Data-Free Layer-Adaptive Merging via Fisher Information for Long-to-Short Reasoning LLMs

• URL: http://arxiv.org/abs/2603.21705v1
• Date: Mon, 23 Mar 2026 08:45:37 GMT
• Title: Data-Free Layer-Adaptive Merging via Fisher Information for Long-to-Short Reasoning LLMs
• Abstract summary: We provide the first theoretical justification for layer-adaptive merging.<n>We propose textbfFIM-Merging, which computes diagonal FIM using only random token inputs.<n>Our framework also provides a unified theoretical explanation for why existing layer-adaptive methods such as ACM empirically outperform uniform merging.
• Score: 3.18088418556364
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Model merging has emerged as a practical approach to combine capabilities of specialized large language models (LLMs) without additional training. In the Long-to-Short (L2S) scenario, merging a base model with a long-chain-of-thought reasoning model aims to preserve reasoning accuracy while reducing output length. Existing methods rely on Task Arithmetic and its variants, which implicitly assume that model outputs vary linearly with the merging coefficient -- an assumption we show is systematically violated in L2S settings. We provide the first theoretical justification for layer-adaptive merging: we prove that merging error is bounded by a term proportional to the per-layer Hessian norm (Proposition~1), and establish that the Fisher Information Matrix (FIM) is a principled, computable proxy for this bound via the Fisher-Hessian equivalence at local optima. Building on this theory, we propose \textbf{FIM-Merging}, which computes diagonal FIM using only random token inputs (no domain-specific calibration data required) and uses it to assign per-layer merging coefficients. On the 7B L2S benchmark, FIM-TIES achieves state-of-the-art performance on five out of six evaluation benchmarks, including a \textbf{+6.2} point gain on MATH500 over ACM-TIES (90.2 vs.\ 84.0), while requiring no calibration data. On the 1.5B benchmark, FIM-TIES achieves an average accuracy of \textbf{47.3}, surpassing the previous best ACM-TIES (43.3) by \textbf{+3.9} points, while reducing average response length by \textbf{91.9\%} relative to the long-CoT model. Our framework also provides a unified theoretical explanation for why existing layer-adaptive methods such as ACM empirically outperform uniform merging.

