# F_Structure_LM audit paper — arXiv submission package Author: yxpil Artefact under study: ## Title **A Published "Fourier Language Model" Is a Retrieval Index, Not a Model: Provable Order Blindness and a Held-Out Audit of a 134 MB Chat Artefact** ## Suggested arXiv classification - Primary: `cs.CL` (Computation and Language) — the object is a claimed chat language model and the measurement is next-token accuracy against classical $n$-gram baselines. - Cross-lists: `cs.LG` (Machine Learning, for the kNN/FNet comparison and the index-density result), `cs.IR` (Information Retrieval, because the artefact is in fact a cosine nearest-neighbour index), `cs.SE` (Software Engineering, for the reproducibility findings: the shipped payload does not reproduce the outputs printed on its own model card). `cs.CL` is the right primary. The paper is a measurement audit of a public model release, not a new architecture, and arXiv's moderation reads that material as NLP. If a moderator objects that nothing here *is* a model, `cs.LG` is the natural fallback primary and `cs.CL` the cross-list. ## Abstract (verbatim) > A public model repository named F_Structure_LM advertises "a Fourier transform > that replaces the self-attention of a Transformer" and shows a fluent reply to > a prompt that is not in its training data. We read all 140,569,669 bytes of > its payload and report what it is: 1,849,576 rows of 17 float32 numbers, each > paired with one token label, plus three integers — and no learnable parameter > of any kind. Inference is cosine nearest-neighbour lookup in that table. > Because each row is the magnitude spectrum of raw byte-level BPE identifiers, > two failure modes are theorems rather than measurements: the spectrum is > invariant to time reversal, so reversing a context cannot change what is > retrieved (99.05% of 4,000 held-out contexts retrieve the identical > neighbour), and the zeroth bin is the unordered sum of the identifiers, > carrying 24.0% of a typical key's energy. On the official LCCC valid and test > splits the published index predicts the next token correctly for 2.90% of > 4,000 sampled contexts — below its own constant-label baseline (5.48%) and far > below a unigram over the same corpus (34.48%), against bigram 18.05%, trigram > 11.63%, exact 12-gram 0.43%. Rebuilding the identical feature recipe on 50,000 > sampled training dialogues, with 92.7 rows per dialogue instead of the > published 37.0, lifts the same decoder to 21.63%: the artefact's failure sits > in index density and label coverage, not in order blindness alone. At > generation time it lands on points of its own table (mean top-1 cosine > 0.998–1.000 over 896 steps), none of the three replies printed on its model > card reproduce, and 32.4% of rows carry a label that cannot be decoded without > an adjacent one. What it does genuinely well is cheap: 139 tokens/s and 841 MB > resident on a CPU, no GPU. We close by stating what a "Fourier language model" > claim would have to measure to be checkable. ## BibTeX entry (after announcement) ```bibtex @misc{yxpil2026fourierlm, author = {Yang, Daozhendong}, title = {A Published "Fourier Language Model" Is a Retrieval Index, Not a Model: Provable Order Blindness and a Held-Out Audit of a 134 MB Chat Artefact}, year = {2026}, note = {arXiv:XXXX.XXXXX [cs.CL]} } ``` ## Files | path | role | | --- | --- | | `main.tex` | the paper, one column-balanced build, 9 pages | | `common.tex` | shared preamble, byte-identical to `../_shared/common.tex` | | `refs.bib` | 13 entries, all real and all cited | | `figures/fig_energy.pdf` | per-bin energy share of the published keys | | `figures/fig_cone.pdf` | cosine distribution of 199,994 random key pairs | | `figures/fig_methods.pdf` | the four held-out decoders as a bar chart | | `figures/fig_samples.pdf` | greedy continuations, rendered with a CJK font | | `scripts/inspect_ckpt.py` | tensor shapes, dtypes, learnable-parameter count | | `scripts/headline_facts.py` | structure, DC energy, reversal, scaling, cone | | `scripts/analyze_index.py` | label frequency, throughput, latency, RSS | | `scripts/build_replication.py` | rebuilds the index from an LCCC train sample | | `scripts/eval_heldout.py` | held-out accuracy, band ablations, $n$-gram baselines, leakage | | `scripts/stratum_eval.py` | the same queries split into clean vs boundary-straddling | | `scripts/boundary_stat.py` | how many sampled positions cross a dialogue boundary | | `scripts/generate_samples.py` | reproduces the published greedy decoder on 7 prompts | | `scripts/token_decodability.py` | which emitted labels cannot be printed