---
project: modelmap
document: Phase 1 notes — §4.7 Cross-model and cross-scale comparison
author: Simon-Pierre Boucher
contact: contact@spboucher.ai
website: https://modelmap.io
created: 2026-08-12
status: draft
---

# §4.7 — Cross-model and cross-scale comparison

## A1. CKA / SVCCA / RSA as similarity metrics for LLMs
- **Key papers:** SVCCA: https://arxiv.org/abs/1706.05806 ; CKA: https://arxiv.org/abs/1905.00414 ; survey: Klabunde et al. 2023 (rev. 2025), https://arxiv.org/abs/2305.06329 ; **ReSi benchmark (24 measures, ICLR 2025): https://arxiv.org/abs/2408.00531** ; LLM-specific: https://arxiv.org/abs/2312.02730
- **Pathologies:** outlier-direction sensitivity (Davari et al., https://arxiv.org/abs/2210.16156); score saturation for LLM pairs (most non-Llama pairs >0.8); naive estimator drifts to 1 as feature/sample ratio grows → false alignment discoveries. ReSi: different measures rank model pairs inconsistently — **metric choice is itself a confounder, must be part of provenance.**
- **Cost:** cheap (minibatch-CKA on cached activations, NumPy/Accelerate/MLX). Fully feasible 0.5B–14B.
- **Epistemic status:** Established tool; **contested as evidence** — every convergence claim needs baseline calibration (A6).

## A2. Universal neurons across seeds (Gurnee et al.)
- **Key papers:** https://arxiv.org/abs/2401.12181 (2024); follow-up with ablation-based functional impact (2025): https://arxiv.org/abs/2508.00903
- **Claims:** only **1–5% of MLP neurons are universal** across independently seeded GPT-2 runs (activation correlation over 100M tokens); these are disproportionately interpretable (unigram, alphabet, position, entropy-regulation families). Negative half: ~95% of neurons are seed-specific — single-neuron catalogs are mostly noise.
- **Methodology template for modelmap:** correlation-over-corpus → taxonomize → ablate.
- **Cost:** paired capture over ~10⁸ tokens — heavy but streamable; feasible ≤1B pairs on 32–64 GB with disk-backed store (expH regime).
- **Epistemic status:** Established (replicated, causally confirmed).

## A3. Universality of induction heads
- **Key papers:** Olsson et al. 2022, https://arxiv.org/abs/2209.11895 ; ICL essentiality: https://arxiv.org/abs/2407.07011 ; cross-architecture (Transformer vs Mamba): https://arxiv.org/abs/2410.06672 ; https://arxiv.org/abs/2411.07071
- **Substance:** strongest known case of circuit universality — appears in essentially every transformer LM, and analogues in Mamba. **A natural "known landmark" for calibrating any cross-model coordinate system: if an alignment method can't match induction heads across two models, it fails the sanity check.**
- **Cost:** cheap — one forward pass with attention capture; feasible to 32B quantized via MLX.
- **Epistemic status:** Established (multi-team, cross-architecture).

## A4. Cross-scale circuit evolution
- **Key papers:** Lieberum et al. 2023 (Chinchilla 70B), https://arxiv.org/abs/2307.09458 ; **Tigges et al. 2024 (Pythia 70M–2.8B across checkpoints): https://arxiv.org/abs/2407.10827**
- **Substance:** circuit-analysis methods scale to 70B but head-level semantics get muddier; task circuits emerge at consistent token budgets and algorithms stay roughly stable while component identities drift — supports longitudinal/cross-scale maps (Experiment G). The Tigges regime (70M–2.8B, full patching) is comfortably Mac-feasible — **the right scale band for expG**.
- **Epistemic status:** Established small-scale; partially established at 70B.

## A5. Feature universality via SAEs; universal SAEs; crosscoder diffing
- **Key papers:** Lan et al. 2024/2025, https://arxiv.org/abs/2410.06981 ; universal SAEs: Thasarathan et al. 2025, https://arxiv.org/abs/2502.03714 ; Anthropic model diffing: https://transformer-circuits.pub/2024/model-diffing/index.html , https://transformer-circuits.pub/2025/crosscoder-diffing-update/index.html ; sparsity artifacts: Minder et al. 2025, https://arxiv.org/abs/2504.02922 ; open replication: https://www.lesswrong.com/posts/srt6JXsRMtmqAJavD/
- **Substance:** moderate feature-space overlap across families, strongest mid-layers and concrete concepts. **Caveat chain:** SAE features are seed-unstable (~30% overlap — see §4.8); crosscoder "model-exclusive" latents partly sparsity artifacts. Any cross-model feature atlas must control for both.
- **Cost:** SAE training is the expensive item (10⁸–10⁹ activations/layer); ≤3B feasible; crosscoders double storage. SAELens MPS throughput unbenchmarked — genuine expH deliverable.
- **Epistemic status:** Contested/emerging — real signal, magnitude method- and seed-dependent.

