Ported multi-token prediction from modded-nanogpt. Instead of predicting just the next token, predict the next n tokens at each position with weighted loss.
### Implementation
- Instead of calling the loss `n_predict` times, uses a fancy batched computation using `unfold` + `gather` + cross-entropy decomposition (`CE = logsumexp - logits[target]`)
- Schedule anneals from 3-token to 1-token prediction:
**Conclusion:** Negative result for nanochat. The extra memory and compute overhead from predicting multiple tokens doesn't pay off, in fact the results get worse. The auxiliary loss signal may help in other settings (larger models, different architectures?), but for our setup it's pure overhead at the moment.
- New `--window_pattern` CLI arg and `GPTConfig.window_pattern` field
- Pattern is tiled across layers (e.g., `SSSL` for 20 layers → `SSSLSSSLSSSLSSSLSSSL`)
- Final layer always forced to L (full context) regardless of pattern
- Short window = `sequence_len // 2`
- Long window = `sequence_len` (full context)
- All previous models so far have been simply `L` and checkpoint loading is modified accordingly to fill in this param for old models, see `_patch_missing_config_keys`
Quick experiments showed `SSSL` (every 4th layer is long) works well - provides a good balance between compute savings and model quality. This is now the default.
- **~9% improvement in tok/sec** during training out of the box
- Benchmarks showed FA3 is 2x faster than FA2 at realistic training sizes (batch=32, seq=2048)
- FA3 supports sliding window via `window_size=(left, 0)`, which is huge and expected to give further improvements. This is ready to tune but keeping full context for now.
- Optimal LR varies by depth; default of 0.5 is reasonable, but 0.6 is better for d12
- Adding resid_lambdas (with 0.01x LR) gives small additional improvement over x0 alone
### Meta Device Footgun
Important lesson: `__init__` runs in meta device context, so any tensor values set there are fake. Must initialize actual values in `init_weights()`. Added docstring warning to `__init__`.
### Summary
Added `--scalar_lr` (default 0.5) controlling learnable per-layer scalars. The formula `x = resid_lambdas[i] * x + x0_lambdas[i] * x0` gives the model control over residual scaling and direct shortcuts to the initial embedding. Solid improvement with essentially no compute overhead.
Cherry-picked improvements from NorMuon (modded-nanogpt) into our simpler Muon implementation. Decided against using NorMuon directly due to hard-coded architecture assumptions (expects 32 params split 10 attn + 22 mlp), parameter labeling requirements, and complexity.
### Changes Made
**1. Polar Express Orthogonalization**
- Replaced Newton-Schulz iteration with "Polar Express Sign Method" from [arxiv.org/pdf/2505.16932](https://arxiv.org/pdf/2505.16932)
- Uses 5 different coefficient tuples (one per iteration) instead of fixed coefficients
- Both methods kept in code for easy comparison (`zeropower_via_polar_express` vs `zeropower_via_newtonschulz5`)
- **Result:** No dramatic/noticeable difference in training, but keeping the new Polar Express as default.
**2. Variance Reduction (NorMuon-style)**
- Added low-rank variance estimator similar to Adafactor ([arxiv.org/pdf/2510.05491](https://arxiv.org/pdf/2510.05491))
- Maintains `second_momentum_buffer` with shape `[rows, 1]` or `[1, cols]` (whichever is smaller)
- Normalizes updates based on running per-row/col variance estimate (beta2=0.95)
- Memory overhead: ~1/max(rows, cols) per param, negligible
- **Result:** Led to a very small improvement, kept and enabled by default.
**3. Cautious Weight Decay**
- Only decays weights where `update * weight >= 0` (same sign) from [arxiv.org/abs/2411.16085](https://arxiv.org/abs/2411.16085)
- Standard WD always pulls toward zero; cautious WD skips decay when gradient is pushing weight away from zero
- **Implementation note:** Had to inline the logic rather than use a separate `@torch.compile` function. Passing changing float values (like `weight_decay` during scheduling) as function arguments triggers recompilation. Reading from `group["weight_decay"]` inside the step avoids this.
- **Result:** Solid improvements, especially the cautious version was better than standard wd.
- Now defaults to ON for Muon via the `weight_decay` param. AdamW still has no weight decay and is hardcoded to 0 weight decay, might try to re-tune this later.
**4. Weight decay schedule**
- Added a linear schedule to weight decay that is default on from 1.0 to 0.0 (i.e. start with max weight decay in the beginning of training, them ramp to 0 by the end). Worked better than a static setting in experiments. (modded-nanogpt has the same schedule but it is imlpemented in a more confusing way by multiplying twice by the learning rate, which is already wired up to a decay schedule).
### Weight Decay Scaling Experiments
Swept weight decay values at d8, d12, d16, d20 to find optimal values and scaling law.
**Optimal Values Found:**
| Depth | Width (channels) | Optimal WD |
|-------|------------------|------------|
| d8 | 512 | ~0.40 |
| d12 | 768 | ~0.22 |
| d16 | 1024 | ~0.10 |
| d20 | 1280 | ~0.08 |
**Scaling Law:**
- Fit power law: `WD = k / channels^α` in log-log space
- Found α ≈ 1.97 (approximately 2), meaning WD ∝ 1/width²
Example: If d12 optimal is 0.22, then d20 optimal ≈ 0.22 × (12/20)² ≈ 0.08
**Reference:** Moonlight paper uses fixed WD=0.1 for their 15B MoE model. Our experiments indicated a scaling law where the optimal WD changed with depth, so we go along with the empirical scaling law.
### Summary
Muon was changed to use Polar Express, added Adafactor-style variance reduction, and cautious weight decay with schedule that ramps linearly to zero. All of these changes follow modded-nanogpt repo, but all of them were also validated piece by piece to yield improvements in nanochat with the exception of the Polar Express change which was in the noise. This is default on and configurable with `--weight_decay`, using simply 0.2 and ∝ 1/width² scaling. The kwarg `--weight_decay` is therefore changing as of this change. It used to configure AdamW via standard weight decay and now it becomes exclusively used in Muon (AdamW is hardcoded to 0.0), and it is scaled based on depth.
**Hypothesis:** Gradient clipping may be unnecessary overhead. Tested L2 norm clipping at various thresholds (0.25, 0.5, 1.0, 2.0) and elementwise clipping.
**Results:**
- No benefit at any scale tested (d12, d20)
- All variants within noise (~0.9827 val_bpb)
- Grad norm never exceeds 1.0 naturally, so clipping is always inactive
- Clipping adds ~2% time overhead from the all-reduce
**Bug Found:** Original implementation clipped local gradients before sync. Since this codebase doesn't use DDP (gradient sync is in the optimizers), each rank was clipping based on its own local norm. Fixed on the branch with proper distributed all-reduce.
**Observartion:** modded-nanogpt does not appear to clip either right now.
**Summary:** Deleted all grad-clip code paths. The code naturally produces well-behaved gradients. This improves a bit of MFU because we don't have to calculate and sync grad norms.
