# Zenodo Upload: Toroidal Logit Bias for Hallucination Reduction (v7 — Replication Update)

**DOI: https://doi.org/10.5281/zenodo.18512373**

## Title
Toroidal Logit Bias for Hallucination Reduction in Large Language Models — Replication Update

## Authors
Sylvain Cormier (Paraxiom Research)

## Description

An inference-time intervention that imposes toroidal topological constraints on token selection in large language models.

**v7 — Replication Update (March 2026)**

This version corrects the empirical claims from v2. A comprehensive independent replication (6 experimental phases, 4 models, 3 benchmarks, n=100–200 per condition) found that the toroidal logit bias does not produce statistically significant hallucination reduction. The v2 results (+0.2pp to +2.8pp) were within sampling variance of the LLM judge.

**v2 Original Results (817 samples, LLM-judged — NOT REPLICATED):**

| Model | Baseline T&I | Toroidal T&I | Delta |
|-------|-------------|-------------|-------|
| Qwen 0.5B | 16.9% | 17.1% | +0.2pp |
| Qwen 1.5B | 32.2% | 32.8% | +0.6pp |
| Qwen 7B | 75.6% | 77.7% | +2.1pp |
| Mistral 7B | 74.4% | 77.2% | +2.8pp |

**v7 Replication Results:**

*Phase 1 — Greedy Decoding (4 models × 3 benchmarks):* All null. α=0.3 bias (~0.9 max logit shift) too small to change argmax.

*Phase 2 — Sampling with T&I Judge (exact match to v2 methodology):*

| Metric | Baseline | Toroidal | Delta | p-value |
|--------|----------|----------|-------|---------|
| T&I % (Qwen 7B, n=200) | 76.5% | 74.5% | **−2.0pp** | 0.22 |

Our baseline (76.5%) closely matches the v2 baseline (75.6%), confirming correct methodology. The toroidal condition shows −2.0pp (opposite direction from v2's +2.1pp), not statistically significant (McNemar p=0.22).

*Phase 3 — Alpha Sweep (Qwen 7B, semantic torus mapping, n=100):*

| Alpha | TriviaQA H% | NQ-Open H% |
|-------|------------|------------|
| baseline | 50.0% | 70.7% |
| 0.3 | 50.0% (0pp) | 69.6% (−1.1pp) |
| 1.0 | 51.1% (+1.1pp) | 71.4% (+0.8pp) |
| 3.0 | 53.8% (+3.9pp) | 71.3% (+0.6pp) |
| 5.0 | 75.6% (+25.6pp) | 78.2% (+7.5pp) |
| 10.0 | 96.0% (+46.0pp) | 92.0% (+21.4pp) |

Higher alpha monotonically degrades output quality. No beneficial sweet spot found.

*Phase 4 — Factorial Decomposition:*
The "hardening" system prompt ("Answer concisely and truthfully") accounts for −14pp hallucination reduction on TriviaQA (p=0.05). This prompt engineering effect, not the toroidal bias, was the active ingredient in the Coherence Shield pipeline.

**What remains valid:**
- Theoretical framework (toroidal topology, Lean 4 proofs, spectral gap bounds)
- Toy model validation (40% drift reduction vs random masking negative control)
- Rust/Python library primitives (torus mapping, bias computation, mask generation)
- Hardening prompt as an effective hallucination reduction technique
- PQ attestation and audit trail infrastructure (Coherence Shield)
- Training-time Karmonic spectral regularization (untested — promising direction)

**What is corrected:**
- The v2 TruthfulQA improvements (+0.2pp to +2.8pp) were within LLM judge sampling variance
- "Improvement scales with model capacity" is not supported — all effects are null
- The OLMo +15.4% result was from a 100-configuration hyperparameter sweep (overfitting)

**Method:**
- Map vocabulary tokens to positions on a 12×12 torus
- Bias logits toward tokens "near" recent tokens in toroidal space
- Only bias high-frequency tokens (first 1K–3K of vocabulary)
- α=0.3, radius=2.0 (published parameters)

**Scope:** The theoretical framework (topological constraints on latent dynamics) remains formally valid. The inference-time logit bias intervention does not produce measurable hallucination reduction at practical bias strengths. Training-time integration (Karmonic regularization) remains untested and is the recommended direction for future work.

## Keywords
- large language models
- hallucination reduction
- inference-time intervention
- logit bias
- toroidal topology
- factual accuracy
- TruthfulQA
- replication
- null result

## Related Identifiers
- GitHub: https://github.com/Paraxiom/topological-coherence
- PyPI: https://pypi.org/project/topological-coherence/
- Crates.io: https://crates.io/crates/topological-coherence
- HuggingFace Demo: https://huggingface.co/spaces/paraxiom-research/topological-coherence
- Related work: DOI 10.5281/zenodo.18187835 (Topological Constraints theory paper)
- Replication scripts: https://github.com/Paraxiom/topological-coherence/tree/main/experiments

## License
CC-BY-4.0

## Upload Type
Publication / Preprint

## Publication Date
March 2026

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## Files to Upload
1. `toroidal_hallucination_reduction_2026.pdf` - Main paper (v7, with replication addendum)
2. `toroidal_hallucination_reduction_2026.tex` - LaTeX source (optional)
3. `replication_data/` - Raw JSON results from all 6 replication phases (optional)

## Upload Instructions
1. Go to https://zenodo.org/deposit/18512373 (existing record)
2. Click "New version"
3. Upload updated PDF
4. Copy description above into the Description field
5. Publish
