Daily Papers

Accurately predicting experimentally realizable 3D molecular crystal structures from their 2D chemical graphs is a long-standing open challenge in computational chemistry called crystal structure prediction (CSP). Efficiently solving this problem has implications ranging from pharmaceuticals to organic semiconductors, as crystal packing directly governs the physical and chemical properties of organic solids. In this paper, we introduce OXtal, a large-scale 100M parameter all-atom diffusion model that directly learns the conditional joint distribution over intramolecular conformations and periodic packing. To efficiently scale OXtal, we abandon explicit equivariant architectures imposing inductive bias arising from crystal symmetries in favor of data augmentation strategies. We further propose a novel crystallization-inspired lattice-free training scheme, Stoichiometric Stochastic Shell Sampling (S^4), that efficiently captures long-range interactions while sidestepping explicit lattice parametrization -- thus enabling more scalable architectural choices at all-atom resolution. By leveraging a large dataset of 600K experimentally validated crystal structures (including rigid and flexible molecules, co-crystals, and solvates), OXtal achieves orders-of-magnitude improvements over prior ab initio machine learning CSP methods, while remaining orders of magnitude cheaper than traditional quantum-chemical approaches. Specifically, OXtal recovers experimental structures with conformer RMSD_1<0.5 Å and attains over 80\% packing similarity rate, demonstrating its ability to model both thermodynamic and kinetic regularities of molecular crystallization.

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we would like to verify that they are bound to meaningful patterns in the data. In this paper, we propose to make similarities interpretable by augmenting them with an explanation in terms of input features. We develop BiLRP, a scalable and theoretically founded method to systematically decompose similarity scores on pairs of input features. Our method can be expressed as a composition of LRP explanations, which were shown in previous works to scale to highly nonlinear functions. Through an extensive set of experiments, we demonstrate that BiLRP robustly explains complex similarity models, e.g. built on VGG-16 deep neural network features. Additionally, we apply our method to an open problem in digital humanities: detailed assessment of similarity between historical documents such as astronomical tables. Here again, BiLRP provides insight and brings verifiability into a highly engineered and problem-specific similarity model.

Accurately modeling protein 3D structure is essential for the design of functional proteins. An important sub-task of structure modeling is protein side-chain packing: predicting the conformation of side-chains (rotamers) given the protein's backbone structure and amino-acid sequence. Conventional approaches for this task rely on expensive sampling procedures over hand-crafted energy functions and rotamer libraries. Recently, several deep learning methods have been developed to tackle the problem in a data-driven way, albeit with vastly different formulations (from image-to-image translation to directly predicting atomic coordinates). Here, we frame the problem as a joint regression over the side-chains' true degrees of freedom: the dihedral chi angles. We carefully study possible objective functions for this task, while accounting for the underlying symmetries of the task. We propose Holographic Packer (H-Packer), a novel two-stage algorithm for side-chain packing built on top of two light-weight rotationally equivariant neural networks. We evaluate our method on CASP13 and CASP14 targets. H-Packer is computationally efficient and shows favorable performance against conventional physics-based algorithms and is competitive against alternative deep learning solutions.

In this work, we introduce a novel approach for predicting thermodynamic properties of binary mixtures, which we call the similarity-based method (SBM). The method is based on quantifying the pairwise similarity of components, which we achieve by comparing quantum-chemical descriptors of the components, namely σ-profiles. The basic idea behind the approach is that mixtures with similar pairs of components will have similar thermodynamic properties. The SBM is trained on a matrix that contains some data for a given property for different binary mixtures; the missing entries are then predicted by the SBM. As an example, we consider the prediction of isothermal activity coefficients at infinite dilution (γ^infty_{ij}) and show that the SBM outperforms the well-established physical methods modified UNIFAC (Dortmund) and COSMO-SAC-dsp. In this case, the matrix is only sparsely occupied, and it is shown that the SBM works also if only a limited number of data for similar mixtures is available. The SBM idea can be transferred to any mixture property and is a powerful tool for generating essential data for many applications.

Work in psychology has highlighted that the geometric model of similarity standard in deep learning is not psychologically plausible because its metric properties such as symmetry do not align with human perception. In contrast, Tversky (1977) proposed an axiomatic theory of similarity based on a representation of objects as sets of features, and their similarity as a function of common and distinctive features. However, this model has not been used in deep learning before, partly due to the challenge of incorporating discrete set operations. We develop a differentiable parameterization of Tversky's similarity that is learnable through gradient descent, and derive neural network building blocks such as the Tversky projection layer, which unlike the linear projection layer can model non-linear functions such as XOR. Through experiments with image recognition and language modeling, we show that the Tversky projection layer is a beneficial replacement for the linear projection layer, which employs geometric similarity. On the NABirds image classification task, a frozen ResNet-50 adapted with a Tversky projection layer achieves a 24.7% relative accuracy improvement over the linear layer adapter baseline. With Tversky projection layers, GPT-2's perplexity on PTB decreases by 7.5%, and its parameter count by 34.8%. Finally, we propose a unified interpretation of both projection layers as computing similarities of input stimuli to learned prototypes, for which we also propose a novel visualization technique highlighting the interpretability of Tversky projection layers. Our work offers a new paradigm for thinking about the similarity model implicit in deep learning, and designing networks that are interpretable under an established theory of psychological similarity.