Related papers

• Models for minimalist RAG: B1ade 335M Embedding and 1B Parameter Small Language Models [2.1665689529884697]
  We present B1ade, an efficient RAG architecture comprising two purpose-built components: a compact embedding model and a purpose-built SLM.<n>B1ade-embed, a 335M parameter retrieval model constructed via parameter-free fusion of five pretrained encoders achieves top MTEB scores among sub-500M models with zero additional training.<n>B1ade-1B cites retrieved passages in 42.4% of responses, exceeding the attribution rate of its training distribution by 5.5 percentage points.
  arXiv  Detail & Related papers  (2026-07-29T22:41:25Z)
• Constrained Decoding for Diffusion Language Models via Efficient Inference over Finite Automata [57.27430779838529]
  We present an exact and tractable algorithm for sampling from the constrained mean-field posterior under any constraint expressible as a finite automaton.<n>The approach guarantees constraint satisfaction by construction, supports both greedy and sampling-based decoding, and is compatible with parallel and block-wise decoding.<n> Empirical evaluations on Dream-7B and LLaDA-8 show substantial accuracy gains across various tasks.
  arXiv  Detail & Related papers  (2026-07-08T05:48:57Z)
• Closed-Form Spectral Regularization for Multi-Task Model Merging [96.82449201305234]
  Model merging combines several independently fine-tuned experts into a single multi-task model without any training data.<n>State-of-the-art merging methods formulate merging as a layer-wise interference problem.<n>We propose SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent.
  arXiv  Detail & Related papers  (2026-06-05T14:00:47Z)
• LimiX-2M: Mitigating Low-Rank Collapse and Attention Bottlenecks in Tabular Foundation Models [56.999481798138625]
  LimiX-2M is a 2M- parameter model that outperforms larger TabPFN-v2 and TabICL baselines on widely used benchmarks.<n>We present a unified tokenize-and-route framework for strong Tabular foundation models (TFMs)<n>Results highlight value-aware tokenization and readout-aligned routing as key levers for improving the accuracy--efficiency trade-off in TFMs.
  arXiv  Detail & Related papers  (2026-06-03T06:07:33Z)
• Bayesian Model Merging [17.887004278413915]
  Model merging aims to combine multiple task-specific expert models into a single model without joint retraining.<n>This paper introduces Bayesian Model Merging (BMM), a plug-and-play bi-level optimization framework.<n>BMM consistently outperforms all plug-and-play anchor baselines.
  arXiv  Detail & Related papers  (2026-05-13T00:36:47Z)
• REAL: Regression-Aware Reinforcement Learning for LLM-as-a-Judge [83.2858110368572]
  We propose textbfREAL (underlineREgression-underlineAware Reinforcement underlineLThought), a principled RL framework designed to optimize regression rewards.<n>We show that REAL consistently outperforms both regression-aware SFT baselines and standard RL methods.
  arXiv  Detail & Related papers  (2026-03-17T21:19:08Z)
• Functionality-Oriented LLM Merging on the Fisher--Rao Manifold [14.349284217707575]
  Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining.<n>We derive a practical fixed-point algorithm using a lightweight spherical proxy that preserves norms and generalizes directly to multi-expert merging.
  arXiv  Detail & Related papers  (2026-03-05T09:08:38Z)
• Correct, Concise and Complete: Multi-stage Training For Adaptive Reasoning [11.179446105672461]
  We propose a multi-stage efficient reasoning method that combines supervised fine-tuning and reinforcement learning.<n>Our approach reduces response length by an average of 28% for 8B models and 40% for 32B models.<n>It achieves a superior trade-off compared to more complex state-of-the-art efficient reasoning methods.
  arXiv  Detail & Related papers  (2026-01-06T12:31:51Z)
• DiSC-AMC: Token- and Parameter-Efficient Discretized Statistics In-Context Automatic Modulation Classification [19.190236060870184]
  Large Language Models (LLMs) can perform Automatic Modulation Classification (AMC) in an open-set manner without fine-tuning.<n>We present Discretized Statistics in-Context Automatic Modulation Classification (DiSC-AMC)<n>DiSC-AMC is a token- and parameter-efficient variant that discretizes higher-order statistics and cumulants into compact symbolic tokens.
  arXiv  Detail & Related papers  (2025-09-30T22:20:57Z)
• LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Models [95.77351099118323]
  Masked Diffusion Models (MDMs) present a promising paradigm for language modeling.<n>The challenge arises from the high variance in Evidence Lower Bound (ELBO)-based likelihood estimates required for preference optimization.<n>We propose Variance-Reduced Preference Optimization (VRPO), a framework that formally analyzes the variance of ELBO estimators and derives on both the bias and variance of preference optimization gradients.
  arXiv  Detail & Related papers  (2025-05-25T16:36:20Z)
• Token-Efficient RL for LLM Reasoning [0.02488650627593658]
  We propose reinforcement learning strategies tailored for reasoning in large language models (LLMs) under strict memory and compute limits.<n>Building on early policy gradient methods with baseline subtraction, we design critic-free methods that operate on a small, informative subset of output tokens.<n>We show that our methods raise accuracy on the SVAMP benchmark from 46% to over 70% and show strong performance on multi-digit multiplication.
  arXiv  Detail & Related papers  (2025-04-29T14:58:43Z)
• Training Deep Learning Models with Norm-Constrained LMOs [56.00317694850397]
  We propose a new family of algorithms that uses the linear minimization oracle (LMO) to adapt to the geometry of the problem.<n>We demonstrate significant speedups on nanoGPT training using our algorithm, Scion, without any reliance on Adam.
  arXiv  Detail & Related papers  (2025-02-11T13:10:34Z)
• ProofAug: Efficient Neural Theorem Proving via Fine-grained Proof Structure Analysis [50.020850767257095]
  We propose ProofAug, a procedure that equips LLMs with automation methods at various granularities.<n>Our method is validated on the miniF2F benchmark using the open-source deep-math-7b-base model and the Isabelle proof assistant.<n>We also implement a Lean 4 version of ProofAug that can improve the pass@1 performance of Kimina-Prover-seek-Distill-1.5B from 44.3% to 50.4%.
  arXiv  Detail & Related papers  (2025-01-30T12:37:06Z)
• Generative Lines Matching Models [2.6089354079273512]
  We propose a new probability flow model, which matches globally straight lines interpolating the two distributions.<n>We demonstrate that the flow fields produced by the LMM exhibit notable temporal consistency, resulting in trajectories with excellent straightness scores.<n>Overall, the LMM achieves state-of-the-art FID scores with minimal NFEs on established benchmark datasets.
  arXiv  Detail & Related papers  (2024-12-09T11:33:38Z)
• Bypass Back-propagation: Optimization-based Structural Pruning for Large Language Models via Policy Gradient [57.9629676017527]
  We propose an optimization-based structural pruning that learns the pruning masks in a probabilistic space directly by optimizing the loss of the pruned model.<n>We achieve this by learning an underlying Bernoulli distribution to sample binary pruning masks.<n>Experiments conducted on LLaMA, LLaMA-2, LLaMA-3, Vicuna, and Mistral models demonstrate the promising performance of our method in efficiency and effectiveness.
  arXiv  Detail & Related papers  (2024-06-15T09:31:03Z)
• DFedADMM: Dual Constraints Controlled Model Inconsistency for Decentralized Federated Learning [52.83811558753284]
  Decentralized learning (DFL) discards the central server and establishes a decentralized communication network. Existing DFL methods still suffer from two major challenges: local inconsistency and local overfitting.
  arXiv  Detail & Related papers  (2023-08-16T11:22:36Z)
• Squeezeformer: An Efficient Transformer for Automatic Speech Recognition [99.349598600887]
  Conformer is the de facto backbone model for various downstream speech tasks based on its hybrid attention-convolution architecture. We propose the Squeezeformer model, which consistently outperforms the state-of-the-art ASR models under the same training schemes.
  arXiv  Detail & Related papers  (2022-06-02T06:06:29Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.