{"id":51716524,"url":"https://github.com/appleweiping/inr-aliasing-limits","last_synced_at":"2026-07-17T03:36:14.598Z","repository":{"id":371025530,"uuid":"1296789623","full_name":"appleweiping/inr-aliasing-limits","owner":"appleweiping","description":"Learned Nyquist: fundamental aliasing limits of implicit neural representations (IEEE ICASSP SPTM). Achievability + converse, Monte-Carlo-validated, real data both sides.","archived":false,"fork":false,"pushed_at":"2026-07-12T19:36:40.000Z","size":14154,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-07-12T21:11:12.257Z","etag":null,"topics":["aliasing","fourier-features","icassp","implicit-neural-representation","neural-fields","reproducible-research","sampling-theory","signal-processing"],"latest_commit_sha":null,"homepage":null,"language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/appleweiping.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2026-07-10T18:19:33.000Z","updated_at":"2026-07-12T19:36:44.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/appleweiping/inr-aliasing-limits","commit_stats":null,"previous_names":["appleweiping/inr-aliasing-limits"],"tags_count":null,"template":false,"template_full_name":null,"purl":"pkg:github/appleweiping/inr-aliasing-limits","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/appleweiping%2Finr-aliasing-limits","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/appleweiping%2Finr-aliasing-limits/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/appleweiping%2Finr-aliasing-limits/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/appleweiping%2Finr-aliasing-limits/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/appleweiping","download_url":"https://codeload.github.com/appleweiping/inr-aliasing-limits/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/appleweiping%2Finr-aliasing-limits/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":35566571,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-07-17T02:00:06.162Z","response_time":116,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["aliasing","fourier-features","icassp","implicit-neural-representation","neural-fields","reproducible-research","sampling-theory","signal-processing"],"created_at":"2026-07-17T03:36:13.968Z","updated_at":"2026-07-17T03:36:14.592Z","avatar_url":"https://github.com/appleweiping.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Silent Aliasing and Certified Sampling Design for Fixed Fourier-Feature Models\n\nIdentifiability analysis and a **constructive, certified anti-aliasing sampling design**\nfor coordinate models built on a **fixed finite set of Fourier features** — the linear\ncore of Fourier-feature implicit neural representations. Target venue: IEEE ICASSP 2027\n(Signal Processing Theory \u0026 Methods).\n\n**Scope, stated up front.** Every theorem is about the fixed-feature, linear-coefficient\nmodel (least squares on an exponential dictionary Λ). Trained nonlinear networks\n(Fourier-feature MLPs, SIRENs) are an **explicitly labeled empirical extension** — and the\nextension **fails for SIRENs**, which we report. Adaptive / learned frequency sets are\n**outside** the theory. This is not a theory of \"all INRs\".\n\n## The three-act contribution\n\n1. **Structured indistinguishability (T1).** A visibility/aliasability calculus shows that\n   *arbitrary nonuniform subsets of a rate-Q sampling grid inherit the grid's aliasing\n   equivalence classes*: an integer tone with ν ≡ ω (mod Q) is **exactly** indistinguishable\n   from the model atom ω — zero training residual, full-energy reconstruction failure, and\n   (two-point argument) no estimator can avoid error ≥ |a|/√2. **Irregular-on-a-grid\n   sampling does not break exact aliasing** — the paper's central corrective.\n2. **Randomization breaks it, at a rate (T3).** Off-grid jitter destroys the fold with\n   visibility equal to the jitter characteristic function (Gaussian: `v ≈ 2π|r|Q·σ_t`);\n   i.i.d. sampling gives a finite-N, dictionary-referenced concentration bound on\n   worst-case aliasability over a finite candidate set.\n3. **Certified design (`design.py`).** The anti-aliasing objective is a **Ds-optimal\n   (nuisance-parameter) / LCMV null-steering** criterion on sample times — *we credit that\n   classical principle and do not claim it as new*. Our additions: the identifiability\n   reading (which cross-terms to null, and why grid designs can't — T1), a fast joint\n   surrogate that an **ablation shows is necessary** (coherence-only wrecks conditioning;\n   condition-only leaves aliasing), and — the genuinely new tool — a **continuum\n   aliasability certificate**: because `a_T(ν)²` is a real trig polynomial in ν, a\n   Bernstein/Lipschitz bound certifies the worst case over an *entire band* from the\n   samples alone, which the finite-candidate bound and random designs cannot.\n\n**Honest novelty position** (full audit in [`docs/novelty-matrix.md`](docs/novelty-matrix.md)\nand the claim ledger [`docs/claim-ledger.md`](docs/claim-ledger.md)): T2 (Riesz\nbookkeeping) and T4 (noncentral-χ² detection) are standard and live in the supplement; the\ndefensible, non-derivable pieces are the **T1 grid-inheritance corrective**, the **T3\nfinite-N dictionary-referenced quantification**, and the **continuum certificate** plus its\nidentifiability-driven design use. Full proofs: [`paper/supplement.pdf`](paper/supplement.tex).