loss-functions
Complete guide to SimPO loss functions and mathematical formulations.
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Content
# Loss Functions
Complete guide to SimPO loss functions and mathematical formulations.
## Overview
SimPO supports two loss types:
- **Sigmoid** (default) - Smooth, differentiable loss
- **Hinge** - Margin-based, sparse loss
Both are reference-free (no reference model needed).
## SimPO Loss Formula
### Core Calculation
**Step 1: Log probability ratio**:
```
pi_logratios = log P_θ(y_chosen|x) - log P_θ(y_rejected|x)
```
**Step 2: Apply target margin**:
```
logits = pi_logratios - γ/β
```
Where:
- γ/β = `gamma_beta_ratio` (target margin)
**Step 3: Compute loss** (depends on loss type)
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