We consider the Similarity Sketching problem: Given a universe [u] = {0,ldots, u-1} we want a random function S mapping subsets Asubseteq [u] into vectors S(A) of size t, such that the Jaccard similarity J(A,B) = |Acap B|/|Acup B| between sets A and B is preserved. More precisely, define X_i = [S(A)[i] = S(B)[i]] and X = sum_{iin [t]} X_i. We want E[X_i]=J(A,B), and we want X to be strongly concentrated around E[X] = t cdot J(A,B) (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, large-scale classification, computer vision, similarity search, etc. via the classic MinHash algorithm. The vectors S(A) are also called sketches. Strong concentration is critical, for often we want to sketch many sets B_1,ldots,B_n so that we later, for a query set A, can find (one of) the most similar B_i. It is then critical that no B_i looks much more similar to A due to errors in the sketch. The seminal ttimesMinHash algorithm uses t random hash functions h_1,ldots, h_t, and stores left ( min_{ain A} h_1(A),ldots, min_{ain A} h_t(A) right ) as the sketch of A. The main drawback of MinHash is, however, its O(tcdot |A|) running time, and finding a sketch with similar properties and faster running time has been the subject of several papers. (continued...)

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

A recurring challenge in self-supervised learning is preventing representation collapse. Existing solutions typically rely on global regularization, such as maximizing distances, decorrelating dimensions or enforcing certain distributions. We instead reinterpret representation learning as a discrete packing problem, where preserving information simplifies to maintaining injectivity. We operationalize this in Hypersolid, a method using short-range hard-ball repulsion to prevent local collisions. This constraint results in a high-separation geometric regime that preserves augmentation diversity, excelling on fine-grained and low-resolution classification tasks.

Quantifying the similarity between a group of companies has proven to be useful for several purposes, including company benchmarking, fraud detection, and searching for investment opportunities. This exercise can be done using a variety of data sources, such as company activity data and financial data. However, ledger account data is widely available and is standardized to a large extent. Such ledger accounts within a financial statement can be represented by means of a tree, i.e. a special type of graph, representing both the values of the ledger accounts and the relationships between them. Given their broad availability and rich information content, financial statements form a prime data source based on which company similarities or distances could be computed. In this paper, we present a graph distance metric that enables one to compute the similarity between the financial statements of two companies. We conduct a comprehensive experimental study using real-world financial data to demonstrate the usefulness of our proposed distance metric. The experimental results show promising results on a number of use cases. This method may be useful for investors looking for investment opportunities, government officials attempting to identify fraudulent companies, and accountants looking to benchmark a group of companies based on their financial statements.

Unsupervised hashing methods typically aim to preserve the similarity between data points in a feature space by mapping them to binary hash codes. However, these methods often overlook the fact that the similarity between data points in the continuous feature space may not be preserved in the discrete hash code space, due to the limited similarity range of hash codes. The similarity range is bounded by the code length and can lead to a problem known as similarity collapse. That is, the positive and negative pairs of data points become less distinguishable from each other in the hash space. To alleviate this problem, in this paper a novel Similarity Distribution Calibration (SDC) method is introduced. SDC aligns the hash code similarity distribution towards a calibration distribution (e.g., beta distribution) with sufficient spread across the entire similarity range, thus alleviating the similarity collapse problem. Extensive experiments show that our SDC outperforms significantly the state-of-the-art alternatives on coarse category-level and instance-level image retrieval. Code is available at https://github.com/kamwoh/sdc.

Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a fundamental challenge. This problem is the local analogue of Hilbert's 18th problem, bridging geometry, number theory, and information theory. Although significant progress has been made through lattices and codes, the irregularities of high-dimensional geometry, dimensional structure variability, and combinatorial explosion beyond Go limit the scalability and generality of existing methods. Here we model the problem as a two-player matrix completion game and train the reinforcement learning system, PackingStar, to play the games. The matrix entries represent pairwise cosines of sphere center vectors. One player fills entries while another corrects suboptimal ones to improve exploration quality, cooperatively maximizing the matrix size, corresponding to the kissing number. These matrices are decomposed into representative substructures, providing diverse bases and structural constraints that steer subsequent games and make extremely large spaces tractable. PackingStar surpasses records from dimensions 25 to 31 and sets new lower bounds for generalized kissing numbers under various angular constraints. It achieves the first breakthrough beyond rational structures from 1971 in 13 dimensions and discovers over 6000 new structures in other dimensions. Notably, some configurations challenge long-held antipodal paradigms, revealing algebraic correspondences with finite simple groups as well as geometric relationships across dimensions. Inspired by these patterns, humans devised further improved constructions. These results demonstrate AI's power to explore high-dimensional spaces beyond human intuition via extreme-scale reinforcement learning and open new pathways for the Kissing Number Problem and broader geometry research.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

In large language model training, input documents are typically concatenated together and then split into sequences of equal length to avoid padding tokens. Despite its efficiency, the concatenation approach compromises data integrity -- it inevitably breaks many documents into incomplete pieces, leading to excessive truncations that hinder the model from learning to compose logically coherent and factually consistent content that is grounded on the complete context. To address the issue, we propose Best-fit Packing, a scalable and efficient method that packs documents into training sequences through length-aware combinatorial optimization. Our method completely eliminates unnecessary truncations while retaining the same training efficiency as concatenation. Empirical results from both text and code pre-training show that our method achieves superior performance (e.g., relatively +4.7% on reading comprehension; +16.8% in context following; and +9.2% on program synthesis), and reduces closed-domain hallucination effectively by up to 58.3%.

