PACT: Preserving Anchored Cores in Task-vectors for Model Merging

Abstract: Model merging has emerged as a training-free alternative to multi-task learning, aiming to combine multiple task-specific fine-tuned models into a single multi-task model. Most existing model merging approaches follow the Task Arithmetic paradigm, which decomposes fine-tuned weights into pre-trained parameters and task vectors, and performs merging exclusively in the task-vector space. The effectiveness of this paradigm implicitly relies on the assumption that task-specific knowledge is encoded solely within task vectors. We argue that this assumption generally does not hold due to the intrinsic task preferences of pre-trained models. Specifically, we identify \textbf{Load-Bearing Wall (LBW) dimensions}, namely some task-critical knowledge that remains embedded in the pre-trained weights rather than being fully transferred into task vectors. We characterize LBW dimensions from both scalar-weight and subspace perspectives, thereby covering the major paradigms of existing model merging methods. Our analysis reveals that, by ignoring LBW dimensions, task-vector-based approaches fail to fully resolve task conflicts and may inadvertently damage task-specific knowledge encoded in the pre-trained model, leading to degradation. To address this issue, we propose PACT, which preserves the anchored task-specific cores (i.e., LBW dimensions) within task vectors by aligning their orthogonal complements with the subspace of the pre-trained weights. These aligned subspace components are then removed from the task vectors before applying existing model merging algorithms. Furthermore, we develop an efficient variant based on randomized SVD to improve scalability. PACT can be seamlessly integrated with existing methods. Extensive experiments across multiple benchmarks demonstrate that PACT consistently enhances mainstream model merging approaches and establishes new state-of-the-art performance.

Ningyuan Shi
Zhipeng Zhou
Hao Wang
Chunyan Miao
Peilin Zhao


Essential Subspace Merging for Multi-Task Learning

Abstract: Model merging aims to enable multi-task learning by integrating the capabilities of multiple models fine-tuned from the same pre-trained checkpoint into a single model. Its core challenge is inter-task interference among task-specific parameter updates. In this paper, we analyze the output shifts induced by task updates and observe that their energy is concentrated in a small number of principal directions. We call the subspace spanned by these directions the essential subspace. In contrast, most remaining directions carry little task-relevant energy, but their accumulation across multiple task updates can cause severe interference during merging. Motivated by this observation, we propose Essential Subspace Decomposition (ESD), which decomposes each task update according to the principal components of its activation shift. Based on ESD, we introduce Essential Subspace Merging (ESM), a training-free static merging method that orthogonalizes and fuses essential components into one compact multi-task model. We further extend ESM to ESM++, a training-free dynamic merging method that decomposes task-specific residuals into low-rank experts and selects the most relevant expert through prototype-based routing during forward inference. Extensive experiments across multiple task sets and model scales demonstrate that ESM and ESM++ effectively preserves task knowledge while reducing inter-task interference.


Enhancing Multilingual Reasoning via Steerable Model Merging

Abstract: Model merging is an effective technique for composing the capabilities of a multilingual model and a reasoning model. It has achieved promising generalization in multilingual reasoning tasks by aligning feature spaces of different models. However, the merged single model often fails to address the conflicts between source models, leading to suboptimal performance. In other words, the one-size-fits-all merging strategy may not align with the characteristics of different inputs which may require prioritizing certain models over others. To this end, we propose a Steerable Model Merging (ST-Merge) framework to modulate the contribution of each source model. To realize this idea, we introduce a gated cross-attention mechanism to weight or filter the two attended source models in an adaptive manner. Extensive experiments demonstrate that ST-Merge consistently outperforms multiple strong baselines on four multilingual reasoning benchmarks across 21 different languages.

