-1}, implementing the symplectic shear q_t = q_t + γp_t on queries and keys. We identify a fundamental Symplectic-Filter Duality: the physical shear is mathematically equivalent to a High-Pass Filter. This duality is our cornerstone contribution -- by injecting kinematic momentum, we sidestep the topological depth constraint (L geq 2) for induction head formation. While standard architectures require two layers for induction from static positions, our extension grants direct access to velocity, enabling Single-Layer Induction and Spectral Forensics via Bode Plots. We formalize an Orthogonality Theorem proving that DC (semantic) and AC (mechanistic) signals segregate into orthogonal frequency bands when Low-Pass RoPE interacts with High-Pass Momentum. Validated through 5,100+ controlled experiments (documented in Supplementary Appendices A--R and 27 Jupyter notebooks), our 125M Momentum model exceeds expectations on induction-heavy tasks while tracking a 350M baseline within sim2.9% validation loss. Dedicated associative recall experiments reveal a scaling law γ^* = 4.17 times N^{-0.74} establishing momentum-depth fungibility. We offer this framework as a complementary analytical toolkit connecting Generative AI, Hamiltonian Physics, and Signal Processing.

Building efficient and effective generative models for neural network weights has been a research focus of significant interest that faces challenges posed by the high-dimensional weight spaces of modern neural networks and their symmetries. Several prior generative models are limited to generating partial neural network weights, particularly for larger models, such as ResNet and ViT. Those that do generate complete weights struggle with generation speed or require finetuning of the generated models. In this work, we present DeepWeightFlow, a Flow Matching model that operates directly in weight space to generate diverse and high-accuracy neural network weights for a variety of architectures, neural network sizes, and data modalities. The neural networks generated by DeepWeightFlow do not require fine-tuning to perform well and can scale to large networks. We apply Git Re-Basin and TransFusion for neural network canonicalization in the context of generative weight models to account for the impact of neural network permutation symmetries and to improve generation efficiency for larger model sizes. The generated networks excel at transfer learning, and ensembles of hundreds of neural networks can be generated in minutes, far exceeding the efficiency of diffusion-based methods. DeepWeightFlow models pave the way for more efficient and scalable generation of diverse sets of neural networks.

Linear Recurrent Neural Networks (LRNNs) such as Mamba, RWKV, GLA, mLSTM, and DeltaNet have emerged as efficient alternatives to Transformers for long sequences. However, both Transformers and LRNNs struggle to perform state-tracking, which may impair performance in tasks such as code evaluation. In one forward pass, current architectures are unable to solve even parity, the simplest state-tracking task, which non-linear RNNs can handle effectively. Recently, Sarrof et al. (2024) demonstrated that the failure of LRNNs like Mamba to solve parity stems from restricting the value range of their diagonal state-transition matrices to [0, 1] and that incorporating negative values can resolve this issue. We extend this result to non-diagonal LRNNs such as DeltaNet. We prove that finite precision LRNNs with state-transition matrices having only positive eigenvalues cannot solve parity, while non-triangular matrices are needed to count modulo 3. Notably, we also prove that LRNNs can learn any regular language when their state-transition matrices are products of identity minus vector outer product matrices, each with eigenvalues in the range [-1, 1]. Our experiments confirm that extending the eigenvalue range of Mamba and DeltaNet to include negative values not only enables them to solve parity but consistently improves their performance on state-tracking tasks. We also show that state-tracking enabled LRNNs can be pretrained stably and efficiently at scale (1.3B parameters), achieving competitive performance on language modeling and showing promise on code and math tasks.

Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) in various fields by minimizing a weighted sum of PDE loss and boundary loss. However, there are several critical challenges in the training of PINNs, including the lack of theoretical frameworks and the imbalance between PDE loss and boundary loss. In this paper, we present an analysis of second-order non-homogeneous PDEs, which are classified into three categories and applicable to various common problems. We also characterize the connections between the training loss and actual error, guaranteeing convergence under mild conditions. The theoretical analysis inspires us to further propose MultiAdam, a scale-invariant optimizer that leverages gradient momentum to parameter-wisely balance the loss terms. Extensive experiment results on multiple problems from different physical domains demonstrate that our MultiAdam solver can improve the predictive accuracy by 1-2 orders of magnitude compared with strong baselines.

Orthogonal gradient updates have emerged as a promising direction in optimization for machine learning. However, traditional approaches such as SVD/QR decomposition incur prohibitive computational costs of O(n^3) and underperform compared to well-tuned SGD with momentum, since momentum is applied only after strict orthogonalization. Recent advances, such as Muon, improve efficiency by applying momentum before orthogonalization and producing semi-orthogonal matrices via Newton-Schulz iterations, reducing complexity to O(n^2). Nevertheless, quadratic costs remain a bottleneck. In this work, we study the semi-orthogonal properties of momentum-based updates and develop a method to bound momentum updates under a spectral-norm trust region, preserving directional information without requiring explicit semi-orthogonalization. We propose AuON (Alternative Unit-norm momentum updates by Normalized nonlinear scaling), a linear-time optimizer that achieves strong performance without constructing semi-orthogonal matrices, while preserving structural alignment and reconditioning ill-posed updates. Our approach combines hyperbolic-cosine RMS scaling transformations with normalization, demonstrating both effectiveness and computational efficiency compared to Newton-Schulz methods. We further introduce a hybrid variant (Hybrid-AuON) that applies a single Newton-Schulz iteration. Experiments across vision and language benchmarks show that AuON and its hybrid variant achieve performance comparable to strong baselines such as AdamW and Muon. Code is available at: https://github.com/ryyzn9/AuON

Flow based generative models have charted an impressive path across multiple visual generation tasks by adhering to a simple principle: learning velocity representations of a linear interpolant. However, we observe that training velocity solely from the final layer output underutilizes the rich inter layer representations, potentially impeding model convergence. To address this limitation, we introduce DeepFlow, a novel framework that enhances velocity representation through inter layer communication. DeepFlow partitions transformer layers into balanced branches with deep supervision and inserts a lightweight Velocity Refiner with Acceleration (VeRA) block between adjacent branches, which aligns the intermediate velocity features within transformer blocks. Powered by the improved deep supervision via the internal velocity alignment, DeepFlow converges 8 times faster on ImageNet with equivalent performance and further reduces FID by 2.6 while halving training time compared to previous flow based models without a classifier free guidance. DeepFlow also outperforms baselines in text to image generation tasks, as evidenced by evaluations on MSCOCO and zero shot GenEval.

