Negative squaring – pre-tilted 3-bit quantization beat naive 4-bit

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GitHub - elpinyeknom/negative-squaring-: Pre-tilting weights before quantization to preserve reasoning — toy experiments · GitHub

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2_gradient_attempt.py

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3_final_with_clipping.py

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Negative Squaring — Toy Experiments

Code accompanying the writeup "Negative Squaring: Pre-Tilting Weights to<br>Preserve Reasoning in Quantized Models" (July 2026). See<br>negative-squaring-paper_1.md in this repository for the full plain-language paper.

The idea in one line

Before quantizing a model, tilt each weight against the error the rounding<br>will cause across the model's whole multi-step reasoning trajectory — clipped<br>to half a quantization step, so the tilt only decides which way borderline<br>weights round.

What's here

File<br>What it does<br>Key result

1_first_experiment.py<br>Random-search pre-tilt vs naive 4-bit quantization on a 12-layer, 30-step recurrent toy network<br>~18% trajectory error removed; decision flips 14/20 → 8/20

2_gradient_attempt.py<br>Straight-through gradient search, unconstrained<br>Backfires — test error gets worse (documented negative result)

3_final_with_clipping.py<br>Gradient + random + combo searches, with tilts clipped to half a quantization step<br>77% error removed; decision flips 20/50 → 4-5/50

Run it

Requires only Python 3 and numpy:

pip install numpy<br>python 3_final_with_clipping.py

Each script is self-contained, seeded, and reproduces the numbers in the<br>writeup. Runtime is seconds to a few minutes on any laptop. To reproduce the 3-bit and 2-bit cliff results, change BITS = 4 to 3 or 2 on line 4 of script 3.

Honest limitations

Toy scale: ~49k weights, tanh recurrence, not a transformer.

The toy's dynamics dampen errors; real LLMs often amplify them. Untested there.

Full-trajectory backprop is expensive at real scale; the clipping constraint<br>shrinks the search space (only near-boundary weights matter) but efficient<br>scaling is unsolved.

Open invitation

If you have compute and want to try trajectory-aware rounding on a real<br>sub-1B model, or you know prior literature that already does this<br>(AdaRound optimizes rounding decisions per-layer; we're looking for<br>whole-trajectory versions), please reach out in the thread or open an<br>issue here.

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Pre-tilting weights before quantization to preserve reasoning — toy experiments

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