spb/modelmap Public License

1---2project: modelmap3document: Phase 1 notes — §4.5 Weight-space cartography (no forward pass required)4author: Simon-Pierre Boucher5contact: contact@spboucher.ai6website: https://modelmap.io7created: 2026-08-128status: draft9---1011# §4.5 — Weight-space cartography1213## A1. LASER — layer-selective rank reduction (SVD spectra as intervention targets)14- **Key paper:** Sharma, Ash, Misra, ICLR 2024, https://arxiv.org/abs/2312.13558 ; code https://github.com/pratyushasharma/laser15- **Claims:** Replacing individual weight matrices (esp. late-layer MLP down-projections) with low-rank truncations can *improve* QA accuracy up to 20–30 points.16- **Type:** Causal on behavior; correlational on interpretation ("noise in high components").17- **Cost:** SVD of 4096×11008 = seconds on M-series CPU (Accelerate/LAPACK); full per-matrix sweep of a 7B = CPU-minutes; behavioral validation is the expensive part (hours).18- **Failure modes:** task/matrix-specific gains; (layer, matrix, rank) sweep invites multiple-comparison illusions.19- **Epistemic status:** Established phenomenon; contested interpretation.2021## A2. Heavy-tailed spectral analysis / WeightWatcher — **closest prior art to the weight-only pre-screen hypothesis**22- **Key papers:** Martin & Mahoney 2019, https://arxiv.org/abs/1901.08278 ; Martin, Peng, Mahoney 2020 (Nature Comms 2021), https://arxiv.org/abs/2002.06716 ; tool: https://github.com/CalculatedContent/WeightWatcher (pip, pure CPU, **runs natively on Apple Silicon today**)23- **Claims:** Power-law exponents ("alpha") of per-matrix spectral densities predict relative test quality across model zoos **with zero data, zero forward passes**; per-layer alpha profiles diagnose over/under-training.24- **Cost:** cheapest technique surveyed — full 7B scan in minutes on any Mac.25- **Failure modes:** power-law fitting finicky (fit-range sensitivity); documented Simpson's-paradox failure (https://arxiv.org/abs/2106.00734); predicts trends, not absolute capability; **largely untested as a predictor of internal/activation-level structure — that's the modelmap gap.**26- **Epistemic status:** Established for accuracy-trend prediction; contested at fine granularity.2728## A3. Outlier channels, super weights, massive activations, attention sinks29- **Key papers:** LLM.int8 outliers: Dettmers et al. 2022, https://arxiv.org/abs/2208.07339 ; massive activations: Sun et al. 2024, https://arxiv.org/abs/2402.17762 ; sinks: Xiao et al. 2023, https://arxiv.org/abs/2309.17453 ; Gu et al. 2024, https://arxiv.org/abs/2410.10781 ; **super weights: Yu et al. (Apple) 2024, https://arxiv.org/abs/2411.07191** (https://machinelearning.apple.com/research/the-super-weight)30- **Weight-visible vs activation-only:** LLM.int8 outliers and massive activations are activation-level; **super weights are weight-visible** (extreme entries in specific matrices, typically early-layer `mlp.down_proj`) — a single scalar whose removal collapses perplexity by 3 orders of magnitude and which *induces* the massive activations. The crucial bridge from weight space to activation space.31- **Cost:** weight scan CPU-seconds; verification (zero one weight, measure PPL) minutes on a Mac at 7B 4-bit/MLX.32- **Epistemic status:** Established phenomena; causal story settled for super weights, active for sinks (2026: https://arxiv.org/html/2605.08504 ; survey https://arxiv.org/pdf/2604.10098).3334## A4. Cross-layer/cross-model similarity (CKA, SVCCA, Procrustes) and CKA's pathologies35- **Key papers:** CKA: Kornblith et al. 2019, https://arxiv.org/abs/1905.00414 ; SVCCA: https://arxiv.org/abs/1706.05806 ; **pathologies: Davari et al., ICLR 2023, https://arxiv.org/abs/2210.16156 ; Ding, Denain, Steinhardt 2021, https://arxiv.org/abs/2108.01661**36- **Substance:** CKA dominated by outlier directions, arbitrarily manipulable without functional change; CKA/CCA disagree and fail sanity checks. **Interacts badly with A3: LLM CKA scores can be dominated by sink dimensions unless removed.** Canonical CKA needs activations; weight-only analogues (Procrustes/subspace angles between weight matrices, 2026: https://arxiv.org/pdf/2601.10266) exist but are less validated.37- **Rule for modelmap:** report ≥2 similarity metrics + Ding-style statistical tests; strip outlier dims as a control.38- **Epistemic status:** Established tool, **debunked-in-part** as a standalone measure.3940## A5. Layer redundancy maps (similarity-guided depth pruning)41- **Key papers:** Gromov et al. 2024, https://arxiv.org/abs/2403.17887 ; ShortGPT: Men et al. 2024, https://arxiv.org/abs/2403.0385342- **Claims:** Angular similarity between layer input/output identifies deletable deep-layer blocks — an internal depth-redundancy map. Causal (delete-and-measure).43- **Note:** needs a small calibration set (minutes on Mac). **A candidate target that weight-only spectra (A2) might predict — explicit modelmap experiment.