We introduce Gradient Descent with Adaptive Momentum Scaling (Grams), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning. Unlike traditional optimizers that directly integrate momentum into updates, Grams separates the update direction, derived from current gradients, from momentum, which is used solely for adaptive magnitude scaling. This approach enables Grams to achieve improved loss descent compared to state-of-the-art cautious and momentum-based optimizers. We establish a global convergence guarantee for Grams and validate its effectiveness through extensive empirical evaluations. The results demonstrate Grams' superior performance, including faster convergence and better generalization, compared to widely-used optimizers such as Adam, Lion, and their cautious variants. Our results highlight Grams' potential as a transformative approach for efficient optimization in large-scale machine learning.

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parametrizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that compares the physics of the generated PINN to the requested PDE and uses the discrepancy to generate a "delta" PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves over 100x gain in average L_2 loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems with significantly improved accuracy and reduced computational cost.

We propose MUltiway Dynamic Dense (MUDD) connections, a simple yet effective method to address the limitations of residual connections and enhance cross-layer information flow in Transformers. Unlike existing dense connection approaches with static and shared connection weights, MUDD generates connection weights dynamically depending on hidden states at each sequence position and for each decoupled input stream (the query, key, value or residual) of a Transformer block. MUDD connections can be seamlessly integrated into any Transformer architecture to create MUDDFormer. Extensive experiments show that MUDDFormer significantly outperforms Transformers across various model architectures and scales in language modeling, achieving the performance of Transformers trained with 1.8X-2.4X compute. Notably, MUDDPythia-2.8B matches Pythia-6.9B in pretraining ppl and downstream tasks and even rivals Pythia-12B in five-shot settings, while adding only 0.23% parameters and 0.4% computation. Code in JAX and PyTorch and pre-trained models are available at https://github.com/Caiyun-AI/MUDDFormer .

Differentiable architecture search (DARTS) provided a fast solution in finding effective network architectures, but suffered from large memory and computing overheads in jointly training a super-network and searching for an optimal architecture. In this paper, we present a novel approach, namely, Partially-Connected DARTS, by sampling a small part of super-network to reduce the redundancy in exploring the network space, thereby performing a more efficient search without comprising the performance. In particular, we perform operation search in a subset of channels while bypassing the held out part in a shortcut. This strategy may suffer from an undesired inconsistency on selecting the edges of super-net caused by sampling different channels. We alleviate it using edge normalization, which adds a new set of edge-level parameters to reduce uncertainty in search. Thanks to the reduced memory cost, PC-DARTS can be trained with a larger batch size and, consequently, enjoys both faster speed and higher training stability. Experimental results demonstrate the effectiveness of the proposed method. Specifically, we achieve an error rate of 2.57% on CIFAR10 with merely 0.1 GPU-days for architecture search, and a state-of-the-art top-1 error rate of 24.2% on ImageNet (under the mobile setting) using 3.8 GPU-days for search. Our code has been made available at: https://github.com/yuhuixu1993/PC-DARTS.

Currently, the neural network architecture design is mostly guided by the indirect metric of computation complexity, i.e., FLOPs. However, the direct metric, e.g., speed, also depends on the other factors such as memory access cost and platform characterics. Thus, this work proposes to evaluate the direct metric on the target platform, beyond only considering FLOPs. Based on a series of controlled experiments, this work derives several practical guidelines for efficient network design. Accordingly, a new architecture is presented, called ShuffleNet V2. Comprehensive ablation experiments verify that our model is the state-of-the-art in terms of speed and accuracy tradeoff.

This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the relationship between a genotype - the hypernetwork - and a phenotype - the main network. Though they are also reminiscent of HyperNEAT in evolution, our hypernetworks are trained end-to-end with backpropagation and thus are usually faster. The focus of this work is to make hypernetworks useful for deep convolutional networks and long recurrent networks, where hypernetworks can be viewed as relaxed form of weight-sharing across layers. Our main result is that hypernetworks can generate non-shared weights for LSTM and achieve near state-of-the-art results on a variety of sequence modelling tasks including character-level language modelling, handwriting generation and neural machine translation, challenging the weight-sharing paradigm for recurrent networks. Our results also show that hypernetworks applied to convolutional networks still achieve respectable results for image recognition tasks compared to state-of-the-art baseline models while requiring fewer learnable parameters.

Long-sequence modeling faces a fundamental trade-off between the efficiency of compressive fixed-size memory in RNN-like models and the fidelity of lossless growing memory in attention-based Transformers. Inspired by the Multi-Store Model in cognitive science, we introduce a memory framework of artificial neural networks. Our method maintains a sliding window of the Transformer's KV cache as lossless short-term memory, while a learnable module termed Artificial Hippocampus Network (AHN) recurrently compresses out-of-window information into a fixed-size compact long-term memory. To validate this framework, we instantiate AHNs using modern RNN-like architectures, including Mamba2, DeltaNet, and Gated DeltaNet. Extensive experiments on long-context benchmarks LV-Eval and InfiniteBench demonstrate that AHN-augmented models consistently outperform sliding window baselines and achieve performance comparable or even superior to full-attention models, while substantially reducing computational and memory requirements. For instance, augmenting the Qwen2.5-3B-Instruct with AHNs reduces inference FLOPs by 40.5% and memory cache by 74.0%, while improving its average score on LV-Eval (128k sequence length) from 4.41 to 5.88. Code is available at: https://github.com/ByteDance-Seed/AHN.

Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and flow-based models. In this paper, we propose a new paradigm called Drifting Models, which evolve the pushforward distribution during training and naturally admit one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet at 256 x 256 resolution, with an FID of 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.