Many real-world tasks require models to compare images along multiple similarity conditions (e.g. similarity in color, category or shape). Existing methods often reason about these complex similarity relationships by learning condition-aware embeddings. While such embeddings aid models in learning different notions of similarity, they also limit their capability to generalize to unseen categories since they require explicit labels at test time. To address this deficiency, we propose an approach that jointly learns representations for the different similarity conditions and their contributions as a latent variable without explicit supervision. Comprehensive experiments across three datasets, Polyvore-Outfits, Maryland-Polyvore and UT-Zappos50k, demonstrate the effectiveness of our approach: our model outperforms the state-of-the-art methods, even those that are strongly supervised with pre-defined similarity conditions, on fill-in-the-blank, outfit compatibility prediction and triplet prediction tasks. Finally, we show that our model learns different visually-relevant semantic sub-spaces that allow it to generalize well to unseen categories.

Robotics and automation are increasingly influential in logistics but remain largely confined to traditional warehouses. In grocery retail, advancements such as cashier-less supermarkets exist, yet customers still manually pick and pack groceries. While there has been a substantial focus in robotics on the bin picking problem, the task of packing objects and groceries has remained largely untouched. However, packing grocery items in the right order is crucial for preventing product damage, e.g., heavy objects should not be placed on top of fragile ones. However, the exact criteria for the right packing order are hard to define, in particular given the huge variety of objects typically found in stores. In this paper, we introduce LLM-Pack, a novel approach for grocery packing. LLM-Pack leverages language and vision foundation models for identifying groceries and generating a packing sequence that mimics human packing strategy. LLM-Pack does not require dedicated training to handle new grocery items and its modularity allows easy upgrades of the underlying foundation models. We extensively evaluate our approach to demonstrate its performance. We will make the source code of LLMPack publicly available upon the publication of this manuscript.

Transfer learning is crucial for medical imaging, yet the selection of source datasets - which can impact the generalizability of algorithms, and thus patient outcomes - often relies on researchers' intuition rather than systematic principles. This study investigates these decisions through a task-based survey with machine learning practitioners. Unlike prior work that benchmarks models and experimental setups, we take a human-centered HCI perspective on how practitioners select source datasets. Our findings indicate that choices are task-dependent and influenced by community practices, dataset properties, and computational (data embedding), or perceived visual or semantic similarity. However, similarity ratings and expected performance are not always aligned, challenging a traditional "more similar is better" view. Participants often used ambiguous terminology, which suggests a need for clearer definitions and HCI tools to make them explicit and usable. By clarifying these heuristics, this work provides practical insights for more systematic source selection in transfer learning.

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension n=8, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions 4-16, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

When robots learn reward functions using high capacity models that take raw state directly as input, they need to both learn a representation for what matters in the task -- the task ``features" -- as well as how to combine these features into a single objective. If they try to do both at once from input designed to teach the full reward function, it is easy to end up with a representation that contains spurious correlations in the data, which fails to generalize to new settings. Instead, our ultimate goal is to enable robots to identify and isolate the causal features that people actually care about and use when they represent states and behavior. Our idea is that we can tune into this representation by asking users what behaviors they consider similar: behaviors will be similar if the features that matter are similar, even if low-level behavior is different; conversely, behaviors will be different if even one of the features that matter differs. This, in turn, is what enables the robot to disambiguate between what needs to go into the representation versus what is spurious, as well as what aspects of behavior can be compressed together versus not. The notion of learning representations based on similarity has a nice parallel in contrastive learning, a self-supervised representation learning technique that maps visually similar data points to similar embeddings, where similarity is defined by a designer through data augmentation heuristics. By contrast, in order to learn the representations that people use, so we can learn their preferences and objectives, we use their definition of similarity. In simulation as well as in a user study, we show that learning through such similarity queries leads to representations that, while far from perfect, are indeed more generalizable than self-supervised and task-input alternatives.

Similarity between training examples is used to curate pretraining datasets for language models by many methods -- for diversification and to select examples similar to high-quality data. However, similarity is typically measured with off-the-shelf embedding models that are generic or trained for tasks such as retrieval. This paper introduces a framework to analyze the suitability of embedding models specifically for data curation in the language model pretraining setting. We quantify the correlation between similarity in the embedding space to similarity in pretraining loss between different training examples, and how diversifying in the embedding space affects pretraining quality. We analyze a variety of embedding models in our framework, with experiments using the Pile dataset for pretraining a 1.7B parameter decoder-only language model. We find that the embedding models we consider are all useful for pretraining data curation. Moreover, a simple approach of averaging per-token embeddings proves to be surprisingly competitive with more sophisticated embedding models -- likely because the latter are not designed specifically for pretraining data curation. Indeed, we believe our analysis and evaluation framework can serve as a foundation for the design of embedding models that specifically reason about similarity in pretraining datasets.