Zhuoran Li
Rui Xu
Jian Yang
Junnan Liu
Zhijun Chen
Qianren Mao
Hongcheng Guo
Jiaheng Liu
Likang Xiao
Ming Li
Xiaojie Wang


Task-Restricted Symmetries in Recurrent Weight Space

Abstract: Recurrent networks can contain substantial functional redundancy in weight space: changing a recurrent matrix may leave the input-output rollout nearly unchanged on a task distribution, while similar-scale changes can destroy the same behavior. We study this redundancy in one-layer tanh RNNs using ordered real Schur coordinates. The Schur form separates spectral blocks from directed nonnormal couplings, giving a diagnostic basis for structured ablations that keep the input and readout maps fixed. In a fixed-length copy task, selected nonnormal Schur couplings can be removed with little loss in some trained solutions, whereas other couplings are necessary for accurate autonomous replay. Across flip-flop, sine generation, and context-dependent integration, the loss-preserving ablation profile varies across tasks and trained solutions. These results identify candidate approximate functional invariances, not universal symmetries of recurrent weight space. Schur-coordinate ablations provide a practical diagnostic for which structured perturbations preserve a trained recurrent solution and which ones disrupt its computation.


Post-Hoc Merging is Not Enough: Many-Shot Model Merging with Loss-Gap Balancing

Abstract: Model merging has become a practical post-training strategy for building a single multi-task large language model (LLM) by combining multiple task-specialized models. However, most existing approaches rely on post-hoc merging, in which task-specific models are merged only once after training. This one-shot aggregation often suffers from task interference, leading to information erasure across individual tasks. In this work, we show that replacing post-hoc merging with an iterative many-shot merging protocol is effective in improving multi-task performance. Building on this insight, we propose METIS, Mitigating Erasure from Task Interference for Stable many-shot merging. METIS is a loss-aware many-shot merging method that addresses information erasure in post-hoc merging through task-wise loss-gap weighting and consensus-based masking. Notably, METIS exhibits significant performance improvement on the worst-performing task, effectively mitigating information erasure. (Project page: https://imkyungjin.github.io/METIS/)

Kyungjin Im
Miru Kim
Chanin Eom
Minhae Kwon


From Parameters to Feature Space: Task Arithmetic for Backdoor Mitigation in Model Merging

Abstract: Model merging (MM) has gained significant attention as a cost-effective approach to integrate multiple task-specific models into a unified model. However, recent work reveals that MM is highly susceptible to backdoor attacks. Existing defenses based on task arithmetic often fail to eliminate backdoors without substantially degrading clean-task performance, owing to their reliance on direct parameter-space editing. To address this gap, we propose Linear Feature Path Minimization (LFPM), a backdoor mitigation framework for model merging, which introduces an anti-backdoor task vector into the backdoored merged model. Unlike prior approaches, LFPM formulates the backdoor robustness of the merged model from a unified feature-space perspective under the Cross-Task Linearity (CTL) framework, which leverages the approximate linearity of features across tasks. This perspective guides the optimization of the anti-backdoor task to suppress backdoors while preserving clean-task performance. Furthermore, we introduce an effective optimization mechanism based on gradient accumulation and loss path-integral, ensuring robust backdoor suppression along the interpolation path. Extensive experiments demonstrate that LFPM consistently exhibits strong robustness against backdoor attacks in both full fine-tuning and Parameter-Efficient Fine-Tuning (PEFT) settings.

Zhenqian Zhu
Yamin Hu
Yiya Diao
Weixiang Li
Haodong Li
Wenjian Luo


Closed-Form Spectral Regularization for Multi-Task Model Merging

Abstract: Model merging combines several independently fine-tuned experts into a single multi-task model without any training data, reducing the storage, serving, and decentralized-development costs of large foundation models. State-of-the-art merging methods formulate merging as a layer-wise quadratic interference minimization problem. Although this problem admits an exact closed-form pseudoinverse solution, that solution underperforms hundreds of iterations of gradient descent in practice. The iterative loop dominates the cost of the pipeline, yet its effectiveness has remained unexplained. We revisit this regime and show that the iterative solver does not primarily act as an optimizer; rather, it serves as an implicit spectral regularizer for an ill-posed normal equation, where small-eigenvalue directions of the per-layer interference operator amplify proxy noise. Building on this finding, we formalize multi-task model merging as a noisy linear inverse problem and propose a spectral filtering estimator parameterized by a per-direction filter. We instantiate this estimator with SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent, with a hard top-K truncation that suppresses noise-amplifying small-eigenvalue directions. Furthermore, we propose SWUDI-A, an adaptive variant that replaces the global rank hyperparameter with per-layer rank rules, further improving robustness across architectures. Both variants share a single symmetric eigendecomposition per linear layer and require no training data or optimizer state. Across four general benchmarks and a multimodal merging benchmark spanning VQA, Geometry, Chart, OCR, Grounding, and modality merging, our proposed spectral solvers match or outperform state-of-the-art merging methods. Crucially, they reduce wall-clock time by 28-72x and peak GPU memory by up to 50%.