The deployment of efficient long-context LLMs in applications like autonomous agents, long-chain reasoning, and creative writing is fundamentally bottlenecked by the linear growth of KV cache memory. Existing compression and eviction methods often struggle to balance accuracy, compression ratio, and hardware efficiency. We propose DeltaKV, a residual-based KV cache compression framework motivated by two empirical findings: long-range inter-token similarity and highly shared latent components in KV representations. Instead of discarding tokens, DeltaKV encodes semantic residuals relative to retrieved historical references, preserving fidelity while substantially reducing storage. To translate compression gains into real system speedups, we further introduce Sparse-vLLM, a high-performance inference engine with decoupled memory management and kernels optimized for sparse and irregular KV layouts. Experiments show that DeltaKV reduces KV cache memory to 29\% of the original while maintaining near-lossless accuracy on LongBench, SCBench, and AIME. When integrated with Sparse-vLLM, it achieves up to 2times throughput improvement over vLLM in long-context scenarios, demonstrating a practical path toward scalable long-context LLM deployment. Code, model checkpoints, and datasets are available at https://github.com/CURRENTF/Sparse-vLLM.

Large pre-trained, zero-shot capable models have shown considerable success both for standard transfer and adaptation tasks, with particular robustness towards distribution shifts. In addition, subsequent fine-tuning can considerably improve performance on a selected downstream task. However, through naive fine-tuning, these zero-shot models lose their generalizability and robustness towards distribution shifts. This is a particular problem for tasks such as Continual Learning (CL), where continuous adaptation has to be performed as new task distributions are introduced sequentially. In this work, we showcase that where fine-tuning falls short to adapt such zero-shot capable models, simple momentum-based weight interpolation can provide consistent improvements for CL tasks in both memory-free and memory-based settings. In particular, we find improvements of over +4% on standard CL benchmarks, while reducing the error to the upper limit of jointly training on all tasks at once in parts by more than half, allowing the continual learner to inch closer to the joint training limits.

Recent methods such as Score Distillation Sampling (SDS) and Variational Score Distillation (VSD) using 2D diffusion models for text-to-3D generation have demonstrated impressive generation quality. However, the long generation time of such algorithms significantly degrades the user experience. To tackle this problem, we propose DreamPropeller, a drop-in acceleration algorithm that can be wrapped around any existing text-to-3D generation pipeline based on score distillation. Our framework generalizes Picard iterations, a classical algorithm for parallel sampling an ODE path, and can account for non-ODE paths such as momentum-based gradient updates and changes in dimensions during the optimization process as in many cases of 3D generation. We show that our algorithm trades parallel compute for wallclock time and empirically achieves up to 4.7x speedup with a negligible drop in generation quality for all tested frameworks.

Despite the impressive performance of diffusion models such as Stable Diffusion (SD) in image generation, their slow inference limits practical deployment. Recent works accelerate inference by distilling multi-step diffusion into one-step generators. To better understand the distillation mechanism, we analyze U-Net/DiT weight changes between one-step students and their multi-step teacher counterparts. Our analysis reveals that changes in weight direction significantly exceed those in weight norm, highlighting it as the key factor during distillation. Motivated by this insight, we propose the Low-rank Rotation of weight Direction (LoRaD), a parameter-efficient adapter tailored to one-step diffusion distillation. LoRaD is designed to model these structured directional changes using learnable low-rank rotation matrices. We further integrate LoRaD into Variational Score Distillation (VSD), resulting in Weight Direction-aware Distillation (WaDi)-a novel one-step distillation framework. WaDi achieves state-of-the-art FID scores on COCO 2014 and COCO 2017 while using only approximately 10% of the trainable parameters of the U-Net/DiT. Furthermore, the distilled one-step model demonstrates strong versatility and scalability, generalizing well to various downstream tasks such as controllable generation, relation inversion, and high-resolution synthesis.

FloodNet is a high-resolution image dataset acquired by a small UAV platform, DJI Mavic Pro quadcopters, after Hurricane Harvey. The dataset presents a unique challenge of advancing the damage assessment process for post-disaster scenarios using unlabeled and limited labeled dataset. We propose a solution to address their classification and semantic segmentation challenge. We approach this problem by generating pseudo labels for both classification and segmentation during training and slowly incrementing the amount by which the pseudo label loss affects the final loss. Using this semi-supervised method of training helped us improve our baseline supervised loss by a huge margin for classification, allowing the model to generalize and perform better on the validation and test splits of the dataset. In this paper, we compare and contrast the various methods and models for image classification and semantic segmentation on the FloodNet dataset.

Hypernetworks, or hypernets in short, are neural networks that generate weights for another neural network, known as the target network. They have emerged as a powerful deep learning technique that allows for greater flexibility, adaptability, dynamism, faster training, information sharing, and model compression etc. Hypernets have shown promising results in a variety of deep learning problems, including continual learning, causal inference, transfer learning, weight pruning, uncertainty quantification, zero-shot learning, natural language processing, and reinforcement learning etc. Despite their success across different problem settings, currently, there is no review available to inform the researchers about the developments and to help in utilizing hypernets. To fill this gap, we review the progress in hypernets. We present an illustrative example to train deep neural networks using hypernets and propose categorizing hypernets based on five design criteria as inputs, outputs, variability of inputs and outputs, and architecture of hypernets. We also review applications of hypernets across different deep learning problem settings, followed by a discussion of general scenarios where hypernets can be effectively employed. Finally, we discuss the challenges and future directions that remain under-explored in the field of hypernets. We believe that hypernetworks have the potential to revolutionize the field of deep learning. They offer a new way to design and train neural networks, and they have the potential to improve the performance of deep learning models on a variety of tasks. Through this review, we aim to inspire further advancements in deep learning through hypernetworks.

