TL;DR — The current paper centers on first-divergence factorial diffing. At the first shared-history token where a pretrained checkpoint and its post-trained descendant prefer different next tokens, we cross upstream residual state with downstream late stack and measure the divergent-token margin. Across six dense PT/IT pairs, including Qwen2.5-32B, late-stack effects are much larger from IT-shaped upstream state than from PT-shaped upstream state. The factual/reasoning stress test shows why one-cell late-only patching can mislead, while convergence-gap curves, matched-prefix graft/swap, MLP write-out, natural-rollout residual-opposition checks, and behavior remain supporting context rather than the headline.
Figure 1. Current paper headline: upstream-state x late-stack interaction at first-divergence prefixes. The inference target is the interaction on the IT-vs-PT divergent-token margin, conditional on the six released dense PT/IT checkpoint pairs.
If you are new to the repo, these are the most useful entrypoints:
- docs/EXPERIMENT_REGISTRY.md: canonical experiment map and path conventions
- scripts/README.md: grouped script layout and common commands
uv run python scripts/infra/repo_doctor.py: lightweight repo health check- paper_draft/PAPER_DRAFT_v25.md: current paper framing, including the reproducibility and artifact map
- paper_draft/PAPER_DRAFT_v25.pdf: rendered PDF of the current draft
The repo has been reorganized into descriptive canonical paths:
- experiment code:
src/poc/exp##_descriptive_name/ - results:
results/exp##_descriptive_name/ - scripts:
scripts/run/,scripts/plot/,scripts/analysis/,scripts/infra/, etc.
A few flat script aliases are still kept where practical, but results now live only under the descriptive canonical paths.
For review and public release, paper-facing summaries and plots are committed under results/, including JSON/CSV/MD tables, bootstrap intervals, human-evaluation summaries, and final figures for the main claims. Reviewers can mechanically check the headline numbers with bash scripts/reproduce/reproduce_claims_from_summaries.sh; raw or cached shard validation is routed through bash scripts/reproduce/reproduce_minimal.sh. Large regenerated intermediates such as raw activation arrays, model/probe tensors, tuned-lens checkpoints, and multi-gigabyte raw per-token traces stay out of git, with scripts, prompt datasets, archive pointers, and the reproducibility guide in REPRODUCIBILITY.md.
The current paper-facing story is best understood in three layers:
| Layer | Best current claim | Main evidence |
|---|---|---|
| Primary estimand | Late-stack effects are non-additive with upstream residual state at first PT/IT disagreement | exp23 residual-state x late-stack factorial + label-swap null |
| Supporting decomposition | Middle-positioned substitutions transfer token identity more often; late-positioned substitutions affect margin/readout more | exp20 first-divergence identity/margin + exp21 MLP write-out |
| Layerwise context | IT checkpoints show delayed stabilization, motivating late-window interventions | exp09, exp11, exp14, exp16, exp19, exp22 |
What is strongest right now:
- first-divergence 2x2 interaction: Dense-6 family-balanced interaction
+2.44logits, positive in every family and+1.71without Gemma - label-swap null and prompt/position/domain stratifications showing that the interaction is PT/IT-label aligned and not only an immediate-token artifact
- content/reasoning extension where the interaction remains positive while the PT-upstream late-only term flips negative, strengthening the "conditional, not portable" interpretation
- external and staged checks: Qwen2.5-32B is included as the sixth dense core pair, and an OLMo-2 Base/SFT/DPO/Instruct case study shows positive local transition interactions with the strongest adjacent signal at Base→SFT
- identity/margin decomposition: middle-positioned windows transfer token identity more often, while late-positioned windows supply stronger margin/readout pressure
- delayed-stabilization, matched random late-MLP controls, and Exp27 natural-rollout residual-opposition ablations as auxiliary layerwise/geometric context
What remains intentionally careful:
- the main first-divergence factorial synthesis pools six dense PT/IT pairs; Dense-5 rows are support analyses where Qwen2.5-32B was not rerun, and DeepSeek-V2-Lite is an MoE side case only
- first-divergence prefixes are selected natural disagreement events, strongest in early response formation, not random token positions
- causal language refers to measured effects in constructed hybrid forward passes, not complete natural-model circuit recovery
KL(layer || own final)is useful layerwise context but endpoint-relative and no longer the headline causal claim
Figure 2. Supporting matched-prefix graft/swap context. These older paper-facing plots localize late-window leverage on delayed stabilization; the current headline result is the first-divergence factorial above.