Yongxian Wei
Runxi Cheng
Xingxuan Zhang
Li Shen
Chun Yuan
Peng Cui
Dacheng Tao


TaDA: Calibrated Probe Gating for Task-Domain LoRA Merging

Abstract: Combining a task LoRA adapter with a domain LoRA adapter into a single unified model is a practical yet largely unexplored challenge. Existing methods treat both adapters as symmetric peers, applying uniform weights across all layers. We argue that task and domain adapters exhibit a consistent depth-dependent asymmetry across transformer architectures. Domain dominance increases with layer depth, while shallower layers retain stronger task-relevant signals. Motivated by this observation, we propose $\textbf{TaDA}$ ($\textbf{Ta}$sk-$\textbf{D}$omain LoR$\textbf{A}$ Merging), a training-free algorithm that exploits this structure through calibrated probe-guided per-layer gating and per-component subspace-aware merging. The gating assigns individual weights per layer and projection type using a probe signal proved invariant to adapter weight magnitude. The merging discards conflicting singular directions before combining the remaining components. $\textbf{TaDA}$ produces a standard rank-$r$ LoRA adapter with zero inference overhead. On six scientific QA benchmarks with Llama-2-7B, TaDA achieves an average accuracy of 0.452, outperforming DARE-TIES by +3.6 percentage points and obtaining the best result on all six benchmarks. On six image classification benchmarks with ViT-L/16, TaDA reaches 85.9\% average accuracy, improving over the strongest merging baseline while leading in three of the six individual benchmarks.

Huy Quoc To
Fuyi Li
Guangyan Huang
Ming Liu


RogueMerge: Robust and Unified Attacks against LLM Model Merging

Abstract: Model merging composes specialized capabilities into a single LLM by aggregating task vectors sourced from unverified public platforms, exposing a critical supply-chain attack surface: Because any malicious behavior can be encoded into a task vector, and merging grants third-party vectors direct write access to model weights, an attacker-provided task vector can enable or amplify diverse downstream threats. Prior work studies only backdoor attacks against model merging for classifiers using static arithmetic heuristics, which fail to effectively handle diverse attacks on generative LLMs for three reasons. (i) LLMs rely on autoregressive decoding, where the minor parameter drift introduced by merging compounds across tokens and rapidly degrades the attack. (ii) Attackers have no knowledge of the victim's merging configurations, causing a static attack vector optimized in isolation to be easily diluted or destroyed. (iii) Practical threat induction must generalize to attack prompts unseen during optimization, which static vectors cannot adequately encode. We present RogueMerge, the first principled, unified framework that addresses all three challenges. To handle autoregressive generation, we replace static arithmetic with a joint optimization that explicitly enforces attack success after merging. To handle unknown merging settings, we formulate attack injection as a stochastic min-max problem and solve it via meta-learning-style simulation. To generalize across heterogeneous attack prompts, we employ distributionally robust optimization and derive a tractable first-order Taylor approximation at LLM scale, with a provable error bound. Across four threats, six merging algorithms, and over 170 merged LLMs, RogueMerge consistently outperforms existing attacks. It also remains stable across diverse merging settings and resists standard defenses.