Training large models with distributed data parallelism (DDP) requires frequent communication of gradients across workers, which can saturate bandwidth. Infrequent communication strategies (e.g., Local SGD) reduce this overhead but, when applied to adaptive optimizers, often suffer a performance gap relative to fully synchronous DDP. We trace this gap to a time-scale mismatch: the optimizer's fast-moving momentum, tuned for frequent updates, decays too quickly to smooth gradients over long intervals, leading to noise-dominated optimization. To address this, we propose MT-DAO, a family of optimizers that employs multiple slow- and fast-moving first momenta or the gradient to track update dynamics across different time scales, for which we provide the first convergence guarantees. Empirically, for language-model pre-training, this eliminates the performance gap with DDP, outperforming infrequent-communication baselines in perplexity and reducing iso-token wall-clock time by 6-27% on Ethernet interconnects. At the 720M scale, MT-DAO reaches a target perplexity in 24% fewer steps and 35% less time than the single-momentum DDP baseline. MT-DAO enables effective cross-datacenter training and training over wide geographic areas.

In machine learning applications, it is well known that carefully designed learning rate (step size) schedules can significantly improve the convergence of commonly used first-order optimization algorithms. Therefore how to set step size adaptively becomes an important research question. A popular and effective method is the Polyak step size, which sets step size adaptively for gradient descent or stochastic gradient descent without the need to estimate the smoothness parameter of the objective function. However, there has not been a principled way to generalize the Polyak step size for algorithms with momentum accelerations. This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.

We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and alternating updates. Our method gives real-valued parameter updates, making it a drop-in replacement for standard optimizers. We empirically demonstrate that complex-valued momentum can improve convergence in realistic adversarial games - like generative adversarial networks - by showing we can find better solutions with an almost identical computational cost. We also show a practical generalization to a complex-valued Adam variant, which we use to train BigGAN to better inception scores on CIFAR-10.

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model's performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Large Language Models (LLMs) have demonstrated exceptional performance across diverse tasks, yet their training remains highly resource-intensive and susceptible to critical challenges such as training instability. A predominant source of this instability stems from gradient and loss spikes, which disrupt the learning process, often leading to costly interventions like checkpoint recovery and experiment restarts, further amplifying inefficiencies. This paper presents a comprehensive investigation into gradient spikes observed during LLM training, revealing their prevalence across multiple architectures and datasets. Our analysis shows that these spikes can be up to 1000times larger than typical gradients, substantially deteriorating model performance. To address this issue, we propose Spike-Aware Adam with Momentum Reset SPAM, a novel optimizer designed to counteract gradient spikes through momentum reset and spike-aware gradient clipping. Extensive experiments, including both pre-training and fine-tuning, demonstrate that SPAM consistently surpasses Adam and its variants across various tasks, including (1) LLM pre-training from 60M to 1B, (2) 4-bit LLM pre-training,(3) reinforcement learning, and (4) Time Series Forecasting. Additionally, SPAM facilitates memory-efficient training by enabling sparse momentum, where only a subset of momentum terms are maintained and updated. When operating under memory constraints, SPAM outperforms state-of-the-art memory-efficient optimizers such as GaLore and Adam-Mini. Our work underscores the importance of mitigating gradient spikes in LLM training and introduces an effective optimization strategy that enhances both training stability and resource efficiency at scale. Code is available at https://github.com/TianjinYellow/SPAM-Optimizer.git

Sparse Mixture of Experts (SMoE) has become the key to unlocking unparalleled scalability in deep learning. SMoE has the potential to exponentially increase parameter count while maintaining the efficiency of the model by only activating a small subset of these parameters for a given sample. However, it has been observed that SMoE suffers from unstable training and has difficulty adapting to new distributions, leading to the model's lack of robustness to data contamination. To overcome these limitations, we first establish a connection between the dynamics of the expert representations in SMoEs and gradient descent on a multi-objective optimization problem. Leveraging our framework, we then integrate momentum into SMoE and propose a new family of SMoEs named MomentumSMoE. We theoretically prove and numerically demonstrate that MomentumSMoE is more stable and robust than SMoE. In particular, we verify the advantages of MomentumSMoE over SMoE on a variety of practical tasks including ImageNet-1K object recognition and WikiText-103 language modeling. We demonstrate the applicability of MomentumSMoE to many types of SMoE models, including those in the Sparse MoE model for vision (V-MoE) and the Generalist Language Model (GLaM). We also show that other advanced momentum-based optimization methods, such as Adam, can be easily incorporated into the MomentumSMoE framework for designing new SMoE models with even better performance, almost negligible additional computation cost, and simple implementations.

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative L_{1} error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

Vision-Language Pretraining (VLP) has shown impressive results on diverse downstream tasks by offline training on large-scale datasets. Regarding the growing nature of real-world data, such an offline training paradigm on ever-expanding data is unsustainable, because models lack the continual learning ability to accumulate knowledge constantly. However, most continual learning studies are limited to uni-modal classification and existing multi-modal datasets cannot simulate continual non-stationary data stream scenarios. To support the study of Vision-Language Continual Pretraining (VLCP), we first contribute a comprehensive and unified benchmark dataset P9D which contains over one million product image-text pairs from 9 industries. The data from each industry as an independent task supports continual learning and conforms to the real-world long-tail nature to simulate pretraining on web data. We comprehensively study the characteristics and challenges of VLCP, and propose a new algorithm: Compatible momentum contrast with Topology Preservation, dubbed CTP. The compatible momentum model absorbs the knowledge of the current and previous-task models to flexibly update the modal feature. Moreover, Topology Preservation transfers the knowledge of embedding across tasks while preserving the flexibility of feature adjustment. The experimental results demonstrate our method not only achieves superior performance compared with other baselines but also does not bring an expensive training burden. Dataset and codes are available at https://github.com/KevinLight831/CTP.

Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been proposed to enhance the robustness of D-SGD to such machines, previous works either resort to strong assumptions (trusted server, homogeneous data, specific noise model) or impose a gradient computational cost that is several orders of magnitude higher than that of D-SGD. We present MoNNA, a new algorithm that (a) is provably robust under standard assumptions and (b) has a gradient computation overhead that is linear in the fraction of faulty machines, which is conjectured to be tight. Essentially, MoNNA uses Polyak's momentum of local gradients for local updates and nearest-neighbor averaging (NNA) for global mixing, respectively. While MoNNA is rather simple to implement, its analysis has been more challenging and relies on two key elements that may be of independent interest. Specifically, we introduce the mixing criterion of (alpha, lambda)-reduction to analyze the non-linear mixing of non-faulty machines, and present a way to control the tension between the momentum and the model drifts. We validate our theory by experiments on image classification and make our code available at https://github.com/LPD-EPFL/robust-collaborative-learning.

