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Functionality-Oriented LLM Merging on the Fisher--Rao Manifold

Jiayu Wang, Zuojun Ye, Wenpeng Yin · Mar 5, 2026 · Citations: 0

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Mar 5, 2026, 9:08 AM

Fresh

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Mar 7, 2026, 2:50 AM

Fresh

Extraction source

Persisted extraction

Confidence 0.35

Abstract

Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear averaging, task vectors, and related rules operate on Euclidean coordinates, even though the desired goal is to merge functionality, i.e., predictive behaviors across tasks. Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades accuracy. Third, many geometry-inspired methods are most natural for two-model interpolation and do not extend cleanly to merging N>2 experts with a principled objective. We address these issues by formulating model merging as computing a weighted Karcher mean on the Fisher--Rao manifold, which is locally equivalent to minimizing a KL-based function distance between predictive distributions. We derive a practical fixed-point algorithm using a lightweight spherical proxy that preserves norms and generalizes directly to multi-expert merging. Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.

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  • Extraction confidence is 0.35 (below strong-reference threshold).
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HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

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Background context only

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Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

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Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

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Field Provenance & Confidence

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Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics.

Evaluation Modes

partial

Automatic Metrics

Confidence: Low Source: Persisted extraction evidenced

Includes extracted eval setup.

Evidence snippet: Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics.

Reported Metrics

partial

Accuracy

Confidence: Low Source: Persisted extraction evidenced

Useful for evaluation criteria comparison.

Evidence snippet: Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades accuracy.

Rater Population

partial

Domain Experts

Confidence: Low Source: Persisted extraction evidenced

Helpful for staffing comparability.

Evidence snippet: Third, many geometry-inspired methods are most natural for two-model interpolation and do not extend cleanly to merging N>2 experts with a principled objective.

Human Data Lens

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

Evaluation Lens

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.35
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

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

Reported Metrics

accuracy

Research Brief

Deterministic synthesis

Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades… HFEPX signals include Automatic Metrics with confidence 0.35. Updated from current HFEPX corpus.

Generated Mar 7, 2026, 2:50 AM · Grounded in abstract + metadata only

Key Takeaways

  • Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage…
  • Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Validate metric comparability (accuracy).

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, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades…
  • Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.

Why It Matters For Eval

  • Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • 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.

  • Pass: Metric reporting is present

    Detected: accuracy

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