** Caveat: benchmark loss ≠ capability loss (deep-layer deletion selectively harms reasoning even when perplexity survives).4445## A6. Model stitching46- **Key papers:** Lenc & Vedaldi 2015, https://arxiv.org/abs/1411.5908 ; Bansal, Nakkiran, Barak 2021, https://arxiv.org/abs/2106.0768247- **Claims:** low stitching penalty = functionally interchangeable representations — stronger, task-grounded similarity than CKA. Quasi-causal.48- **Cost:** train stitching layers — hours per pair on Mac for small LLMs.49- **Failure modes:** stitcher capacity confounds (expressive stitcher "repairs" dissimilar reps); direction asymmetry. Mostly vision; LLM stitching thin.50- **Epistemic status:** Established in vision; under-explored for LLMs.5152## A7. Permutation alignment / Git Re-Basin53- **Key papers:** Ainsworth et al., ICLR 2023, https://arxiv.org/abs/2209.04836 ; REPAIR: https://arxiv.org/abs/2211.08403 ; Sinkhorn re-basin: https://arxiv.org/abs/2212.12042 ; 2024: https://arxiv.org/abs/2404.0649854- **Reality check:** **transformers align poorly** — permutation symmetry broken by residual streams, LayerNorm, head structure; unproven at 7B scale; moot for LLMs anyway (nobody retrains from different seeds). The useful LLM analogue is alignment across *sizes/families* — open (Q3 / Experiment G).55- **Epistemic status:** Established for MLPs/ResNets; contested/unproven for LLM transformers.5657## A8. Mode connectivity58- **Key papers:** Garipov et al. 2018, https://arxiv.org/abs/1802.10026 ; Frankle et al. 2019, https://arxiv.org/abs/1912.05671 ; Entezari conjecture 2021, https://arxiv.org/abs/2110.06296 ; mechanistic mode connectivity: Lubana et al. 2022, https://arxiv.org/abs/2211.0842259- **For modelmap:** the cheap artifact is the **base↔instruct linear interpolation loss/behavior profile** — weight lerp is free, evals are the cost. Loss connectivity ≠ mechanism connectivity.6061## A9. Task arithmetic / delta analysis62- **Key papers:** task vectors: Ilharco et al., ICLR 2023, https://arxiv.org/abs/2212.04089 (code https://github.com/mlfoundations/task_vectors — device-agnostic state-dict math) ; TIES: https://arxiv.org/abs/2306.01708 ; DARE: https://arxiv.org/abs/2311.03099 (90%+ of delta entries droppable)63- **Claims:** θ_ft − θ_base is a manipulable task vector; deltas are highly sparse/redundant. Causal (weight edit → behavior).64- **Cost:** weight arithmetic free; fully Mac-feasible 7–14B.65- **⚑ Gap:** **delta maps (base vs instruct: per-matrix delta norms, delta effective rank, delta spectra) have no published systematic atlas — an ideal cheap modelmap artifact.**6667## A10. Model diffing via crosscoders — and 2025 weight-first convergence68- **Key papers:** Anthropic crosscoders 2024, https://transformer-circuits.pub/2024/crosscoders/index.html ; sparsity artifacts fix: Minder et al. 2025, https://arxiv.org/abs/2504.02922 ; narrow-finetuning traces: https://arxiv.org/abs/2510.13900 ; cross-architecture (2026): https://arxiv.org/pdf/2602.11729 ; post-mortem: https://www.lesswrong.com/posts/xmpauEXEerzYcJKNm/69- **Cost:** heavy (paired activation capture + SAE-style training). Mac: ≤2B pairs feasible with MLX + streamed stores; 7B pairs at the edge of 64 GB (Experiment H territory).70- **Weight-side complements (2025) — direct evidence the field converges on modelmap's weight-first thesis:** *Watch the Weights* https://arxiv.org/pdf/2508.00161 (monitoring fine-tunes from weight diffs alone); *Learning to Interpret Weight Differences* https://arxiv.org/html/2510.05092v4 ; *Steering LMs with Weight Arithmetic* https://www.alignmentforum.org/posts/HYTbakdHpxfaCowYp/71- **Epistemic status:** Promising but contested; methodology moving.7273## A11. MoE router / expert structure74- **Key papers:** Mixtral: https://arxiv.org/abs/2401.04088 (routing more syntactic/positional than semantic) ; DeepSeekMoE: https://arxiv.org/abs/2401.06066 ; *Myth of Expert Specialization* (2026): https://arxiv.org/html/2604.09780v175- **Substance:** router weights are weight-only artifacts (expert similarity, router row norms: CPU-minutes); "expert = topic" readings largely debunked; load-balancing losses confound structure. Structure-of-routers is an open, cheap mapping target. Mixtral 8x7B strains 64 GB except 4-bit.7677## A12. Weight-space learning (weights as data) — and the pre-screen novelty check78- **Key sources:** Unterthiner et al. 2020, https://arxiv.org/abs/2002.11448 ; Eilertsen et al. 2020, https://arxiv.org/abs/2002.05688 ; Schürholt hyper-representations: https://kschuerholt.github.io/publications/ ; **ICLR 2025 Workshop on Weight Space Learning: https://weight-space-learning.github.io/** ; WeightCLIP (2026): https://arxiv.org/html/2607.03551v179- **Claims:** model properties predictable from raw weights; but almost all results on tiny CNNs/ViTs — the LLM regime (few, huge models) breaks the model-zoo assumption.8081## ⚑ Novelty check for the core hypothesis (weight-only maps → activation-level properties)82Partially anticipated but **not occupied**: WeightWatcher predicts behavioral quality (not internal structure); Super Weight links one weight-visible phenomenon to activations; Watch-the-Weights monitors fine-tuning; weight-space learning predicts global properties; LASER flags behaviorally-loaded components; QK/OV composition scores (Elhage et al. 2021 framework) are weight-only circuit hints. **Missing and open after aggressive 2025–2026 search: a systematic study of weight-only statistics predicting probe accuracy, localization, quantization drift, or working sets on the same model.** This is Experiment E's claim to novelty.83