Accurate air quality forecasting is crucial for protecting public health and guiding environmental policy, yet it remains challenging due to nonlinear spatiotemporal dynamics, wind-driven transport, and distribution shifts across regions. Physics-based models are interpretable but computationally expensive and often rely on restrictive assumptions, whereas purely data-driven models can be accurate but may lack robustness and calibrated uncertainty. To address these limitations, we propose Neural Dynamic Diffusion-Advection Fields (NeuroDDAF), a physics-informed forecasting framework that unifies neural representation learning with open-system transport modeling. NeuroDDAF integrates (i) a GRU-Graph Attention encoder to capture temporal dynamics and wind-aware spatial interactions, (ii) a Fourier-domain diffusion-advection module with learnable residuals, (iii) a wind-modulated latent Neural ODE to model continuous-time evolution under time-varying connectivity, and (iv) an evidential fusion mechanism that adaptively combines physics-guided and neural forecasts while quantifying uncertainty. Experiments on four urban datasets (Beijing, Shenzhen, Tianjin, and Ancona) across 1-3 day horizons show that NeuroDDAF consistently outperforms strong baselines, including AirPhyNet, achieving up to 9.7% reduction in RMSE and 9.4% reduction in MAE on long-term forecasts. On the Beijing dataset, NeuroDDAF attains an RMSE of 41.63 μg/m^3 for 1-day prediction and 48.88 μg/m^3 for 3-day prediction, representing the best performance among all compared methods. In addition, NeuroDDAF improves cross-city generalization and yields well-calibrated uncertainty estimates, as confirmed by ensemble variance analysis and case studies under varying wind conditions.

Zero-shot Neural Architecture Search (NAS) typically optimises the architecture search process by exploiting the network or gradient properties at initialisation through zero-cost proxies. The existing proxies often rely on labelled data, which is usually unavailable in real-world settings. Furthermore, the majority of the current methods focus either on optimising the convergence and generalisation attributes or solely on the expressivity of the network architectures. To address both limitations, we first demonstrate how channel collinearity affects the convergence and generalisation properties of a neural network. Then, by incorporating the convergence, generalisation and expressivity in one approach, we propose a zero-cost proxy that omits the requirement of labelled data for its computation. In particular, we leverage the Singular Value Decomposition (SVD) of the neural network layer features and the extrinsic curvature of the network output to design our proxy. %As a result, the proposed proxy is formulated as the simplified harmonic mean of the logarithms of two key components: the sum of the inverse of the feature condition number and the extrinsic curvature of the network output. Our approach enables accurate prediction of network performance on test data using only a single label-free data sample. Our extensive evaluation includes a total of six experiments, including the Convolutional Neural Network (CNN) search space, i.e. DARTS and the Transformer search space, i.e. AutoFormer. The proposed proxy demonstrates a superior performance on multiple correlation benchmarks, including NAS-Bench-101, NAS-Bench-201, and TransNAS-Bench-101-micro; as well as on the NAS task within the DARTS and the AutoFormer search space, all while being notably efficient. The code is available at https://github.com/rohanasthana/Dextr.

Continuous-time Consistency Models (CMs) promise efficient few-step generation but face significant challenges with training instability. We argue this instability stems from a fundamental conflict: by training a network to learn only a shortcut across a probability flow, the model loses its grasp on the instantaneous velocity field that defines the flow. Our solution is to explicitly anchor the model in the underlying flow during training. We introduce the Flow-Anchored Consistency Model (FACM), a simple but effective training strategy that uses a Flow Matching (FM) task as an anchor for the primary CM shortcut objective. This Flow-Anchoring approach requires no architectural modifications and is broadly compatible with standard model architectures. By distilling a pre-trained LightningDiT model, our method achieves a state-of-the-art FID of 1.32 with two steps (NFE=2) and 1.76 with just one step (NFE=1) on ImageNet 256x256, significantly outperforming previous methods. This provides a general and effective recipe for building high-performance, few-step generative models. Our code and pretrained models: https://github.com/ali-vilab/FACM.

Large language models (LLM) have become a critical component in many applications of machine learning. However, standard approaches to training LLM require a large number of tightly interconnected accelerators, with devices exchanging gradients and other intermediate states at each optimization step. While it is difficult to build and maintain a single computing cluster hosting many accelerators, it might be easier to find several computing clusters each hosting a smaller number of devices. In this work, we propose a distributed optimization algorithm, Distributed Low-Communication (DiLoCo), that enables training of language models on islands of devices that are poorly connected. The approach is a variant of federated averaging, where the number of inner steps is large, the inner optimizer is AdamW, and the outer optimizer is Nesterov momentum. On the widely used C4 dataset, we show that DiLoCo on 8 workers performs as well as fully synchronous optimization while communicating 500 times less. DiLoCo exhibits great robustness to the data distribution of each worker. It is also robust to resources becoming unavailable over time, and vice versa, it can seamlessly leverage resources that become available during training.

Denoising Diffusion Probabilistic Models (DDPMs) have garnered popularity for data generation across various domains. However, a significant bottleneck is the necessity for whole-network computation during every step of the generative process, leading to high computational overheads. This paper presents a novel framework, Denoising Diffusion Step-aware Models (DDSM), to address this challenge. Unlike conventional approaches, DDSM employs a spectrum of neural networks whose sizes are adapted according to the importance of each generative step, as determined through evolutionary search. This step-wise network variation effectively circumvents redundant computational efforts, particularly in less critical steps, thereby enhancing the efficiency of the diffusion model. Furthermore, the step-aware design can be seamlessly integrated with other efficiency-geared diffusion models such as DDIMs and latent diffusion, thus broadening the scope of computational savings. Empirical evaluations demonstrate that DDSM achieves computational savings of 49% for CIFAR-10, 61% for CelebA-HQ, 59% for LSUN-bedroom, 71% for AFHQ, and 76% for ImageNet, all without compromising the generation quality. Our code and models will be publicly available.