\n\n## Experiments (theory ↔ experiment closed loop)\n\n| # | Script | What it validates |\n|---|---|---|\n| E1 | `run_synthetic_matrix.py` | T1 grid persistence vs i.i.d. (fixed \u0026 adversarial tones), T3 jitter law + concentration bound, error decomposition |\n| E2 | `run_diagnostic_roc.py` | detection: coherent fold vs its in-band twin sits at chance (all 5 detectors, CI covers 0.5); visible tones follow the exact noncentral-χ² power curve; calibration/test separated |\n| E3 | `run_real_signal.py` | sample-only bandwidth selection vs an evaluation-only oracle; anti-aliased decimation; 9 speech segments; paired CIs |\n| **E6** | **`run_aliasguard.py`** | **certified design: ablation (joint objective needed), held-out \u0026 misspecified generalization, budget sweep, signal-domain payoff, continuum certificate, 1-D \u0026 2-D** |\n| E4 | `run_nonlinear.py` | trained-net extension: 20 seeds × 3 archs, NTK-prediction, **SIREN failure reported** |\n| E5 | `run_image2d.py` | 2-D exact fold (linear) + lattice-vs-random masks (trained), all PSNR variants separate |\n\nHeadline E6 numbers (from `results/aliasguard.json`, regenerated by the script; the paper\npulls them via `paper/sync_macros.py`, no hand-entered numbers): designed on a focused\nconcern set and evaluated on **held-out unseen frequencies**, worst-case aliasability drops\nto ≈0.19 vs ≈0.63 (random jitter) / ≈0.59 (E-optimal), holds under candidate-set\nmisspecification, and is **certified ≤ ≈0.29 over an entire continuous band** vs ≈0.57 for\nrandom; the 2-D design gives ≈0.18 vs ≈0.68.\n\n## Reproduction\n\n```bash\nuv venv --python 3.11 \u0026\u0026 source .venv/bin/activate   # Windows: .venv/Scripts/activate\nuv pip install -r requirements.lock \u0026\u0026 uv pip install -e . --no-deps\npython -m pytest -q                     # 39 theorem/design tests (CPU)\npython experiments/run_all.py           # CPU reproduction (E1-E3, E6, E5 part A)\npython experiments/run_all.py --full    # + trained-network studies (torch + GPU)\n```\n\n`requirements.lock` pins the CPU stack. Torch experiments were run with torch 2.8.0+cu128\non an RTX 4090 (recorded per-JSON in `_meta`); GPU training uses\n`torch.use_deterministic_algorithms(True, warn_only=True)`, but bitwise reproducibility\nacross CUDA versions is not guaranteed. The CPU pipeline is deterministic (fixed seeds).\n\nBuild the paper + supplement:\n```bash\ncd paper \u0026\u0026 python sync_macros.py       # regenerate macros_ag.tex from results/aliasguard.json\npdflatex main \u0026\u0026 bibtex main \u0026\u0026 pdflatex main \u0026\u0026 pdflatex main\npdflatex supplement \u0026\u0026 pdflatex supplement\n```\n\n## Data provenance \u0026 licenses\n\n| Data | Source | Terms | Processing |\n|---|---|---|---|\n| Speech (3 recordings) | Open Speech Repository, Harvard sentences | Freely available per OSR (see source page); **not** covered by this repo's MIT license | SHA-256 in `data/speech_provenance.json`; 2-s segments; `resample_poly` anti-aliasing |\n| Mauna Loa CO₂ | NOAA GML | Public (NOAA disclaimer) | monthly means, full record, linear detrend |\n| Sunspots (daily + smoothed) | SILSO, Royal Observatory of Belgium | CC BY-NC 4.0 | smoothed series is an intentionally low-pass **proxy**, labeled everywhere |\n\nMIT license covers **code only**; third-party data remain under their own terms.\n\n## Repository layout\n\n```\nsrc/inralias/  identifiability.py (T1-T4 objects)  design.py (AliasGuard + certificate)\n               sampling.py  limits.py (background)  inr.py  diagnostics.py  signals.py\nexperiments/   run_synthetic_matrix  run_diagnostic_roc  run_real_signal  run_aliasguard\n               run_nonlinear  run_image2d  run_all\ntests/         test_identifiability  test_theory_vs_sim  test_sampling  test_diagnostics_inr\n               test_design           (39 tests; GitHub Actions on every push)\npaper/         main.tex  supplement.tex (full proofs)  sync_macros.py  figures  refs.bib\ndocs/          novelty-matrix.md  claim-ledger.md  CHANGELOG-major-revision.md\nresults/       *.json (with _meta provenance) + figures/\nsubmission/    ICASSP 2027 submission package (see submission/README.md)\n```\n\n## Honesty notes\n\n* AliasGuard is a Ds-optimal / null-steering design — **classical principle, credited**;\n  the new pieces are the identifiability use and the continuum certificate.\n* AliasGuard needs a **focused** concern set (K = O(N)); for a broad band with K ≫ N no\n  design beats random much, and a badly misspecified set loses the edge — reported.\n* The concentration bound is a loose union bound, plotted against the empirics.\n* Trained-net extension **fails for SIRENs**; all seed-level failures are released.\n* CV bandwidth selection is reported even where it underperforms.\n* Detection thresholds come only from `null_calibrated_threshold` (calibration null).\n* \"Monte-Carlo-validated\" = closed forms asserted against independent simulation in\n  `tests/`; not a substitute for the proofs (supplement).\n\n## Review process (ICASSP 2027)\n\nICASSP 2027 uses **single-anonymous** review (reviewers see author names); no manuscript\nanonymization is required, so this public repository and the author name on the PDF are\ncompliant. The submission package is in [`submission/`](submission/).\n\n## AI assistance disclosure\n\nSubstantial portions of the code, experiments, and manuscript were produced with AI\nassistance (Anthropic Claude) under the author's direction; all results were generated by\nthe released, reproducible code. AI is not an author. Git history records this via\n`Co-Authored-By` trailers and is not rewritten. This is disclosed in the paper's\nCompliance-with-Ethical-Standards statement.\n\n## License\n\nMIT (code only; see `LICENSE`). Third-party data under their own terms (table above).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fappleweiping%2Finr-aliasing-limits","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fappleweiping%2Finr-aliasing-limits","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fappleweiping%2Finr-aliasing-limits/lists"}