Embedding based product recommendations have gained popularity in recent years due to its ability to easily integrate to large-scale systems and allowing nearest neighbor searches in real-time. The bulk of studies in this area has predominantly been focused on similar item recommendations. Research on complementary item recommendations, on the other hand, still remains considerably under-explored. We define similar items as items that are interchangeable in terms of their utility and complementary items as items that serve different purposes, yet are compatible when used with one another. In this paper, we apply a novel approach to finding complementary items by leveraging dual embedding representations for products. We demonstrate that the notion of relatedness discovered in NLP for skip-gram negative sampling (SGNS) models translates effectively to the concept of complementarity when training item representations using co-purchase data. Since sparsity of purchase data is a major challenge in real-world scenarios, we further augment the model using synthetic samples to extend coverage. This allows the model to provide complementary recommendations for items that do not share co-purchase data by leveraging other abundantly available data modalities such as images, text, clicks etc. We establish the effectiveness of our approach in improving both coverage and quality of recommendations on real world data for a major online retail company. We further show the importance of task specific hyperparameter tuning in training SGNS. Our model is effective yet simple to implement, making it a great candidate for generating complementary item recommendations at any e-commerce website.

Measuring the similarity of the internal representations of deep neural networks is an important and challenging problem. Model stitching has been proposed as a possible approach, where two half-networks are connected by mapping the output of the first half-network to the input of the second one. The representations are considered functionally similar if the resulting stitched network achieves good task-specific performance. The mapping is normally created by training an affine stitching layer on the task at hand while freezing the two half-networks, a method called task loss matching. Here, we argue that task loss matching may be very misleading as a similarity index. For example, it can indicate very high similarity between very distant layers, whose representations are known to have different functional properties. Moreover, it can indicate very distant layers to be more similar than architecturally corresponding layers. Even more surprisingly, when comparing layers within the same network, task loss matching often indicates that some layers are more similar to a layer than itself. We argue that the main reason behind these problems is that task loss matching tends to create out-of-distribution representations to improve task-specific performance. We demonstrate that direct matching (when the mapping minimizes the distance between the stitched representations) does not suffer from these problems. We compare task loss matching, direct matching, and well-known similarity indices such as CCA and CKA. We conclude that direct matching strikes a good balance between the structural and functional requirements for a good similarity index.

As models and data scale, independently trained networks often induce analogous notions of similarity. But, matching similarities is weaker than establishing an explicit correspondence between the representation spaces, especially for multimodal models, where consistency must hold not only within each modality, but also for the learned image-text coupling. We therefore ask: given two independently trained multimodal contrastive models (with encoders (f, g) and (f,g)) -- trained on different distributions and with different architectures -- does a systematic geometric relationship exist between their embedding spaces? If so, what form does it take, and does it hold uniformly across modalities? In this work, we show that across model families such as CLIP, SigLIP, and FLAVA, this geometric relationship is well approximated by an orthogonal map (up to a global mean shift), i.e., there exists an orthogonal map Q where Q^top Q = I such that f(x)approx Q f(x) for paired images x. Strikingly, the same Q simultaneously aligns the text encoders i.e., g(y)approx Q g(y) for texts y. Theoretically, we prove that if the multimodal kernel agrees across models on a small anchor set i.e. langle f(x), g(y)rangle approx langle f(x), g(y)rangle, then the two models must be related by a single orthogonal map Q and the same Q maps images and text across models. More broadly, this finding enables backward-compatible model upgrades, avoiding costly re-embedding, and has implications for the privacy of learned representations. Our project page: https://canonical-multimodal.github.io/

In recent years, many deep neural architectures have been developed for image classification. Whether they are similar or dissimilar and what factors contribute to their (dis)similarities remains curious. To address this question, we aim to design a quantitative and scalable similarity measure between neural architectures. We propose Similarity by Attack Transferability (SAT) from the observation that adversarial attack transferability contains information related to input gradients and decision boundaries widely used to understand model behaviors. We conduct a large-scale analysis on 69 state-of-the-art ImageNet classifiers using our proposed similarity function to answer the question. Moreover, we observe neural architecture-related phenomena using model similarity that model diversity can lead to better performance on model ensembles and knowledge distillation under specific conditions. Our results provide insights into why developing diverse neural architectures with distinct components is necessary.

Requirement traceability is the process of identifying the inter-dependencies between requirements. It poses a significant challenge when conducted manually, especially when dealing with requirements at various levels of abstraction. In this work, we propose a novel approach to automate the task of linking high-level business requirements with more technical system requirements. The proposed approach begins by representing each requirement using a Bag of-Words (BOW) model combined with the Term Frequency-Inverse Document Frequency (TF-IDF) scoring function. Then, we suggested an enhanced cosine similarity that uses recent advances in word embedding representation to correct traditional cosine similarity function limitations. To evaluate the effectiveness of our approach, we conducted experiments on three well-known datasets: COEST, WARC(NFR), and WARC(FRS). The results demonstrate that our approach significantly improves efficiency compared to existing methods. We achieved better results with an increase of approximately 18.4% in one of the datasets, as measured by the F2 score.

Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications. Graph-based indices are currently the best performing techniques for billion-scale similarity search. However, their random-access memory pattern presents challenges to realize their full potential. In this work, we present new techniques and systems for creating faster and smaller graph-based indices. To this end, we introduce a novel vector compression method, Locally-adaptive Vector Quantization (LVQ), that uses per-vector scaling and scalar quantization to improve search performance with fast similarity computations and a reduced effective bandwidth, while decreasing memory footprint and barely impacting accuracy. LVQ, when combined with a new high-performance computing system for graph-based similarity search, establishes the new state of the art in terms of performance and memory footprint. For billions of vectors, LVQ outcompetes the second-best alternatives: (1) in the low-memory regime, by up to 20.7x in throughput with up to a 3x memory footprint reduction, and (2) in the high-throughput regime by 5.8x with 1.4x less memory.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

Effective training of today's large language models (LLMs) depends on large batches and long sequences for throughput and accuracy. To handle variable-length sequences on hardware accelerators, it is common practice to introduce padding tokens, so that all sequences in a batch have the same length. We show in this paper that the variation in sequence lengths in common NLP datasets is such that up to 50% of all tokens can be padding. In less common, but not extreme, cases (e.g. GLUE-cola with sequence length 128), the ratio is up to 89%. Existing methods to address the resulting inefficiency are complicated by the need to avoid cross-contamination in self-attention, by a reduction in accuracy when sequence ordering information is lost, or by customized kernel implementations only valid for specific accelerators. This paper introduces a new formalization of sequence packing in the context of the well-studied bin packing problem, and presents new algorithms based on this formulation which, for example, confer a 2x speedup for phase 2 pre-training in BERT. We show how existing models can be adapted to ensure mathematical equivalence between the original and packed models, meaning that packed models can be trained with existing pre-training and fine-tuning practices.

A fundamental problem in combinatorial optimization is identifying equivalent formulations, which can lead to more efficient solution strategies and deeper insights into a problem's computational complexity. The need to automatically identify equivalence between problem formulations has grown as optimization copilots--systems that generate problem formulations from natural language descriptions--have proliferated. However, existing approaches to checking formulation equivalence lack grounding, relying on simple heuristics which are insufficient for rigorous validation. Inspired by Karp reductions, in this work we introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings, enabling scalable and reliable equivalence verification. To evaluate our approach, we construct the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.

Similarity is a comparative-subjective measure that varies with the domain within which it is considered. In several NLP applications such as document classification, pattern recognition, chatbot question-answering, sentiment analysis, etc., identifying an accurate similarity score for sentence pairs has become a crucial area of research. In the existing models that assess similarity, the limitation of effectively computing this similarity based on contextual comparisons, the localization due to the centering theory, and the lack of non-semantic textual comparisons have proven to be drawbacks. Hence, this paper presents a multi-layered semantic similarity network model built upon multiple similarity measures that render an overall sentence similarity score based on the principles of Network Science, neighboring weighted relational edges, and a proposed extended node similarity computation formula. The proposed multi-layered network model was evaluated and tested against established state-of-the-art models and is shown to have demonstrated better performance scores in assessing sentence similarity.

Outfits in online fashion data are composed of items of many different types (e.g. top, bottom, shoes) that share some stylistic relationship with one another. A representation for building outfits requires a method that can learn both notions of similarity (for example, when two tops are interchangeable) and compatibility (items of possibly different type that can go together in an outfit). This paper presents an approach to learning an image embedding that respects item type, and jointly learns notions of item similarity and compatibility in an end-to-end model. To evaluate the learned representation, we crawled 68,306 outfits created by users on the Polyvore website. Our approach obtains 3-5% improvement over the state-of-the-art on outfit compatibility prediction and fill-in-the-blank tasks using our dataset, as well as an established smaller dataset, while supporting a variety of useful queries.

Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML complexity using structural entropy, derived from Boltzmann's statistical mechanics. Unlike traditional KPIs such as distance or cost, structural entropy quantifies the cardinality of the configuration space, providing a diagnostic of inherent system disorder. We establish a formal duality with Shannon entropy, linking absolute complexity burden to distributional balance. We apply our entropy framework to 6,112 Amazon last-mile routes across five U.S. cities. Current operations exhibit persistently high normalized entropy, indicating near-maximal fragmentation. A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty. To evaluate spatial consolidation, we develop a system-wide entropy measure accounting for all movements by both carriers and customers. We establish a theoretical conservation principle: under idealized conditions, spatial consolidation merely redistributes entropy from carrier to customer. Both idealizing conditions are violated in practice, thereby increasing total system entropy. Our system-wide measure reveals that spatial consolidation reduces carrier entropy by up to 40% under aggressive adoption but increases total system entropy by activating customer collection trips, though trip chaining can diminish this effect. Temporal consolidation, by contrast, genuinely reduces entropy by decreasing delivery events without creating new movements. By formalizing fragmentation as a measurable structural property, this research provides a new lens for network design, consolidation policy, and evaluation last-mile system performance.

When two different parties use the same learning rule on their own data, how can we test whether the distributions of the two outcomes are similar? In this paper, we study the similarity of outcomes of learning rules through the lens of the Total Variation (TV) distance of distributions. We say that a learning rule is TV indistinguishable if the expected TV distance between the posterior distributions of its outputs, executed on two training data sets drawn independently from the same distribution, is small. We first investigate the learnability of hypothesis classes using TV indistinguishable learners. Our main results are information-theoretic equivalences between TV indistinguishability and existing algorithmic stability notions such as replicability and approximate differential privacy. Then, we provide statistical amplification and boosting algorithms for TV indistinguishable learners.