alone | | `scripts/make_figures.py` | draws all four figures from the JSON evidence | | `scripts/results/*.json` | raw output; every number in the paper traces here | | `README.md` | this file | ## Build ```bash tectonic -X compile main.tex --keep-logs ``` or classically: ```bash pdflatex main && bibtex main && pdflatex main && pdflatex main ``` The build is clean: no undefined references, no overfull boxes, 9 pages. ## Packaging for arXiv ```bash bash ../make_package.sh fourier-lm # paper-only tarball ``` The artifact tarball additionally ships `scripts/` and `scripts/results/`, so a reader can re-run every number. The published payload (`fourier_50K.pt`, 140,569,669 B) is **not** shipped in either tarball; it is downloaded from the ModelScope repository named in the paper. ## Reproduction Requirements: Python 3.11+, `torch` (2.14.1+cpu measured), `numpy` 2.5, `tokenizers` 0.20, `matplotlib`, and network access to ModelScope for two downloads: the model repository and the LCCC-base mirror (`train` 932,644,005 B, `valid`, `test`). Point the scripts at them with `FSLM_DIR` and `LCCC_DIR`. ```bash export FSLM_DIR=$HOME/cache/fslm LCCC_DIR=$HOME/cache/lccc python -X utf8 scripts/inspect_ckpt.py python -X utf8 scripts/headline_facts.py python -X utf8 scripts/analyze_index.py python -X utf8 scripts/build_replication.py # ~32 s, writes a 300 MB cache python -X utf8 scripts/eval_heldout.py # ~6 min python -X utf8 scripts/stratum_eval.py # ~1 min python -X utf8 scripts/boundary_stat.py python -X utf8 scripts/generate_samples.py # ~2 min python -X utf8 scripts/token_decodability.py python -X utf8 scripts/make_figures.py ``` Total wall time on the measured machine is about 15 minutes, dominated by the two full-index searches. Peak RSS is ~3.5 GB during `eval_heldout.py` (both indices are float32-normalised in RAM at once); nothing needs a GPU. ## Submission steps 1. New submission at . 2. Primary `cs.CL`, cross-lists `cs.LG`, `cs.IR`, `cs.SE`. 3. Paste the title and the abstract above; author `Daozhendong Yang`, with the same identity used in the paper and here. 4. Upload the tarball; arXiv detects `main.tex` and runs `pdflatex` + `bibtex`. 5. Inspect the auto-built PDF against the local one (9 pages, 4 figures, 6 tables). 6. Choose a license and submit. ## Provenance and limits of the claims This is an audit of a third-party artefact that happens to be authored by the same person who submitted the paper. Two consequences are handled explicitly in the text rather than hidden: - **No reconstruction claim.** The paper never asserts that the published index was built from a specific corpus or split. LCCC-base is used because the sibling project names it and because the released tokenizer matches its preprocessing; the replication is a like-for-like control, and Section 4 says so. - **Negative results about the author's own artefact are kept, not softened**: the 2.90% figure, the fact that it is below the artefact's own constant-label floor, and the non-reproduction of the three model-card showcase replies are reported as measured, with the caveat that the card's decoding settings are unknown. - **The replication's advantage is reported against itself.** 2.5% of held-out queries match the *replication* index exactly (0.0% for the published index), so the control's 21.63% is if anything inflated; Section 6.3 states this. - **`index_analysis.json` contains three fields that are not cited anywhere** — `highpass`, `mean_proxy`, `duplicates`. They were produced by querying the index with rows drawn from that same index, which makes their top-1 cosine exactly 1.0 and their accuracy meaningless. They are kept in the shipped evidence for transparency and are deliberately excluded from the paper. - **Timing is CPU-only** (14 threads, PyTorch 2.14.1+cpu). The card's memory claim is about VRAM, which was not available; the paper reports the measured CPU resident set and says plainly which claim it could not test. ## What the paper does not claim - It does not claim retrieval-based chat is worthless. kNN-LM and REALM are cited as the legitimate version of the idea, and the artefact's throughput and determinism are reported as genuine properties. - It does not claim the published index was built from LCCC. - It does not claim the model-card screenshots were fabricated; it claims they do not reproduce from the shipped payload under the shipped decoder, and lists the two possible explanations. - It does not report perplexity or cross-entropy, because the sampler has no distribution over the vocabulary to score — that absence is itself a finding, discussed in Section 8.