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Geometric Properties of the Voronoi Tessellation in Latent Semantic Manifolds of Large Language Models

Marshall Brett · Apr 8, 2026 · Citations: 0

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Apr 8, 2026, 7:36 AM

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Apr 10, 2026, 7:12 AM

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Extraction source

Persisted extraction

Confidence 0.15

Abstract

Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold. We study this tessellation empirically on Qwen3.5-4B-Base, making two contributions. First, using float32 margin recomputation to resolve bfloat16 quantization artifacts, we validate Mabrok's (2026) linear scaling law of the expressibility gap with $R^2$ = 0.9997 - the strongest confirmation to date - and identify a mid-layer geometric ambiguity regime where margin geometry is anti-correlated with cross-entropy (layers 24-28, $ρ$ = -0.29) before crystallizing into alignment at the final layer ($ρ$ = 0.836). Second, we show that the Voronoi tessellation of a converged model is reshapable through margin refinement procedures (MRP): short post-hoc optimization runs that widen token-decision margins without retraining. We compare direct margin maximization against Fisher information distance maximization across a dose-response sweep. Both methods find the same ceiling of ~16,300 correctable positions per 256K evaluated, but differ critically in collateral damage. Margin maximization damage escalates with intervention strength until corrections are overwhelmed. Fisher damage remains constant at ~5,300 positions across the validated range ($λ$ = 0.15-0.6), achieving +28% median margin improvement at $λ$ = 0.6 with invariant downstream benchmarks - a geometric reorganization that compresses the expressibility gap while preserving its scaling law. However, frequency and token-class audits reveal that gains concentrate in high-frequency structural tokens (84% of net corrections at $λ$ = 0.6), with content and entity-like contributions shrinking at higher $λ$. Fisher MRP is therefore a viable geometric polishing tool whose practical ceiling is set not by aggregate damage but by the uniformity of token-level benefit.

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HFEPX Relevance Assessment

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Main weakness

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Trust level

Low

Eval-Fit Score

0/100 • Low

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Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

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Field Provenance & Confidence

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Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

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Evidence snippet: Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold.

Evaluation Modes

missing

None explicit

Confidence: Low Source: Persisted extraction missing

Validate eval design from full paper text.

Evidence snippet: Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold.

Reported Metrics

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No metric anchors detected.

Evidence snippet: Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold.

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Law
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes:
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  • Quality controls: Not reported
  • Confidence: 0.15
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

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Research Brief

Deterministic synthesis

Second, we show that the Voronoi tessellation of a converged model is reshapable through margin refinement procedures (MRP): short post-hoc optimization runs that widen token-decision margins without retraining. HFEPX protocol signal is limited in abstract-level metadata, so treat it as adjacent context. Updated from current HFEPX corpus.

Generated Apr 10, 2026, 7:12 AM · Grounded in abstract + metadata only

Key Takeaways

  • Second, we show that the Voronoi tessellation of a converged model is reshapable through margin refinement procedures (MRP): short post-hoc optimization runs that widen…
  • Fisher damage remains constant at ~5,300 positions across the validated range (λ = 0.15-0.6), achieving +28% median margin improvement at λ = 0.6 with invariant downstream…

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Verify metric definitions before comparing against your eval pipeline.

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • Second, we show that the Voronoi tessellation of a converged model is reshapable through margin refinement procedures (MRP): short post-hoc optimization runs that widen token-decision margins without retraining.
  • Fisher damage remains constant at ~5,300 positions across the validated range (λ = 0.15-0.6), achieving +28% median margin improvement at λ = 0.6 with invariant downstream benchmarks - a geometric reorganization that compresses the…
  • However, frequency and token-class audits reveal that gains concentrate in high-frequency structural tokens (84% of net corrections at λ = 0.6), with content and entity-like contributions shrinking at higher λ.

Why It Matters For Eval

  • Fisher damage remains constant at ~5,300 positions across the validated range (λ = 0.15-0.6), achieving +28% median margin improvement at λ = 0.6 with invariant downstream benchmarks - a geometric reorganization that compresses the…

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

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