Humans do not just see attribute similarity -- we also see relational similarity. An apple is like a peach because both are reddish fruit, but the Earth is also like a peach: its crust, mantle, and core correspond to the peach's skin, flesh, and pit. This ability to perceive and recognize relational similarity, is arguable by cognitive scientist to be what distinguishes humans from other species. Yet, all widely used visual similarity metrics today (e.g., LPIPS, CLIP, DINO) focus solely on perceptual attribute similarity and fail to capture the rich, often surprising relational similarities that humans perceive. How can we go beyond the visible content of an image to capture its relational properties? How can we bring images with the same relational logic closer together in representation space? To answer these questions, we first formulate relational image similarity as a measurable problem: two images are relationally similar when their internal relations or functions among visual elements correspond, even if their visual attributes differ. We then curate 114k image-caption dataset in which the captions are anonymized -- describing the underlying relational logic of the scene rather than its surface content. Using this dataset, we finetune a Vision-Language model to measure the relational similarity between images. This model serves as the first step toward connecting images by their underlying relational structure rather than their visible appearance. Our study shows that while relational similarity has a lot of real-world applications, existing image similarity models fail to capture it -- revealing a critical gap in visual computing.

Padding is often used in tuning LLM models by adding special tokens to shorter training examples to match the length of the longest sequence in each batch. While this ensures uniformity for batch processing, it introduces inefficiencies by including irrelevant padding tokens in the computation and wastes GPU resources. On the other hand, the Hugging Face SFT trainer offers the option to use packing to combine multiple training examples up to the maximum sequence length. This allows for maximal utilization of GPU resources. However, without proper masking of each packed training example, attention will not be computed correctly when using SFT trainer. We enable and then analyse packing and Flash Attention with proper attention masking of each example and show the benefits of this training paradigm.

Chemical similarity searches are widely used in-silico methods for identifying new drug-like molecules. These methods have historically relied on structure-based comparisons to compute molecular similarity. Here, we use a chemical language model to create a vector-based chemical search. We extend implementations by creating a prompt engineering strategy that utilizes two different chemical string representation algorithms: one for the query and the other for the database. We explore this method by reviewing the search results from five drug-like query molecules (penicillin G, nirmatrelvir, zidovudine, lysergic acid diethylamide, and fentanyl) and three dye-like query molecules (acid blue 25, avobenzone, and 2-diphenylaminocarbazole). We find that this novel method identifies molecules that are functionally similar to the query, indicated by the associated patent literature, and that many of these molecules are structurally distinct from the query, making them unlikely to be found with traditional chemical similarity search methods. This method may aid in the discovery of novel structural classes of molecules that achieve target functionality.

In contrastive learning, two views of an original image, generated by different augmentations, are considered a positive pair, and their similarity is required to be high. Similarly, two views of distinct images form a negative pair, with encouraged low similarity. Typically, a single similarity measure, provided by a lone projection head, evaluates positive and negative sample pairs. However, due to diverse augmentation strategies and varying intra-sample similarity, views from the same image may not always be similar. Additionally, owing to inter-sample similarity, views from different images may be more akin than those from the same image. Consequently, enforcing high similarity for positive pairs and low similarity for negative pairs may be unattainable, and in some cases, such enforcement could detrimentally impact performance. To address this challenge, we propose using multiple projection heads, each producing a distinct set of features. Our pre-training loss function emerges from a solution to the maximum likelihood estimation over head-wise posterior distributions of positive samples given observations. This loss incorporates the similarity measure over positive and negative pairs, each re-weighted by an individual adaptive temperature, regulated to prevent ill solutions. Our approach, Adaptive Multi-Head Contrastive Learning (AMCL), can be applied to and experimentally enhances several popular contrastive learning methods such as SimCLR, MoCo, and Barlow Twins. The improvement remains consistent across various backbones and linear probing epochs, and becomes more significant when employing multiple augmentation methods.

We study neural network loss landscapes through the lens of mode connectivity, the observation that minimizers of neural networks retrieved via training on a dataset are connected via simple paths of low loss. Specifically, we ask the following question: are minimizers that rely on different mechanisms for making their predictions connected via simple paths of low loss? We provide a definition of mechanistic similarity as shared invariances to input transformations and demonstrate that lack of linear connectivity between two models implies they use dissimilar mechanisms for making their predictions. Relevant to practice, this result helps us demonstrate that naive fine-tuning on a downstream dataset can fail to alter a model's mechanisms, e.g., fine-tuning can fail to eliminate a model's reliance on spurious attributes. Our analysis also motivates a method for targeted alteration of a model's mechanisms, named connectivity-based fine-tuning (CBFT), which we analyze using several synthetic datasets for the task of reducing a model's reliance on spurious attributes.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data-parallel tasks, prior approaches are bottlenecked by algorithms that expose less parallelism, such as k-min selection, or make poor use of the memory hierarchy. We propose a design for k-selection that operates at up to 55% of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5x faster than prior GPU state of the art. We apply it in different similarity search scenarios, by proposing optimized design for brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation enables the construction of a high accuracy k-NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach for the sake of comparison and reproducibility.