Jinghuai Zhang
Yetian He
Kunlin Cai
Han Zhao
Fnu Suya
Yuan Tian


Decentralized Instruction Tuning: Conflict-Aware Splitting and Weight Merging

Abstract: Instruction tuning aligns large language models, including multimodal ones, with diverse user intents, but scaling to heterogeneous mixtures is hindered by gradient interference and bandwidth-heavy synchronization. We ask whether these two bottlenecks can be addressed jointly by training parts of the mixture independently and reconciling them once in parameter space. We develop a local quadratic theory inside a shared flat basin that yields three results: weight merging produces a curvature-weighted variance reduction; PCA-aligned conflict splitting maximizes this gain along high-curvature directions; and merging additionally acts as spectral filtering with implicit norm regularization. These results directly motivate MERIT, a decentralized merge-ready instruction-tuning pipeline that estimates dataset-level gradient conflicts, partitions the mixture along the top PCA conflict axes, fine-tunes each partition independently with no inter-partition communication, and merges once via token-weighted averaging. On Qwen2.5-VL-3B with 136 Vision-FLAN tasks, MERIT improves the 8-benchmark average from 54.3 (joint training) to 57.0. The same recipe scales to a 7B model on a 1.6M-example, 176-source mixture -- matching or exceeding centralized joint training with minimal cost overhead -- and transfers to text-only FLAN. Our code is available at https://github.com/naver-ai/merit.


ThinkSwitch: Context Distillation with LoRA and Weight Interpolation for Specific-Purpose Reasoning Tasks

Abstract: Large language models often improve on difficult tasks by spending inference-time compute on a reasoning trace before producing the final answer. That extra computation can be useful, but it also raises latency, token cost, and deployment complexity. We introduce \textbf{ThinkSwitch}, a low-compute procedure for co-training paired instruct and thinking checkpoints. Starting from compatible Qwen3-4B instruct and thinking models, each iteration asks the thinking checkpoint to generate answers, removes the reasoning trace, distills the answer-only pairs into the instruct checkpoint with QLoRA, and reconstructs a thinking checkpoint with spherical weight interpolation. The only human-supplied inputs are task prompts; the labels are generated by the model itself. On a 30-question AIME 2026 evaluation, ThinkSwitch improves the instruct checkpoint from 10/30 to 20/30 and the thinking checkpoint from 14/30 to 22/30. On a 30-question PubMedQA subset, it improves the instruct checkpoint from 13/30 to 18/30 and the thinking checkpoint from 18/30 to 25/30. The complete experiment uses 15 training prompts per domain and costs \$2.86 on a single cloud RTX 3070. The results are small-scale, but they indicate that targeted distillation loops can move part of the benefit of explicit reasoning into weights while preserving a separate thinking mode.


Saliency-Aware Model Merging

Abstract: Model merging aims to consolidate multiple task-specific models fine-tuned on different datasets into a unified architecture that performs cross-domain proficiency. Current data-free model merging methods often struggle to scale as they rely on simple parameter-level heuristics that ignore inter-layer dependencies and non-uniform distribution of expertise. This work proposes SA-Merging, which is built upon connectivity-based saliency formulations from structural pruning (e.g., SynFlow) and extends them to the data-free model merging setting. We define a saliency score over task vectors relative to a shared base model, and further introduce merge-aware modulation that incorporates agreement across experts to mitigate task interference. Based on this formulation, an iterative saliency-aware merging procedure progressively removes non-informative updates while preserving end-to-end connectivity. Furthermore, we extend SA-Merging to introduce rank-wise saliency decomposition for LoRAs without compromising their structural integrity. Extensive experiments on vision and language tasks demonstrate the effectiveness of our saliency-based approach, further reducing the gap between data-free and test-time adaptation methods.


Access Sets Matter: Budgeting Expert Reads for Scalable Weight-Space Model Merging

Abstract: Weight-space model merging is usually formulated as an algebraic operation on checkpoints, yet at LLM scale the limiting resource is often the set of expert weights that must be read. We introduce MergePipe, a budget-aware execution layer that casts LLM merging as an \emph{expert access-set} problem: given a merge operator and a checkpoint family in a shared weight coordinate system, choose which expert delta blocks to access under an explicit I/O budget. MergePipe indexes parameter blocks, builds deterministic access plans, and executes the induced budgeted merge with replayable manifests. The plan is budget-sound by construction and recovers the full-read merge at full budget; for fixed-coefficient additive operators, the omitted-update error is bounded by the norm of omitted deltas. Across Qwen and Llama merging workloads, MergePipe reduces expert-read I/O by up to an order of magnitude and achieves up to $11\times$ speedups. Representative budget sweeps show $O(10^{-3})$ parameter deviation from full-read merges and no monotonic degradation on downstream benchmarks.