## A6. Platonic Representation Hypothesis and its deflation
- **Key papers:** Huh et al., ICML 2024, https://arxiv.org/abs/2405.07987 ; linear-net proof: https://arxiv.org/abs/2507.01098 ; **Aristotelian critique (2026): https://arxiv.org/abs/2602.14486** ; causes/consequences: https://arxiv.org/abs/2505.13899
- **The load-bearing negative result:** after calibrating for width/depth confounders, **global convergence metrics largely evaporate** (partly a look-elsewhere effect from reporting max similarity over many layer pairs). What survives is **local neighborhood/topological alignment**.
- **Practical rule for the atlas:** cross-model claims use calibrated, local metrics with null baselines from random/width-matched models.
- **Epistemic status:** Contested; global-metric version **debunked-in-part (2026)**; local version live.

## A7. Model stitching as functional similarity
- **Key papers:** Bansal et al. 2021, https://arxiv.org/abs/2106.07682 ; https://arxiv.org/abs/2303.11277 ; **"How Not to Stitch" (2024): https://arxiv.org/abs/2412.11299** ; relative representations line: https://arxiv.org/abs/2406.11014
- **Substance:** low CKA can stitch perfectly and vice versa; results depend heavily on connector expressivity/protocol (affine stitch can "succeed" by relearning); LLM pairs collide with tokenizer mismatch (A9).
- **Epistemic status:** Established as probe; contested as measure.

## A8. Rosetta Neurons (vision precedent)
- **Key paper:** Dravid et al., ICCV 2023, https://arxiv.org/abs/2306.09346 (code https://github.com/yossigandelsman/rosetta_neurons)
- **Substance:** activation-correlation mining finds shared-concept units across 8 heterogeneous vision models without supervision. The matching algorithm (normalized cross-correlation over a shared stimulus set) **transfers directly to LLMs with a shared prompt corpus — a concrete candidate for modelmap's cross-model coordinate system. Untested at LLM scale (gap).**

## A9. Tokenizer effects on comparability
- **Key papers:** TokSuite (2025, models identical except tokenizer): https://arxiv.org/pdf/2512.20757 ; cross-tokenizer distillation: https://arxiv.org/abs/2503.20083 ; tokenisation NP-complete: https://arxiv.org/abs/2412.15210
- **Substance:** **no standard solution** for aligning activations across tokenizers; workarounds (shared-substring boundaries, word/byte pooling, prompt-level mean pooling) each destroy information. **Rule: within-family cross-scale comparison (shared tokenizer) is the safe default; cross-family maps must document the alignment convention in the map schema.**
- **Epistemic status:** Established confound; unsolved methodology (gap).

## A10. Quantization effects on internal representations — **the thin shelf (project bet confirmed)**
As of 2026-08-12 this literature is **~5 papers, recent, shallow** — no systematic multi-technique internal atlas across quantization levels:
- *Interpreting the Effects of Quantization on LLMs* (IJCNLP-AACL 2025): https://arxiv.org/abs/2508.16785 — 4/8-bit vs FP16; breadth-first, small depth.
- *Through a Compressed Lens* (2025): https://arxiv.org/abs/2505.13963 — GPTQ/AWQ on Qwen2.5 7B–72B; effects **inconsistent in direction**, dependent on method × technique × protocol.
- *How Quantization Changes Interpretable Features: An SAE Analysis* (2026): https://arxiv.org/html/2606.03002v1 — first SAE-feature-drift-under-quantization study; **closest existing work to expF**; single-method, worth replicating and extending.
- *The Illusion of Equivalency* (2026): https://arxiv.org/pdf/2607.08734 — benchmark-equivalence masks internal distributional divergence.
- Behavioral-only adjacent: long-context degradation https://arxiv.org/pdf/2505.20276

**Verified absent:** probe-drift-across-Q-levels with controls; circuit survival under quantization; Q2/Q3 extreme-quantization internals; GGUF/llama.cpp-runtime introspection; weight-geometry-predicts-quantization-sensitivity. **expF sits in genuinely open territory — and quantized models are precisely what runs on the target hardware.** MLX ships 4/8-bit natively; FP16/Q8/Q4 triplets fit sequentially in 32–64 GB up to ~14B.
- **Epistemic status:** Emerging; the field's own words ("inconsistent", "illusion of equivalency") mark it unsettled.