Behavioral thermodynamics: a LoRA behavior melts at 3.5× its RMS noise

This is a physics-flavoured robustness probe, not a container. Take a fine-tuned behavior,
add Gaussian noise to every LoRA tensor, and measure the order parameter: SST-2 accuracy on
400 rows.

Reproduce:

python research/thermodynamics.py   # -> research/results/thermodynamics.json

Setup

• Host: 4-bit Qwen3B.
• Behavior: SST-2 sentiment adapter.
• Noise: w + N(0, (σ · RMS)^2) on every LoRA A/B tensor, one seed per σ.
• Adapter RMS: 0.016192.
• Metric: label-token logit accuracy on 400 SST-2 test rows.

The curve

The half-gain noise (accuracy halfway between base 60.8% and adapter 94.5%) is
σ = 3.47 × RMS. Above that the behavior does not decay gracefully back to the base; it
falls to chance. The adapter's signal is replaced by noise, not by the original model.

What this looks like

• A plateau, then a cliff. From 0 to 2× RMS the behavior is essentially unchanged. At 3× it is damaged; at 5× it is gone.
• The collapse overshoots the base. At high noise SST-2 is ~50%, below the base 60.8%. The perturbation does not restore the base; it destroys the adapter's contribution and leaves a chance-level classifier.
• Quantization is far inside the plateau. The 8-bit and 4-bit adapters are exact on this task; their quantization noise is much smaller than the 3.5× RMS meltdown scale.
• This is a first-order-looking curve, but one adapter and one task are not enough to claim a universality class.

Caveats

• Gaussian weight noise is not quantization, pruning, or fine-tuning.
• One adapter, one task, 400 rows, one seed per σ, logit scoring.
• The adapter RMS is global; per-tensor noise scales could change the curve.
• No finite-size scaling or susceptibility measurement yet.

Next experiments

• Repeat on AG News, Dolly QA and the watermark trigger; does the meltdown scale track adapter RMS or task margins?
• Noise only A, only B, or rank-wise; which part of the LoRA carries the behavior?
• Measure the susceptibility (variance of the order parameter across noise seeds) near the transition.
• Compare with quantization: q4/q8 are at a much lower effective temperature; how much headroom is there before a 3-bit adapter melts?
• Test whether a behavioral vaccine raises the melting temperature.

The point is not that a LoRA is thermodynamic. The point is that "how much noise can this
behavior survive?" is a measurable curve, and the answer is not "linearly less accuracy per
bit."