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README.md

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+# SAT Retrofit Experiment: Can AR Models Be Forced to Output Multiple Tokens?
+
+## TL;DR
+**No.** Autoregressive (AR) models cannot be "snapped" to Semi-Autoregressive (SAT) inference. The hidden states only encode single next-token prediction. Joint AR+SAT training from scratch is required.
+
+## Key Results
+
+### Speed
+| Method | Tokens/sec | Speedup |
+|--------|-----------|---------|
+| AR (baseline) | 75.6 | 1.0x |
+| Forced SAT (block=2) | 149.9 | **1.98x** |
+
+### Quality (Perplexity - lower is better)
+| Prompt | AR | Forced SAT | Degradation |
+|--------|-----|------------|-------------|
+| "The quick brown fox" | 16.2 | 424.0 | **26x worse** |
+| "In the beginning" | 7.4 | 69.0 | **9x worse** |
+| "Once upon a time" | 8.9 | 56.5 | **6x worse** |
+| "The scientist discovered" | 10.8 | 296.8 | **27x worse** |
+| "Machine learning is" | 7.7 | 133.6 | **17x worse** |
+
+### Example Outputs
+
+**Prompt:** "The scientist discovered that"
+
+- **AR (good):** "the bacteria were able to grow in the air, and that they could also grow in the water."
+- **Forced SAT (broken):** "the thatched bacteria were roofing able to offload growling the bacteria spores into into the the"
+
+## Why It Fails
+
+AR model hidden states at position N only encode "what is token N+1" - singular. There is no representation for "what are tokens N+1 AND N+2 simultaneously."
+
+When you force 2-token output:
+- Token 1: Predicted from position -1 (correct context) ✓
+- Token 2: Predicted from position -2 (STALE context, one step behind) ✗
+
+This creates alternating reasonable/wrong tokens as the model answers questions about outdated context.
+
+## The Solution: Joint AR+SAT Training
+
+Train the model on BOTH objectives from initialization:
+- AR loss: predict next token
+- SAT loss: predict next N tokens simultaneously
+
+This forces the model to build representations that encode multiple future tokens from each position, enabling both inference modes.
+
+See: [AGILLM-3](https://huggingface.co/OpenTransformer/AGILLM-3-large) for a working implementation.
+
+## Reproducing
+
+```bash
+pip install torch transformers
+python sat_test.py
+```
+
+## Citation
+
+If you use this finding, please cite:
+```
+@misc{sat_retrofit_2026,
+  author = {Scott Bisset},
+  title = {AR Models Cannot Be Retrofitted for SAT Inference},
+  year = {2026},
+  publisher = {OpenTransformers Ltd}
+}
+```
+
+## License
+MIT