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Neuron Populations Exhibit Divergent Selectivity with Scale
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Studies how cross-model Rosetta Neurons scale with model size in language (Pythia/GPT-2/OPT/Qwen2.5 up to 30B) and vision models, finding a sublinear power law, a neuron polarization effect, and domain specialization, explained by a capacity-allocation model.
Problem
Whether neuron populations shared across independently trained networks (Rosetta Neurons) evolve predictably with model scale, beyond macroscopic observables like loss, in terms of their count, selectivity, and specialization.
Approach
Treats cross-model mutual-nearest-neighbor neuron matches as a scaling observable; shows the count follows a sublinear power law, and explains it with a superposition capacity-allocation model (log utility, linear isolation budget) that predicts Rosetta neurons get more selective while the non-Rosetta tail stays polysemantic.
Key results
- Rosetta neuron counts follow sublinear power laws with exponents roughly 0.5-0.7 and R^2 around 0.99 across language (up to 30B) and vision (up to 5B) model families.
- Untrained networks and input-permuted null yield marginal (roughly 20-100) matches with no systematic scaling trend.
- JavaScript filtering with a single Rosetta neuron reaches 0.98 F1 and test PPL 3.02 vs 3.59 for random filtering and 3.01 for oracle.
Surprising findings
- Rosetta neurons occupy a shrinking fraction of total neurons as models grow, even though their absolute count increases.
- Under input permutation, Rosetta counts collapse to roughly 20-100 matches with no scaling trend.
Limitations
- Monosemanticity measured with modality-specific proxies (vocabulary kurtosis, VLM judge), so trends are relative population-level.
- Rosetta neurons capture only a subset of shared structure (circuits, heads, subspaces are excluded).
- Analytical model is phenomenological and not derived from gradient-based training dynamics.
Experimental setup
Datasets: The Pile ImageNet-1k (diffusion-generated images) CodeSearchNet
Benchmarks: CodeSearchNet JavaScript filtering
Metrics: power-law exponent R^2 mean excess kurtosis of vocabulary projections monosemantic fraction (VLM judge) F1 vs ground-truth JavaScript subset test perplexity
Baselines: untrained-network null input-permutation null non-Rosetta neurons
Builds on: Rosetta Neurons (Dravid et al., 2023) superposition (Elhage et al.) neural scaling laws logit lens / vocabulary projections
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