We propose Delta Velocity Rectified Flow (DVRF), a novel inversion-free, path-aware editing framework within rectified flow models for text-to-image editing. DVRF is a distillation-based method that explicitly models the discrepancy between the source and target velocity fields in order to mitigate over-smoothing artifacts rampant in prior distillation sampling approaches. We further introduce a time-dependent shift term to push noisy latents closer to the target trajectory, enhancing the alignment with the target distribution. We theoretically demonstrate that when this shift is disabled, DVRF reduces to Delta Denoising Score, thereby bridging score-based diffusion optimization and velocity-based rectified-flow optimization. Moreover, when the shift term follows a linear schedule under rectified-flow dynamics, DVRF generalizes the Inversion-free method FlowEdit and provides a principled theoretical interpretation for it. Experimental results indicate that DVRF achieves superior editing quality, fidelity, and controllability while requiring no architectural modifications, making it efficient and broadly applicable to text-to-image editing tasks. Code is available at https://github.com/gaspardbd/DeltaVelocityRectifiedFlow.

Pipeline parallelism is one of the key components for large-scale distributed training, yet its efficiency suffers from pipeline bubbles which were deemed inevitable. In this work, we introduce a scheduling strategy that, to our knowledge, is the first to successfully achieve zero pipeline bubbles under synchronous training semantics. The key idea behind this improvement is to split the backward computation into two parts, one that computes gradient for the input and another that computes for the parameters. Based on this idea, we handcraft novel pipeline schedules that significantly outperform the baseline methods. We further develop an algorithm that automatically finds an optimal schedule based on specific model configuration and memory limit. Additionally, to truly achieve zero bubble, we introduce a novel technique to bypass synchronizations during the optimizer step. Experimental evaluations show that our method outperforms the 1F1B schedule up to 23% in throughput under a similar memory limit. This number can be further pushed to 31% when the memory constraint is relaxed. We believe our results mark a major step forward in harnessing the true potential of pipeline parallelism. We open sourced our implementation based on the popular Megatron-LM repository on https://github.com/sail-sg/zero-bubble-pipeline-parallelism.

We present Dress&Dance, a video diffusion framework that generates high quality 5-second-long 24 FPS virtual try-on videos at 1152x720 resolution of a user wearing desired garments while moving in accordance with a given reference video. Our approach requires a single user image and supports a range of tops, bottoms, and one-piece garments, as well as simultaneous tops and bottoms try-on in a single pass. Key to our framework is CondNet, a novel conditioning network that leverages attention to unify multi-modal inputs (text, images, and videos), thereby enhancing garment registration and motion fidelity. CondNet is trained on heterogeneous training data, combining limited video data and a larger, more readily available image dataset, in a multistage progressive manner. Dress&Dance outperforms existing open source and commercial solutions and enables a high quality and flexible try-on experience.

Weight-sharing neural architecture search (NAS) is an effective technique for automating efficient neural architecture design. Weight-sharing NAS builds a supernet that assembles all the architectures as its sub-networks and jointly trains the supernet with the sub-networks. The success of weight-sharing NAS heavily relies on distilling the knowledge of the supernet to the sub-networks. However, we find that the widely used distillation divergence, i.e., KL divergence, may lead to student sub-networks that over-estimate or under-estimate the uncertainty of the teacher supernet, leading to inferior performance of the sub-networks. In this work, we propose to improve the supernet training with a more generalized alpha-divergence. By adaptively selecting the alpha-divergence, we simultaneously prevent the over-estimation or under-estimation of the uncertainty of the teacher model. We apply the proposed alpha-divergence based supernets training to both slimmable neural networks and weight-sharing NAS, and demonstrate significant improvements. Specifically, our discovered model family, AlphaNet, outperforms prior-art models on a wide range of FLOPs regimes, including BigNAS, Once-for-All networks, and AttentiveNAS. We achieve ImageNet top-1 accuracy of 80.0% with only 444M FLOPs. Our code and pretrained models are available at https://github.com/facebookresearch/AlphaNet.

Recent advances in few-step diffusion models have demonstrated their efficiency and effectiveness by shortcutting the probabilistic paths of diffusion models, especially in training one-step diffusion models from scratch (a.k.a. shortcut models). However, their theoretical derivation and practical implementation are often closely coupled, which obscures the design space. To address this, we propose a common design framework for representative shortcut models. This framework provides theoretical justification for their validity and disentangles concrete component-level choices, thereby enabling systematic identification of improvements. With our proposed improvements, the resulting one-step model achieves a new state-of-the-art FID50k of 2.85 on ImageNet-256x256 under the classifier-free guidance setting with one step generation, and further reaches FID50k of 2.53 with 2x training steps. Remarkably, the model requires no pre-training, distillation, or curriculum learning. We believe our work lowers the barrier to component-level innovation in shortcut models and facilitates principled exploration of their design space.

Lion (Evolved Sign Momentum), a new optimizer discovered through program search, has shown promising results in training large AI models. It performs comparably or favorably to AdamW but with greater memory efficiency. As we can expect from the results of a random search program, Lion incorporates elements from several existing algorithms, including signed momentum, decoupled weight decay, Polak, and Nesterov momentum, but does not fit into any existing category of theoretically grounded optimizers. Thus, even though Lion appears to perform well as a general-purpose optimizer for a wide range of tasks, its theoretical basis remains uncertain. This lack of theoretical clarity limits opportunities to further enhance and expand Lion's efficacy. This work aims to demystify Lion. Based on both continuous-time and discrete-time analysis, we demonstrate that Lion is a theoretically novel and principled approach for minimizing a general loss function f(x) while enforcing a bound constraint |x|_infty leq 1/lambda. Lion achieves this through the incorporation of decoupled weight decay, where lambda represents the weight decay coefficient. Our analysis is made possible by the development of a new Lyapunov function for the Lion updates. It applies to a broader family of Lion-kappa algorithms, where the sign(cdot) operator in Lion is replaced by the subgradient of a convex function kappa, leading to the solution of a general composite optimization problem of min_x f(x) + kappa^*(x). Our findings provide valuable insights into the dynamics of Lion and pave the way for further improvements and extensions of Lion-related algorithms.

