fdyrd/QwenMath1.0-1.5B

Traning Configuration

epoch: 2.976
batch_size: 2
learning_rate: 0.00001
train_time: "0:10:11.05"
train_samples_per_second: 2.455
train_steps_per_second: 0.304
train_loss: 0.551
total_flos: "4998063GF"
dataset_size: 500

Validation Set Statistics

$(a:n)$ means accuracy and total number of problems.

Level	Algebra	Intermediate Algebra	Prealgebra	Precalculus	Number Theory	Geometry	Counting & Probability	Average
Level 1	0.681 : 135	0.404 : 52	0.535 : 86	0.263 : 57	0.7 : 30	0.368 : 38	0.538 : 39	0.499
Level 2	0.532 : 201	0.188 : 128	0.446 : 177	0.062 : 113	0.489 : 92	0.232 : 82	0.366 : 101	0.331
Level 3	0.41 : 261	0.072 : 195	0.455 : 224	0.0 : 127	0.41 : 122	0.127 : 102	0.34 : 100	0.259
Level 4	0.329 : 283	0.036 : 248	0.366 : 191	0.018 : 114	0.303 : 142	0.088 : 125	0.216 : 111	0.194
Level 5	0.156 : 307	0.007 : 280	0.202 : 193	0.0 : 135	0.188 : 154	0.008 : 132	0.065 : 123	0.089
Average	0.422	0.141	0.401	0.069	0.418	0.165	0.305	0.249

Test Set Statistics

[
  {
    "dataset": "MATH500",
    "url": "https://huggingface.co/datasets/qq8933/MATH500",
    "accuracy": 0.410
  },
  {
    "dataset": "GSM8K",
    "url": "https://huggingface.co/datasets/openai/gsm8k",
    "accuracy": 0.649
  }
]

Inference Examples

Basic Arithmetic

Q: Evaluate $1+2\times 3$. A: The expression $1+2\times 3$ means $1$ added to $2\times 3$. So, we have $ 1+2\times 3=1+2\cdot 3 =1+6=\boxed{7}$剌猬

Calculus

Q: compute $\int_{0}^{\pi}\sin{x}\cos{x}dx$. A: We use the double angle formula $\sin{2x} = 2\sin{x}\cos{x}$ to get $\int_{0}^{\pi}\sin{x}\cos{x}dx = \frac{1}{2}\int_{0}^{\pi}\sin{2x}dx$. We use the substitution $u = 2x$ to get $\frac{1}{2}\int_{0}^{\pi}\sin{2x}dx = \frac{1}{2}\int_{0}^{2\pi}\sin{u}du = \frac{1}{2}\left[-\cos{u}\right]{0}^{2\pi} = \frac{1}{2}\left(-\cos{2\pi} + \cos{0}\right) = \boxed{0}$. We can also use the identity $\sin{2x} = 2\sin{x}\cos{x}$ to get $\int{0}^{\pi}\sin{x}\cos{x}dx = \frac{1}{2}\int_{0}^{\pi}\sin{2x}dx = \frac{1}{2}\left[-\cos{2x}\right]_{0}^{\pi} = \frac{1}{2}\left(-\cos{2\pi} + \cos{0}\right) = \boxed{0}$.

Linear Algebra

Q: Find the determinant of the matrix $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$. A: The determinant of the matrix $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$ is $1\cdot 4 - 2\cdot 3 = \boxed{-2}$.