Yuanyi Wang
Yanggan Gu
Su Lu
Yifan Yang
Zhaoyi Yan
Congkai Xie
Jianmin Wu
Hongxia Yang


Model Merging by Output-Space Projection

Abstract: Model merging combines fine-tuned checkpoints into a single multi-task model without retraining. Existing methods - such as task arithmetic, model soups, TIES, and DARE - are computationally efficient and empirically successful, but rely on heuristic design choices and lack formal optimality guarantees. We show that merging can be formulated as a convex quadratic programme over residual updates, yielding weights that minimise a squared-output calibration objective using calibration inputs and fine-tuned model outputs, and subsuming existing methods as special cases. Our framework yields a closed-form diagnostic - the fraction of residual energy captured by a chosen basis - that predicts downstream merge quality using only the calibration set. Empirically, the QP matches or outperforms existing methods in the single-layer setting, and we characterise when the optimal basis provides significant gains over the cheaper diagonal QP. We extend to multi-layer merging via a sequential layer-wise algorithm and demonstrate consistent gains across language and vision benchmarks.

Bethan Evans
Benjamin Etheridge
Stephen Roberts
Jared Tanner


What-If World: A Causal Benchmark for General World Models in Embodied Scenarios

Abstract: Video generation models are increasingly used as world simulators for tasks like driving and robotic manipulation. What matters in these settings is not whether a single video looks right, but whether the model's output changes when its input changes. We test this by giving a model two prompts describing the same scene with one physical detail varied, and checking whether the two videos diverge the way physics predicts. The wording difference between the prompts is small by design, since only one variable is changed, but the correct physical difference is not. A model that misses this can still produce two videos that each look plausible individually, and existing benchmarks score videos one at a time and cannot detect this failure. We introduce What-If World, 319 such prompt pairs built on real frames from nuScenes and DROID, organized by a taxonomy of six physical variables shared across driving and manipulation. Each pair is scored with APEO, a four-part rubric checking whether each video follows its prompt (Adherence), is physically consistent (Physics), preserves the shared scene (Environment), and ends in the correct difference (Outcome). Across nine state-of-the-art models, no system exceeds 52% on the paired score, and open-source models cluster near 28%. Every model tested fails on a large fraction of causal interventions, indicating substantial room before these models can reliably support action-conditioned simulation or model-based planning. Where models do score well, performance appears to track the visual prominence of the intervention rather than the tractability of its underlying physics. Some visually subtle interventions score as low as 14.2%, while visually pronounced ones reach 40.4%.

Kunlin Cai
Rui Song
Jinghuai Zhang
Kaiyuan Zhang
Pranav Bodapati
Alicia Yu
Fnu Suya
Mohammad Rostami
Jiaqi Ma
Yuan Tian


Model Merging on Loss Landscape: A Geometry Perspective

Abstract: Model merging offers a promising avenue for knowledge integration and parallel development without retraining. Yet, existing methods either ignore the geometry of the loss landscape or rely on intractable full-space Hessian approximations. We propose EpiMer, a framework that casts model merging as solving the Fréchet mean on a Riemannian manifold and restricts the computation to a low-rank subspace spanned by the task vectors. With the expected Hessian as the metric, we reveal a connection between local curvature and epistemic uncertainty of the parameters. Our theoretical analysis decomposes the merging error bound into the subspace Fréchet variance and the residual energy, and provides a closed-form characterization of when curvature-aware merging provably outperforms flat-geometry methods. In addition, our framework unifies both curvature-aware methods and recent spectral methods as special cases of the subspace Fréchet mean with different geometric metrics. Merging fine-tuned CLIP-ViT models on eight image classification tasks, Epistemic Merging strictly outperforms the baselines on all three CLIP-ViT backbones at matched rank, improving the across-task average accuracy and worst-task accuracy on every backbone.