Differentiable ARchiTecture Search (DARTS) is one of the most trending Neural Architecture Search (NAS) methods. It drastically reduces search cost by resorting to weight-sharing. However, it also dramatically reduces the search space, thus excluding potential promising architectures. In this article, we propose D-DARTS, a solution that addresses this problem by nesting neural networks at the cell level instead of using weight-sharing to produce more diversified and specialized architectures. Moreover, we introduce a novel algorithm that can derive deeper architectures from a few trained cells, increasing performance and saving computation time. In addition, we also present an alternative search space (DARTOpti) in which we optimize existing handcrafted architectures (e.g., ResNet) rather than starting from scratch. This approach is accompanied by a novel metric that measures the distance between architectures inside our custom search space. Our solution reaches competitive performance on multiple computer vision tasks. Code and pretrained models can be accessed at https://github.com/aheuillet/D-DARTS.

Recent work has made clear that the residual pathway is not mere optimization plumbing; it is part of the model's representational machinery. We agree, but argue that the cleanest way to organize this design space is through a two-axis view of the Transformer. A decoder evolves information along two ordered dimensions: sequence position and layer depth. Self-attention already provides adaptive mixing along the sequence axis, whereas the residual stream usually performs fixed addition along the depth axis. If we fix a token position and treat layer index as the ordered variable, then a causal depth-wise residual attention read is exactly the same local operator as causal short sliding-window attention (ShortSWA), except written over depth rather than over sequence. This is the core residual stream duality behind Transformer^2. This perspective also clarifies the recent literature. ELC-BERT and DenseFormer already show that learned aggregation over depth can outperform uniform residual accumulation, while Vertical Attention, DeepCrossAttention (DCA), MUDDFormer, and Attention Residuals move further toward explicit attention-based routing over earlier layers. The key point, however, is that operator-level duality does not imply systems-level symmetry. For large-scale autoregressive models, sequence-axis ShortSWA is usually the more hardware-friendly placement because it reuses token-side sliding-window kernels, KV-cache layouts, and chunked execution. If the goal is instead to change the shortcut itself, Deep Delta Learning (DDL) is the cleaner intervention because it modifies the residual operator directly rather than adding a separate cross-layer retrieval path. Our recommendation is therefore simple: use DDL when the shortcut is the object of interest, and use sequence-axis ShortSWA when the goal is local adaptive mixing.

Lowering the memory requirement in full-parameter training on large models has become a hot research area. MeZO fine-tunes the large language models (LLMs) by just forward passes in a zeroth-order SGD optimizer (ZO-SGD), demonstrating excellent performance with the same GPU memory usage as inference. However, the simulated perturbation stochastic approximation for gradient estimate in MeZO leads to severe oscillations and incurs a substantial time overhead. Moreover, without momentum regularization, MeZO shows severe over-fitting problems. Lastly, the perturbation-irrelevant momentum on ZO-SGD does not improve the convergence rate. This study proposes ZO-AdaMU to resolve the above problems by adapting the simulated perturbation with momentum in its stochastic approximation. Unlike existing adaptive momentum methods, we relocate momentum on simulated perturbation in stochastic gradient approximation. Our convergence analysis and experiments prove this is a better way to improve convergence stability and rate in ZO-SGD. Extensive experiments demonstrate that ZO-AdaMU yields better generalization for LLMs fine-tuning across various NLP tasks than MeZO and its momentum variants.

Computed tomography (CT) serves as an effective tool for lung cancer screening, diagnosis, treatment, and prognosis, providing a rich source of features to quantify temporal and spatial tumor changes. Nonetheless, the diversity of CT scanners and customized acquisition protocols can introduce significant inconsistencies in texture features, even when assessing the same patient. This variability poses a fundamental challenge for subsequent research that relies on consistent image features. Existing CT image standardization models predominantly utilize GAN-based supervised or semi-supervised learning, but their performance remains limited. We present DiffusionCT, an innovative score-based DDPM model that operates in the latent space to transform disparate non-standard distributions into a standardized form. The architecture comprises a U-Net-based encoder-decoder, augmented by a DDPM model integrated at the bottleneck position. First, the encoder-decoder is trained independently, without embedding DDPM, to capture the latent representation of the input data. Second, the latent DDPM model is trained while keeping the encoder-decoder parameters fixed. Finally, the decoder uses the transformed latent representation to generate a standardized CT image, providing a more consistent basis for downstream analysis. Empirical tests on patient CT images indicate notable improvements in image standardization using DiffusionCT. Additionally, the model significantly reduces image noise in SPAD images, further validating the effectiveness of DiffusionCT for advanced imaging tasks.

Recently, non-convolutional models such as the Vision Transformer (ViT) and Vision Mamba (Vim) have achieved remarkable performance in computer vision tasks. However, their reliance on fixed-size patches often results in excessive encoding of background regions and omission of critical local details, especially when informative objects are sparsely distributed. To address this, we introduce a fully differentiable Dynamic Adaptive Region Tokenizer (DART), which adaptively partitions images into content-dependent patches of varying sizes. DART combines learnable region scores with piecewise differentiable quantile operations to allocate denser tokens to information-rich areas. Despite introducing only approximately 1 million (1M) additional parameters, DART improves accuracy by 2.1% on DeiT (ImageNet-1K). Unlike methods that uniformly increase token density to capture fine-grained details, DART offers a more efficient alternative, achieving 45% FLOPs reduction with superior performance. Extensive experiments on DeiT, Vim, and VideoMamba confirm that DART consistently enhances accuracy while incurring minimal or even reduced computational overhead. Code is available at https://github.com/HCPLab-SYSU/DART.