git clone <repo> && cd structral-semantic-features
uv syncuv run python scripts/infra/repo_doctor.pyOptional:
uv run python scripts/infra/repo_doctor.py --pytest# Canonical exp14 matched-prefix causal runner
uv run python -m src.poc.exp14_symmetric_matched_prefix_causality --help
# Canonical exp16 matched-prefix native-JS replay runner
uv run python -m src.poc.exp16_matched_prefix_js_gap --help
# Canonical exp15 free-running behavioral runner
uv run python -m src.poc.exp15_symmetric_behavioral_causality --help
# Local smoke for the exp13+14 causal stack
bash scripts/run/run_exp13_exp14_local.sh --mode smoke --model gemma3_4b --smoke-prompts 8# Current cross-model observational figures
uv run python -m src.poc.exp09_cross_model_observational_replication.plot_replication
# Late-stage support diagnostics
uv run python scripts/analysis/analyze_exp13a_lite.py --help
uv run python scripts/plot/plot_exp13a_lite.py --help
# Matched-prefix late-window localization plots
uv run python scripts/analysis/analyze_exp13_full.py --help
uv run python scripts/plot/plot_exp13_full.py --help
# Exp16 native-JS replay analysis + plots
uv run python scripts/analysis/analyze_exp16.py --help
uv run python scripts/plot/plot_exp16.py --help# Multi-model steering / phase 0
bash scripts/run/run_phase0_multimodel.sh --step precompute
bash scripts/run/run_phase0_multimodel.sh --step steer
# Matched-prefix local causal campaign
bash scripts/run/run_exp13_exp14_local.sh --mode full
# Exp16 local JS replay over the frozen exp14 teacher stream
bash scripts/run/run_exp16_js_replay_local.sh --mode smoke| Model | Layers | d_model | Architecture | Pretraining / Post-training |
|---|---|---|---|---|
| Gemma 3 4B (primary) | 34 | 2560 | GQA, hybrid local/global (5:1) | Undisclosed pretraining / KD + supervised + preference + rule-based stages |
| Llama 3.1 8B | 32 | 4096 | GQA, all global | 15T-token pretraining / iterative supervised + preference optimization |
| Qwen 3 4B | 36 | 2560 | GQA, all global | 36T-token multilingual pretraining / multi-stage SFT + RL post-training |
| Mistral 7B v0.3 | 32 | 4096 | GQA, sliding window (4096) | Undisclosed pretraining / instruct checkpoint |
| OLMo 2 7B | 32 | 4096 | MHA, all global | OLMo-mix-1124 pretraining / Tülu 3-style SFT + DPO + RLVR |
| Qwen2.5 32B | 64 | 5120 | GQA, all global | Qwen2.5 pretraining / instruct checkpoint |
| DeepSeek-V2-Lite | 27 | 2048 | MLA, MoE (2 shared + 64 routed, top-6) | 5.7T-token pretraining / SFT-only chat checkpoint; appendix side case |
OLMo 2 uses a staged base-model recipe with a late Dolmino-mix-1124 curriculum, so the earlier single-dataset shorthand is inaccurate for this checkpoint. DeepSeek-V2-Lite-Chat is both the only MoE family here and an SFT-only chat checkpoint, so we treat it as a post-training outlier rather than as evidence for the dense-family main claim.
All main observational analyses use each IT model's native chat template and raw prompting for PT. Template-free conditions are treated as ablations rather than replacement primaries.
src/poc/
cross_model/ # Shared multi-model infrastructure
exp01_hierarchical_distributional_narrowing/
exp02_ic_ooc_reasoning_mechanistic_comparison/
exp03_corrective_stage_characterization/
exp04_phase_transition_characterization/
exp05_corrective_direction_ablation_cartography/
exp06_corrective_direction_steering/
exp07_methodology_validation_tier0/
exp08_multimodel_steering_phase0/
exp09_cross_model_observational_replication/
exp10_contrastive_activation_patching/
exp11_matched_prefix_mlp_graft/
exp12_free_running_abc_graft/
exp13_late_stage_token_support_analysis/
exp14_symmetric_matched_prefix_causality/
exp15_symmetric_behavioral_causality/
exp16_matched_prefix_js_gap/
exp20_divergence_token_counterfactual/
exp21_productive_opposition/
exp22_endpoint_deconfounded_gap/
exp23_midlate_interaction_suite/
exp23_midlate_kl_factorial/
exp24_32b_external_validity/
exp25_olmo_stage_progression/
exp26_residual_opposition_mediation/
exp27_natural_rollout_residual_opposition_ntp/
scripts/
analysis/ # Post-hoc summaries, cross-checks, paper stats
data/ # Dataset builders / data prep
eval/ # Judge and evaluation entrypoints
infra/ # Modal/Lambda/cloud helpers
merge/ # Worker/shard merge utilities
plot/ # Figure generation
precompute/ # Direction extraction and preprocessing
run/ # Main experiment launchers
scoring/ # Rescoring utilities
results/
cross_model/{model}/
exp01_hierarchical_distributional_narrowing/
...
exp15_symmetric_behavioral_causality/
Canonical experiment/result paths now use descriptive names. Source code now lives only in the canonical named experiment folders. Some legacy result and flat script aliases are still kept during the results/scripts migration so older commands keep working.
For a full index, see docs/EXPERIMENT_REGISTRY.md.
