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Parameter-Efficient Fine-Tuning of LLMs with Mixture of Space Experts

Buze Zhang, Jinkai Tao, Zilang Zeng, Neil He, Ali Maatouk, Menglin Yang, Rex Ying · Feb 16, 2026 · Citations: 0

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Data freshness

Extraction: Fresh

Check recency before relying on this page for active eval decisions. Use stale pages as context and verify against current hub results.

Metadata refreshed

Feb 16, 2026, 6:07 AM

Stale

Extraction refreshed

Apr 13, 2026, 3:34 AM

Fresh

Extraction source

Persisted extraction

Confidence 0.25

Abstract

Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation. However, existing PEFT methods mainly operate in Euclidean space, fundamentally limiting their capacity to capture complex geometric structures inherent in language data. While alternative geometric spaces, like hyperbolic geometries for hierarchical data and spherical manifolds for circular patterns, offer theoretical advantages, forcing representations into a single manifold type ultimately limits expressiveness, even when curvature parameters are learnable. To address this, we propose Mixture of Space (MoS), a unified framework that leverages multiple geometric spaces simultaneously to learn richer, curvature-aware representations. Building on this scheme, we develop MoSLoRA, which extends Low-Rank Adaptation (LoRA) with heterogeneous geometric experts, enabling models to dynamically select or combine appropriate geometric spaces based on input context. Furthermore, to address the computational overhead of frequent manifold switching, we develop a lightweight routing mechanism. Moreover, we provide empirical insights into how curvature optimization impacts training stability and model performance. Our experiments across diverse benchmarks demonstrate that MoSLoRA consistently outperforms strong baselines, achieving up to 5.6% improvement on MATH500 and 15.9% on MAWPS.

Low-signal caution for protocol decisions

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.25 (below strong-reference threshold).
  • No explicit evaluation mode was extracted from available metadata.
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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.

Best use

Background context only

Use if you need

Background context only.

Main weakness

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

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

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Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation.

Evaluation Modes

missing

None explicit

Confidence: Low Source: Persisted extraction missing

Validate eval design from full paper text.

Evidence snippet: Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation.

Benchmarks / Datasets

partial

MATH 500

Confidence: Low Source: Persisted extraction evidenced

Useful for quick benchmark comparison.

Evidence snippet: Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation.

Reported Metrics

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No metric anchors detected.

Evidence snippet: Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation.

Rater Population

partial

Domain Experts

Confidence: Low Source: Persisted extraction evidenced

Helpful for staffing comparability.

Evidence snippet: Building on this scheme, we develop MoSLoRA, which extends Low-Rank Adaptation (LoRA) with heterogeneous geometric experts, enabling models to dynamically select or combine appropriate geometric spaces based on input context.

Human Data Lens

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

Evaluation Lens

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.25
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

MATH-500

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Deterministic synthesis

To address this, we propose Mixture of Space (MoS), a unified framework that leverages multiple geometric spaces simultaneously to learn richer, curvature-aware representations. HFEPX protocol signal is limited in abstract-level metadata, so treat it as adjacent context. Updated from current HFEPX corpus.

Generated Apr 13, 2026, 3:34 AM · Grounded in abstract + metadata only

Key Takeaways

  • To address this, we propose Mixture of Space (MoS), a unified framework that leverages multiple geometric spaces simultaneously to learn richer, curvature-aware representations.
  • Building on this scheme, we develop MoSLoRA, which extends Low-Rank Adaptation (LoRA) with heterogeneous geometric experts, enabling models to dynamically select or combine…
  • Our experiments across diverse benchmarks demonstrate that MoSLoRA consistently outperforms strong baselines, achieving up to 5.6% improvement on MATH500 and 15.9% on MAWPS.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Cross-check benchmark overlap: MATH-500.
  • 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

  • To address this, we propose Mixture of Space (MoS), a unified framework that leverages multiple geometric spaces simultaneously to learn richer, curvature-aware representations.
  • Building on this scheme, we develop MoSLoRA, which extends Low-Rank Adaptation (LoRA) with heterogeneous geometric experts, enabling models to dynamically select or combine appropriate geometric spaces based on input context.
  • Furthermore, to address the computational overhead of frequent manifold switching, we develop a lightweight routing mechanism.

Why It Matters For Eval

  • Our experiments across diverse benchmarks demonstrate that MoSLoRA consistently outperforms strong baselines, achieving up to 5.6% improvement on MATH500 and 15.9% on MAWPS.

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.

  • Pass: Benchmark or dataset anchors are present

    Detected: MATH-500

  • Gap: Metric reporting is present

    No metric terms extracted.

Category-Adjacent Papers (Broader Context)

These papers are nearby in arXiv category and useful for broader context, but not necessarily protocol-matched to this paper.

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