Diffusion models are widely recognized for generating high-quality and diverse images, but their poor real-time performance has led to numerous acceleration works, primarily focusing on UNet-based structures. With the more successful results achieved by diffusion transformers (DiT), there is still a lack of exploration regarding the impact of DiT structure on generation, as well as the absence of an acceleration framework tailored to the DiT architecture. To tackle these challenges, we conduct an investigation into the correlation between DiT blocks and image generation. Our findings reveal that the front blocks of DiT are associated with the outline of the generated images, while the rear blocks are linked to the details. Based on this insight, we propose an overall training-free inference acceleration framework Delta-DiT: using a designed cache mechanism to accelerate the rear DiT blocks in the early sampling stages and the front DiT blocks in the later stages. Specifically, a DiT-specific cache mechanism called Delta-Cache is proposed, which considers the inputs of the previous sampling image and reduces the bias in the inference. Extensive experiments on PIXART-alpha and DiT-XL demonstrate that the Delta-DiT can achieve a 1.6times speedup on the 20-step generation and even improves performance in most cases. In the scenario of 4-step consistent model generation and the more challenging 1.12times acceleration, our method significantly outperforms existing methods. Our code will be publicly available.

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often computationally expensive. Recently, data-driven methods have emerged as alternatives, but they frequently suffer from error accumulation and limited physical consistency, especially in multiphysics and complex geometries. To address these challenges, we propose PEGNet, a Physics-Embedded Graph Network that incorporates PDE-guided message passing to redesign the graph neural network architecture. By embedding key PDE dynamics like convection, viscosity, and diffusion into distinct message functions, the model naturally integrates physical constraints into its forward propagation, producing more stable and physically consistent solutions. Additionally, a hierarchical architecture is employed to capture multi-scale features, and physical regularization is integrated into the loss function to further enforce adherence to governing physics. We evaluated PEGNet on benchmarks, including custom datasets for respiratory airflow and drug delivery, showing significant improvements in long-term prediction accuracy and physical consistency over existing methods. Our code is available at https://github.com/Yanghuoshan/PEGNet.

Existing NAS methods suffer from either an excessive amount of time for repetitive sampling and training of many task-irrelevant architectures. To tackle such limitations of existing NAS methods, we propose a paradigm shift from NAS to a novel conditional Neural Architecture Generation (NAG) framework based on diffusion models, dubbed DiffusionNAG. Specifically, we consider the neural architectures as directed graphs and propose a graph diffusion model for generating them. Moreover, with the guidance of parameterized predictors, DiffusionNAG can flexibly generate task-optimal architectures with the desired properties for diverse tasks, by sampling from a region that is more likely to satisfy the properties. This conditional NAG scheme is significantly more efficient than previous NAS schemes which sample the architectures and filter them using the property predictors. We validate the effectiveness of DiffusionNAG through extensive experiments in two predictor-based NAS scenarios: Transferable NAS and Bayesian Optimization (BO)-based NAS. DiffusionNAG achieves superior performance with speedups of up to 35 times when compared to the baselines on Transferable NAS benchmarks. Furthermore, when integrated into a BO-based algorithm, DiffusionNAG outperforms existing BO-based NAS approaches, particularly in the large MobileNetV3 search space on the ImageNet 1K dataset. Code is available at https://github.com/CownowAn/DiffusionNAG.

Adaptive gradient methods, e.g. Adam, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid training of modern deep neural networks. Nevertheless, they are observed to suffer from compromised generalization ability compared with stochastic gradient descent (SGD) and tend to be trapped in local minima at an early stage during training. Intriguingly, we discover that substituting the gradient in the second raw moment estimate term with its momentumized version in Adam can resolve the issue. The intuition is that gradient with momentum contains more accurate directional information and therefore its second moment estimation is a more favorable option for learning rate scaling than that of the raw gradient. Thereby we propose AdaMomentum as a new optimizer reaching the goal of training fast while generalizing much better. We further develop a theory to back up the improvement in generalization and provide convergence guarantees under both convex and nonconvex settings. Extensive experiments on a wide range of tasks and models demonstrate that AdaMomentum exhibits state-of-the-art performance and superior training stability consistently.

Modern transformer architectures achieve remarkable performance across tasks and domains but remain rigid in how they allocate computation at inference time. Real-world deployment often requires models to adapt to diverse hardware and latency constraints, yet most approaches to dynamic computation focus on a single axis -- such as reducing the number of tokens. We present a novel capability: AdaPerceiver, the first transformer architecture with unified adaptivity across depth, width, and tokens within a single model. We propose an architecture that supports adaptivity along these axes. We couple this with an efficient joint training regime that ensures the model maintains performance across its various configurations. We evaluate AdaPerceiver on image classification, semantic segmentation, and depth estimation tasks. On image classification, AdaPerceiver expands the accuracy-throughput Pareto front. It achieves 85.4% accuracy while yielding 36% higher throughput than FlexiViT-L. On dense prediction, AdaPerceiver matches ViT-H/14 while having sim26x fewer encoder FLOPs (floating-point operations) on semantic segmentation and depth estimation. Finally, we show how AdaPerceiver equipped with a policy can maintain ImageNet1K accuracy (pm0.1 percentage points) while reducing FLOPs by 24-33%.

In the last decade, zero-cost metrics have gained prominence in neural architecture search (NAS) due to their ability to evaluate architectures without training. These metrics are significantly faster and less computationally expensive than traditional NAS methods and provide insights into neural architectures' internal workings. This paper introduces epsinas, a novel zero-cost NAS metric that assesses architecture potential using two constant shared weight initialisations and the statistics of their outputs. We show that the dispersion of raw outputs, normalised by their average magnitude, strongly correlates with trained accuracy. This effect holds across image classification and language tasks on NAS-Bench-101, NAS-Bench-201, and NAS-Bench-NLP. Our method requires no data labels, operates on a single minibatch, and eliminates the need for gradient computation, making it independent of training hyperparameters, loss metrics, and human annotations. It evaluates a network in a fraction of a GPU second and integrates seamlessly into existing NAS frameworks. The code supporting this study can be found on GitHub at https://github.com/egracheva/epsinas.