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

Developing advanced medical imaging retrieval systems is challenging due to the varying definitions of `similar images' across different medical contexts. This challenge is compounded by the lack of large-scale, high-quality medical imaging retrieval datasets and benchmarks. In this paper, we propose a novel methodology that leverages dense radiology reports to define image-wise similarity ordering at multiple granularities in a scalable and fully automatic manner. Using this approach, we construct two comprehensive medical imaging retrieval datasets: MIMIC-IR for Chest X-rays and CTRATE-IR for CT scans, providing detailed image-image ranking annotations conditioned on diverse anatomical structures. Furthermore, we develop two retrieval systems, RadIR-CXR and model-ChestCT, which demonstrate superior performance in traditional image-image and image-report retrieval tasks. These systems also enable flexible, effective image retrieval conditioned on specific anatomical structures described in text, achieving state-of-the-art results on 77 out of 78 metrics.

Large language models achieve high performance on many but not all downstream tasks. The interaction between pretraining data and task data is commonly assumed to determine this variance: a task with data that is more similar to a model's pretraining data is assumed to be easier for that model. We test whether distributional and example-specific similarity measures (embedding-, token- and model-based) correlate with language model performance through a large-scale comparison of the Pile and C4 pretraining datasets with downstream benchmarks. Similarity correlates with performance for multilingual datasets, but in other benchmarks, we surprisingly find that similarity metrics are not correlated with accuracy or even each other. This suggests that the relationship between pretraining data and downstream tasks is more complex than often assumed.

Traditional document similarity measures provide a coarse-grained distinction between similar and dissimilar documents. Typically, they do not consider in what aspects two documents are similar. This limits the granularity of applications like recommender systems that rely on document similarity. In this paper, we extend similarity with aspect information by performing a pairwise document classification task. We evaluate our aspect-based document similarity for research papers. Paper citations indicate the aspect-based similarity, i.e., the section title in which a citation occurs acts as a label for the pair of citing and cited paper. We apply a series of Transformer models such as RoBERTa, ELECTRA, XLNet, and BERT variations and compare them to an LSTM baseline. We perform our experiments on two newly constructed datasets of 172,073 research paper pairs from the ACL Anthology and CORD-19 corpus. Our results show SciBERT as the best performing system. A qualitative examination validates our quantitative results. Our findings motivate future research of aspect-based document similarity and the development of a recommender system based on the evaluated techniques. We make our datasets, code, and trained models publicly available.

Visual similarities discovery (VSD) is an important task with broad e-commerce applications. Given an image of a certain object, the goal of VSD is to retrieve images of different objects with high perceptual visual similarity. Although being a highly addressed problem, the evaluation of proposed methods for VSD is often based on a proxy of an identification-retrieval task, evaluating the ability of a model to retrieve different images of the same object. We posit that evaluating VSD methods based on identification tasks is limited, and faithful evaluation must rely on expert annotations. In this paper, we introduce the first large-scale fashion visual similarity benchmark dataset, consisting of more than 110K expert-annotated image pairs. Besides this major contribution, we share insight from the challenges we faced while curating this dataset. Based on these insights, we propose a novel and efficient labeling procedure that can be applied to any dataset. Our analysis examines its limitations and inductive biases, and based on these findings, we propose metrics to mitigate those limitations. Though our primary focus lies on visual similarity, the methodologies we present have broader applications for discovering and evaluating perceptual similarity across various domains.

The capability of accurately determining code similarity is crucial in many tasks related to software development. For example, it might be essential to identify code duplicates for performing software maintenance. This research introduces a novel ensemble learning approach for code similarity assessment, combining the strengths of multiple unsupervised similarity measures. The key idea is that the strengths of a diverse set of similarity measures can complement each other and mitigate individual weaknesses, leading to improved performance. Preliminary results show that while Transformers-based CodeBERT and its variant GraphCodeBERT are undoubtedly the best option in the presence of abundant training data, in the case of specific small datasets (up to 500 samples), our ensemble achieves similar results, without prejudice to the interpretability of the resulting solution, and with a much lower associated carbon footprint due to training. The source code of this novel approach can be downloaded from https://github.com/jorge-martinez-gil/ensemble-codesim.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

Many tasks revolve around editing a document, whether code or text. We formulate the revision similarity problem to unify a wide range of machine learning evaluation problems whose goal is to assess a revision to an existing document. We observe that revisions usually change only a small portion of an existing document, so the existing document and its immediate revisions share a majority of their content. We formulate five adequacy criteria for revision similarity measures, designed to align them with human judgement. We show that popular pairwise measures, like BLEU, fail to meet these criteria, because their scores are dominated by the shared content. They report high similarity between two revisions when humans would assess them as quite different. This is a fundamental flaw we address. We propose a novel static measure, Excision Score (ES), which computes longest common subsequence (LCS) to remove content shared by an existing document with the ground truth and predicted revisions, before comparing only the remaining divergent regions. This is analogous to a surgeon creating a sterile field to focus on the work area. We use approximation to speed the standard cubic LCS computation to quadratic. In code-editing evaluation, where static measures are often used as a cheap proxy for passing tests, we demonstrate that ES surpasses existing measures. When aligned with test execution on HumanEvalFix, ES improves over its nearest competitor, SARI, by 12% Pearson correlation and by >21% over standard measures like BLEU. The key criterion is invariance to shared context; when we perturb HumanEvalFix with increased shared context, ES' improvement over SARI increases to 20% and >30% over standard measures. ES also handles other corner cases that other measures do not, such as correctly aligning moved code blocks, and appropriately rewarding matching insertions or deletions.

