simpo-implementation

name	simpo-implementation
description	Guidelines for implementing the SimPO loss function as per the SimPO paper.

SimPO Loss Implementation

The SimPO loss is designed to optimize language models by maximizing the gap between positive and negative response log-probabilities, normalized by the length of the response.

Mathematical Formulation

The SimPO loss $L_{SimPO}$ is defined as: $L_{SimPO} = -\mathbb{E}{(x, y_w, y_l) \sim D} \left[ \log \sigma \left( \beta \left( \frac{1}{|y_w|} \log \pi\theta(y_w|x) - \frac{1}{|y_l|} \log \pi_\theta(y_l|x) - \gamma \right) \right) \right]$

Where:

• $y_w$ is the winning response.
• $y_l$ is the losing response.
• $\beta$ is the reward margin scale.
• $\gamma$ is the reward margin threshold.
• $\pi_\theta(y|x)$ is the model's likelihood for sequence $y$ given $x$.

Implementation Steps

1. Calculate Log Probabilities: Use the model to compute the log-likelihood of tokens in $y_w$ and $y_l$.
2. Sum Log Probabilities: Sum the log-likelihoods over the generated sequence.
3. Normalize: Divide the sum by the sequence length (or use a length-normalized log-prob implementation).
4. Compute Margin: Calculate the difference between normalized log-probs of $y_w$ and $y_l$, then subtract $\gamma$.
5. Apply Sigmoid and Log: Apply the sigmoid function to $\beta \times \text{margin}$, take the negative log, and compute the mean over the batch.