The Spectral Geometry of Misalignment

Code, manuscript source, and committed artifacts for a weight-space study of spectral structure, refusal interventions, and matched emergent-misalignment model organisms.

Paper PDF | Theory supplement | Reproducibility guide | Research plan | Citation | License

Overview

For a fine-tuned checkpoint and its base model, define the weight increment

Delta W = W_finetuned - W_base.

This project asks two separate questions:

1. Is the increment spectrally concentrated rather than diffuse?
2. Do directions selected from that geometry become behaviorally relevant under controlled residual-stream interventions?

The first question is descriptive. The second is studied with matched harmful-versus-benign fine-tuning arms, held-out scoring, random-direction controls, and projection or steering interventions. Spectral anisotropy alone is not treated as an alignment detector.

Main Findings

• Instruction-tuning increments are strongly anisotropic. Across all 224 Llama-3-8B Base-to-Instruct linear-map increments, the leading eigenvalue is above the fitted Marchenko-Pastur visibility edge. The exact exceedance count depends on the bulk fit, so the paper treats it as an operational visibility measure rather than a calibrated hypothesis test.
• Measured refusal is sensitive to the leading increment subspace. On the tested harmful-prompt distribution, projecting out the top-128 subspace changes substring refusal on a fixed 128-prompt slice from 98.4% ([94.5,99.6]%) to 14.1% ([9.1,21.1]%), while one seeded equal-dimensional random projection gives 97.7% ([93.3,99.2]%). MMLU, ARC-C, and GSM8K fall substantially more under the spectral projection than under that random projection, showing broad disruption rather than capability preservation.
• Matched medical organisms recover a shared contrast direction. The Qwen2.5-Coder-7B checkpoint, direction, and evaluation artifacts are hash-linked, but the original medical training rows are not present. Projecting out the fitted direction changes the all-output joint misalignment-and-eligibility rate from 2.3% to 0.0% in-sample, while a random direction gives 3.4%.
• The within-organism pattern appears across Qwen, Llama, and Mistral. The Mistral intervention is partial rather than complete. These are controlled model organisms, not evidence about naturally occurring failures.
• Held-out HarmBench prompts reproduce harmful-prompt refusal transfer. The AdvBench-derived subspace reduces measured refusal on 400 HarmBench prompts from 71.2% to 5.8%, versus 65.8% for the random control.
• Several important audits are negative or inconclusive. The cross-type code-organism study does not support positive transfer; the 14B study retains geometry and descriptive held-out ordering but misses its frozen causal criteria. In the matched-fold baseline audit, all three learned methods rank 16/16 pairs correctly; the weight-SVD versus row-mean margin ordering depends on whether projection norm or squared projection norm is reported.

The paper reports confidence intervals, controls, provenance limits, and the full scope of these claims. The short summary above is not a substitute for the methods and limitations in the manuscript.

Repository Layout

alignment-geometry/
├── README.md                 project overview and quick start
├── CITATION.cff              citation metadata
├── PLAN.md                   original research plan and completed audit record
├── LICENSE                   document and source-code licensing terms
├── requirements-local.txt    local figure and validation dependencies
├── code/                     supported producers, launchers, and validators
├── data/                     committed prompts and available training datasets
├── paper/                    self-contained manuscript source and build script
├── docs/
│   ├── paper.pdf             current paper
│   ├── proof.tex             optional extended-theory source
│   ├── proof.pdf             optional extended-theory PDF
│   └── reproducibility.md    local and GPU reproduction guide
└── results/
    ├── data/                 committed summaries, evidence, and run manifests
    └── figures/              generated PDF figures

Large model checkpoints, fine-tuning runs, caches, and operator scratch files are intentionally excluded from Git.

Quick Start

The local pipeline uses Python 3.12 or newer. Tectonic is required to build the paper, and Poppler supplies pdfinfo and pdftoppm for visual-QA receipts.

python3 -m venv .venv
source .venv/bin/activate
python3 -m pip install -r requirements-local.txt

Regenerate committed figures from the committed result summaries:

python3 code/make_figures.py

Build the manuscript and refresh docs/paper.pdf:

bash paper/build.sh

Run the authoritative validation gates:

python3 code/paper_completion_check.py --local
python3 code/paper_completion_check.py --scope external
python3 code/check_citations.py
python3 code/check_uncertainty.py
python3 code/check_figure_palette.py
python3 code/check_secrets.py --history

See docs/reproducibility.md for study launchers, artifact ingestion, run-manifest validation, and visual-QA procedures.

Artifacts and Provenance

The paper is driven by committed artifacts rather than copied values in the manuscript. Important groups include:

Study	Primary artifacts	Main validator
Spectral sweep	results/data/spectral.jsonl, summary.json, full_spectrum.npz	check_paper_numbers.py
Refusal interventions	results/data/behavioral_capture.json, capability.json, capability_evidence.json	check_paper_numbers.py
Medical organisms	results/data/misalignment_eval_medical.json, directions_med.*, detect_med.json	check_direction_study.py
Cross-family replication	results/data/directions_llama.json, directions_mistral.json	check_direction_study.py
Capability audit	results/data/capability.json, capability_evidence.json	check_capability_result.py
HarmBench transfer	results/data/transfer.json, transfer_evidence.json	check_transfer_result.py
Cross-type audit	results/data/cross_organism.json, causal_misalign_code.json	check_cross_type_code_result.py
14B audit	results/data/directions_14b.*, detect_14b.json, scale_14b_attempt_history.json	check_scale_14b_attempt_history.py
Baseline audit	results/data/baselines.json, activation_pca_baseline.json	check_baselines.py

All paths above are under results/data/. Run manifests live in results/data/run_manifests/. The results guide explains the artifact classes and editing policy.

The frozen analysis-input snapshot is indexed by results/data/analysis_manifest.json. Its source revision is 915a4e1b3a9d10232ccdd399a34967a9f7d5c4b6; the manifest is content-addressed and can be verified with:

python3 code/build_analysis_manifest.py --check
python3 code/mp_fit_sensitivity.py --check

Generated figures use the explicit palette in code/figure_palette.py. Behavioral figures use green for benign, safe, preserved, or improved outcomes; red for harmful, misaligned, lost, or adverse outcomes; and gray for controls. Line styles, marker shapes, and dark keylines remain redundant with color.

Reading Order

1. docs/paper.pdf, the current empirical paper.
2. paper/main.tex and paper/sections, the editable manuscript source.
3. docs/proof.pdf, optional extended derivations.
4. PLAN.md, the original roadmap and audit history.
5. docs/reproducibility.md, reproduction procedures.

Citation

Citation metadata is available in CITATION.cff.

@misc{gupta2026checkpointdelta,
  title  = {The Spectral Geometry of Misalignment},
  author = {Aryan Gupta},
  year   = {2026},
  url    = {https://github.com/aryan-cs/alignment-geometry}
}

License

The paper, theory supplement, research plan, and documentation are licensed under CC BY-NC-ND 4.0. The source code is source-available but is not covered by that document license, and no software reuse or redistribution license is granted. See LICENSE for the complete terms.