This paper presents a novel approach for similarity search with complex filtering capabilities on billion-scale datasets, optimized for CPU inference. Our method extends the classical IVF-Flat index structure to integrate multi-dimensional filters. The proposed algorithm combines dense embeddings with discrete filtering attributes, enabling fast retrieval in high-dimensional spaces. Designed specifically for CPU-based systems, our disk-based approach offers a cost-effective solution for large-scale similarity search. We demonstrate the effectiveness of our method through a case study, showcasing its potential for various practical uses.

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

Semantic similarity measures are widely used in natural language processing to catalyze various computer-related tasks. However, no single semantic similarity measure is the most appropriate for all tasks, and researchers often use ensemble strategies to ensure performance. This research work proposes a method for automatically designing semantic similarity ensembles. In fact, our proposed method uses grammatical evolution, for the first time, to automatically select and aggregate measures from a pool of candidates to create an ensemble that maximizes correlation to human judgment. The method is evaluated on several benchmark datasets and compared to state-of-the-art ensembles, showing that it can significantly improve similarity assessment accuracy and outperform existing methods in some cases. As a result, our research demonstrates the potential of using grammatical evolution to automatically compare text and prove the benefits of using ensembles for semantic similarity tasks. The source code that illustrates our approach can be downloaded from https://github.com/jorge-martinez-gil/sesige.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes intractable. We introduce FlowBoost, a closed-loop generative framework that learns to discover rare and extremal geometric structures by combining three components: (i) a geometry-aware conditional flow-matching model that learns to sample high-quality configurations, (ii) reward-guided policy optimization with action exploration that directly optimizes the generation process toward the objective while maintaining diversity, and (iii) stochastic local search for both training-data generation and final refinement. Unlike prior open-loop approaches, such as PatternBoost that retrains on filtered discrete samples, or AlphaEvolve which relies on frozen Large Language Models (LLMs) as evolutionary mutation operators, FlowBoost enforces geometric feasibility during sampling, and propagates reward signal directly into the generative model, closing the optimization loop and requiring much smaller training sets and shorter training times, and reducing the required outer-loop iterations by orders of magnitude, while eliminating dependence on LLMs. We demonstrate the framework on four geometric optimization problems: sphere packing in hypercubes, circle packing maximizing sum of radii, the Heilbronn triangle problem, and star discrepancy minimization. In several cases, FlowBoost discovers configurations that match or exceed the best known results. For circle packings, we improve the best known lower bounds, surpassing the LLM-based system AlphaEvolve while using substantially fewer computational resources.

This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity s_p and minimize the between-class similarity s_n. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed s_n and s_p into similarity pairs and seek to reduce (s_n-s_p). Such an optimization manner is inflexible, because the penalty strength on every single similarity score is restricted to be equal. Our intuition is that if a similarity score deviates far from the optimum, it should be emphasized. To this end, we simply re-weight each similarity to highlight the less-optimized similarity scores. It results in a Circle loss, which is named due to its circular decision boundary. The Circle loss has a unified formula for two elemental deep feature learning approaches, i.e. learning with class-level labels and pair-wise labels. Analytically, we show that the Circle loss offers a more flexible optimization approach towards a more definite convergence target, compared with the loss functions optimizing (s_n-s_p). Experimentally, we demonstrate the superiority of the Circle loss on a variety of deep feature learning tasks. On face recognition, person re-identification, as well as several fine-grained image retrieval datasets, the achieved performance is on par with the state of the art.

Competitive programming benchmarks are widely used in scenarios such as programming contests and large language model assessments. However, the growing presence of duplicate or highly similar problems raises concerns not only about competition fairness, but also about the validity of competitive programming as a benchmark for model evaluation. In this paper, we propose a new problem -- similar question retrieval -- to address this issue. Due to the lack of both data and models, solving this problem is challenging. To this end, we introduce CPRet, a retrieval-oriented benchmark suite for competitive programming, covering four retrieval tasks: two code-centric (i.e., Text-to-Code and Code-to-Code) and two newly proposed problem-centric tasks (i.e., Problem-to-Duplicate and Simplified-to-Full), built from a combination of automatically crawled problem-solution data and manually curated annotations. Our contribution includes both high-quality training data and temporally separated test sets for reliable evaluation. In addition, we develop two task-specialized retrievers based on this dataset: CPRetriever-Code, trained with a novel Group-InfoNCE loss for problem-code alignment, and CPRetriever-Prob, fine-tuned for identifying problem-level similarity. Both models achieve strong results and are open-sourced for local use. Finally, we analyze LiveCodeBench and find that high-similarity problems inflate model pass rates and reduce differentiation, underscoring the need for similarity-aware evaluation in future benchmarks. Code and data are available at: https://github.com/coldchair/CPRet

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.