This index includes historical and supporting experiments. The current paper's main first-divergence factorial claim uses six dense PT/IT pairs; supporting rows are labeled Dense-5 when Qwen2.5-32B was not rerun, and DeepSeek-V2-Lite remains a MoE side case where artifacts exist.
| ID | Analysis | Key result |
|---|---|---|
| L1 | δ-cosine profiles | IT adds more late residual opposition than PT in the dense-family pool, with heterogeneous magnitude and a separate MoE side case |
| L2 | Convergence gap + delayed commitment (5 metrics × 2 lenses) | IT stays farther from its own final distribution through much of the stack; used as layerwise context |
| L3 | Weight change localization | Gemma: concentrated at corrective layers; others: uniform |
| L8 | Geometry follow-up | Exploratory dimensionality / covariance diagnostics are mixed and not part of the core evidence chain |
| L9 | Attention entropy divergence | Architecture-dependent |
| ID | Experiment | Key result |
|---|---|---|
| A1 | α-sweep on corrective layers | Governance dose-response, content flat |
| A1_rand | Random direction control | 3× less governance effect — direction specificity |
| A1_notmpl | No chat template | Dose-response preserved — weight-encoded |
| A2 | Inject into PT | Noisy — PT lacks downstream circuitry |
| A5a | Progressive layer skipping | Final 3 layers: format; earlier: coherence |
| ID | Experiment | Key result |
|---|---|---|
| exp11 | Matched-prefix late IT MLP graft | Late IT MLPs increase late KL-to-own-final and move PT internal predictions toward the IT teacher under shared token history |
| exp13A-lite | Descriptive token-support analysis | Late grafts broadly suppress raw-continuation-like FUNCTION/OTHER candidates and increase support for the eventual teacher token |
| exp16 | Matched-prefix native-JS replay | Direct same-layer JS under frozen exp14 teacher histories removes unmatched-history and own-final-endpoint dependence from the main internal divergence readout |
| exp14 | Symmetric sufficiency / necessity | Late IT→PT graft is the strongest sufficiency window and late PT→IT swap is the strongest necessity window in the dense-family pool on the primary late-region KL metric |
| exp20 | First-divergence identity/margin decomposition | Middle-positioned substitutions transfer token identity more often; late-positioned substitutions affect margin more |
| exp21 | MLP write-out at first divergence | Late IT MLPs provide strong native IT-token support, but the MLP-only late effect is weak from PT upstream state |
| exp23 | Residual-state x late-stack factorial | Current headline: upstream-late interaction on the divergent-token margin, with label-swap, position, subgroup, and content/reasoning checks |
| ID | Experiment | Key result |
|---|---|---|
| exp12 | A/B/C free-running graft comparison | Legacy behavior run: late graft reduces benign false refusals broadly and improves assistant register in several families, but remains far from the full IT endpoint on polished structure |
| exp15 | Symmetric behavioral causality | Current canonical behavioral estimate of the same late intervention family, with the clearest effects on the IT-side necessity test and weaker but real PT-side recovery |
| ID | Test | Result |
|---|---|---|
| 0A | Direction bootstrap stability | cos > 0.993 by n=300 |
| 0B | Matched-token direction | cos = 0.82 (primarily weight-driven) |
| 0C | Projection-matched random | 3× less governance, identical content degradation |
| 0D | Bootstrap 95% CIs | BCa intervals on all metrics |
| 0E | Classifier robustness | Robust to all boundary perturbations |
| 0F | Layer range sensitivity | Stable across 4 overlapping ranges |
| 0G | Tuned-lens commitment | Primary commitment measurement (6 models × 2 variants) |
| 0H | Calibration split | Three disjoint prompt sets → same dose-response |
| 0I | Formula comparison | MLP projection only; attention/residual fail |
| 0J | Onset threshold sensitivity | Robust across σ-based and absolute thresholds |
| Phase | Description | Status |
|---|---|---|
| 1 | Forced-decoding paired data collection | Prototype complete |
| 2 | Ridge probes → convergence direction (d_conv) | Prototype complete |
| 3 | Causal activation patching (5 conditions) | Prototype complete |
| 4 | Steering with d_conv vs d_mean | Prototype: d_mean steers (11–19×), d_conv does not |
The steering pipeline is architecture-agnostic. It operates on raw MLP activations via a model-agnostic adapter system — no transcoders, SAEs, or model-specific decompositions required.
Direction Extraction Steering Evaluation
-------------------- -------------------- --------------------
IT model --+ IT model + hooks LLM judge (G1/G2)
|-- d_mean h += (alpha-1)(d'h)d Programmatic (STR)
PT model --+ per corrective layer IFEval compliance
MMLU / GSM8K / reasoning
The adapter system provides a uniform interface across the dense architectures plus the DeepSeek MoE side case and Gemma's hybrid attention. Extending to a new model requires only registering its architecture in the adapter config.
@article{anonymous2026corrective,
title={First-Divergence Factorial Diffing for Post-Trained Language Models},
author={Anonymous},
year={2026}
}See LICENSE.