tianxiao1430-jpg/rfm-initialization-study

RFM initialization: sign interactions and selection controls

Author: Xiao Tian

Research artifacts accompanying Sign Interactions at Fixed Spectral Amplitudes: Predicting and Intervening on RFM Initialization under a Symmetry Fixed-Point Split, with a separate subsequent initialization-selection control study.

Paper PDF · GitHub source · 中文补充实验报告

What is provided

This dataset contains synthetic modular-addition experiment outputs, not a general-purpose language model or an inference service. One-hot input pairs and labels are deterministically generated from the published modular-arithmetic rules and split plans. There are no human subjects or third-party personal data.

• selection-directions: 200 method/reference rows from 40 independent directions and four selectors. The unmodified reference is already included within the random-full method's computation and is not an extra experiment.

• selection-candidates: 1,360 per-candidate validation/ranking records.

• selection-comparisons: all six prespecified bank-versus-competitor contrasts.

• manuscript-runs: 844 configurations and outcomes, including probes/repeats; this is not 844 independent samples.

• manuscript-confirmation: 80 frozen direction forecasts and outcomes.

• manuscript-intervention: original intervention/control records; see its data dictionary for the row unit and pairing.

• leader-reversal-runs: 844 original trajectories summarized by this later analysis.

• leader-reversal-events: 56,452 records, including two views and overlapping event types; these are not independent samples or unique crossings.

• leader-reversal-timeline: 9,600 direction/view/step rows for the primary 80 directions.

• leader-reversal-endpoint-strata: nine modulus/endpoint strata, including empty ambiguous strata; endpoint conditioning is descriptive.

All table configs use a split named results; they are research results, not training examples for a new predictive model. Some rows reuse the same direction or task. Do not treat rows or individual test points as independent draws.

Subsequent control result

Selector	p=17 held-out accuracy	p=23 held-out accuracy
Full response bank	99.55%	100.00%
Random short-probe	100.00%	100.00%
Greedy short-probe	100.00%	100.00%
Random full-training	97.73%	100.00%

Twenty new directions per modulus were used. Selection reads validation points only; final held-out points are scored after global selection sealing. The bank setup cost is included across a fixed workload of 20 queries. The current pilot does not establish a bank accuracy advantage or statistical equivalence. Perfect small-sample accuracy does not guarantee future success. Empirical bootstrap intervals collapse when all observed directions are perfect.

Training-time leader reversals (September 13 supplement)

An analysis of the original saved trajectories finds that early leaders can be overtaken: all 80 primary directions have at least one test point whose step-5 leader is later beaten. After step 10 this occurs in 5/80 directions (seven test points); pointwise leaders are stable from step 12 through the recorded step 59. Larger initial perturbations produce 27 correct-to-wrong transitions in 3/20 matched directions, and uncentered gradients can delay a reversal to step 18. Stability does not imply correctness or causal locking.

This is a post hoc analysis of existing data, separate from both the paper and the initialization-selection pilot. Report, figures and all tables · 中文报告 · Reproduction guide

Complete archives

Archive	Contents
rfm-manuscript-compact.zip	Publication-ready source/data package, including revision diagnostics.
rfm-mechanism-full.zip	Original study's full recorded trajectories and arrays.
rfm-initialization-selection-full.zip	Full follow-up models, banks, checkpoints, predictions, logs and seals.
rfm-leader-reversals.zip	September 13 post hoc trajectory analysis, all derived tables, figures and verification scripts. Requires the original full-score archive for raw-data recomputation.

SHA-256 hashes and byte sizes are in ARCHIVES.json and ARCHIVE_SHA256SUMS.txt. The compact manuscript archive contains the later manuscript diagnostics; the full original-study archive does not replace those post hoc additions. Original historical reports remain inside archives and refer to their respective execution/package snapshots.

Reproduction and limitations

Follow the GitHub publication READMEs for standard-library data checks and fresh CUDA execution. The measured environment used an RTX 4070, FP64, one PyTorch CPU thread, and TF32 disabled. Eight full-selector reruns matched exactly on the recorded environment. Cross-hardware bitwise reproducibility is not established.

The findings are conditional on Gaussian RFM, the fixed-point split and the common relative-sign candidate space. They do not establish a general neural initialization method or global novelty. This is public research material, not a peer-reviewed acceptance or a verified arXiv publication. The September 7 manuscript, with author-contribution wording revised September 12, remains distinct from the subsequent control study.

Attribution

The RFM implementation derives from marceltomas/breaking-data-symmetries, commit 311273bfc08adcde344c8b021fc5aa8d9970ad98. Code retains GPL-3.0; manuscript rights and existing notices are described in LICENSES.md. OpenAI Codex was used during the research.