$$
Y_{\text{mod}}(t) = A \cdot \ln(t+1) \cdot \frac{a+1}{b+0.5} \cdot e^{-r_{\text{eff}}(t) \cdot t} + C
$$
$$
r_{\text{eff}}(x) =
\begin{cases}
0.01 + 0.000625x & x < 8 \
0.015 & 8 \le x \le 18 \
0.015 + 0.0005(x - 18) & x > 18
\end{cases}
$$
t: Varies from 6h to 24h, representing the basic memory status in the gradient.
a (pick_a): Tracks how many times a memory item has been selected.
b (raised_b): Tracks how many times a memory item has been picked as the final answer.
r_eff(t): A piecewise time-dependent decay rate (learning rate) controlling the forgetting speed.
A, C: Bias terms.
-
Our models are trained using supervised learning to find the closest answer to the next token, so they are more like group B in the graph. However, when we use compare samples to raise the answer dimension, we observe something interesting: different answers appear, and a group of answers clusters around the mean closeness distance line. Many times, we feel that AI is not smart enough and doesn't give us the answer we want because the answers only focus on the surface meaning of the requirement. This is not wrong, because our engineers train them to find the shortest distance to the correct token. However, human-like intelligence is not that simple. We use association in our daily decisions — a combination of common sense, experience, and logic that is not explicitly spoken but exists in our minds.
-
We are not guessing the answers. Even if the LLM makes a mistake once or twice, with the mean Euclidean distance, we always find the correct answer group from the parallel sample universe. As seen in the graph below, when the mean_line_ratio changes, the selected answer varies, but the correct answer group always leads.
-
And comapre samples are different from DFS, they are parallel to each other, as parallel space.
-
Therefore, we find that difficult questions like those in the GPQA benchmark, scientific problems, and the TurtleBench dataset all share something in common: they contain hidden facts not explicitly stated in the question itself, requiring judgment and discovery. For such questions, the correct answer may not be the closest to the question or may be far from the original question. The correct answer requires some association and lies around the mean closeness score.
-
You can use the tools below to find the best mean_line_ratio for individual tests and general use:
-
Obviously, the mean closeness score differs across models and also varies between normal questions and scientific questions. The parameters we use in this project for the GPQA benchmark are in config_adjust.json.
-
Here, mean_line_ratio shifts the mean closeness score up or down to fit different models' answer groups. This parameter should be adjusted based on the behavior of different models and the difficulty of the problems; it is only stable statistically. The temperature is for answer generation with DeepSeek-V3.2-thinking, and temperature_compare is for sample generation with Ernie 4.5. This combination of model APIs considers the ability for different tasks and token pricing.
-
We also add zero-padding techniques and diagonal matrices as commonly used. Contact us for details.
-
We achieve about 1–2% improvement for this part in our final benchmark score.
This repository and the model weights are licensed under the MIT License.