Juanwu Lu
Anand Bhaskar
Brian Axelrod
Ekaterina Tolstaya
Tristan Emrich


On the Limits of Model Merging for Multilinguality in Pre-Training

Abstract: Endowing models with consistent multilingual performance can be achieved by mixing pre-training data, or post-training approaches such as language-specific model merging. In this work, we test whether merging can be applied to monolingually pre-trained models. We conduct a controlled study on the efficacy of mixed, merged, and monolingual pre-training setups. We find that while monolingual pre-training results in strong in-language performance, merging any combination of monolingual models leads to performance collapse due to interference. Our analysis suggests representational similarity is a prerequisite for model merging. We therefore conclude that the flexibility of merging in fine-tuning does not extend trivially to language-specific pre-training.

Seth Aycock
Fedor Vitiugin
Aleksandr Umnov
Christof Monz
Khalil Sima'an


Causal Physics Steering in Video World Models via Concept Activation Vectors

Abstract: Video world models learn representations of physical dynamics, but controlling their physical expectations at inference time remains an open problem. Recent interpretability work identified a Physics Emergence Zone (PEZ), a group of middle transformer layers in VideoMAE where physical plausibility is represented separately from other visual features. However, it remained unclear whether this structure could be used to directly control the model's physics reasoning. We present physics steering, a training-free method that uses the weight vector of a linear probe at a PEZ layer as a Concept Activation Vector (CAV) and injects it into hidden states during inference. This shifts the model's physical expectations without changing any model weights. On the IntPhys benchmark, this intervention reliably shifts the model's plausibility judgment in either direction, depending on the steering sign. The effect appears only when the intervention is applied within the Physics Emergence Zone, suggesting that the relevant physics representation is localized there. We further find that physics is encoded separately from motion direction, and that different intuitive physics principles occupy distinct directions within this representation space. Together, these results show that physical reasoning in VideoMAE is not only readable, but also directly steerable.


GEM-4D: Geometry-Enhanced Video World Models for Robot Manipulation

Abstract: Video world models can generate realistic futures from a single instruction, but they often fail to track the same physical points consistently across time. As a result, the generated videos appear plausible, yet lack the physical grounding required for reliable action execution, such as robot manipulation. We present GEM-4D, a geometry-grounded video world model that resolves this limitation by injecting dense 4D correspondence supervision distilled from a pretrained geometry foundation model into the video generative backbone during training. This supervision enables the model to jointly capture appearance and geometric structure while retaining a single-stream architecture with no additional inference cost. We further introduce an inverse dynamics module that converts correspondence-consistent video rollouts into executable robot trajectories, enabling direct deployment in both real-world and simulated manipulation. GEM-4D achieves state-of-the-art performance on both video prediction and geometric consistency across both simulation and realistic scenarios and improves real-world manipulation success from 61% to 81%. Additional results are available at https://gem-4d.github.io/.

Kaichen Zhou
Yuzhen Chen
Fangneng Zhan
Hang Hua
Grace Chen
Xinhai Chang
Ao Qu
Yilun Du
Zhuang Liu
Paul Pu Liang
Mengyu Wang


Tunable MAGMAX: Preference-Aware Model Merging for Continual Learning

Abstract: Continual learning (CL) aims to train models sequentially on multiple tasks while mitigating catastrophic forgetting of previously learned knowledge. Recent advances in large pre-trained models (LPMs) and model merging techniques, such as MAGMAX, have demonstrated effective CL performance by combining task-specific parameters. However, existing methods primarily focus on average performance across all tasks and do not adequately address how to construct models accommodating different deployment environments or varying user preferences. This paper proposes a model merging framework, termed Tunable MAGMAX, which enables preference-aware control of task-specific performance in CL. Our method introduces a preference vector that controls the number of elements selected from each task vector during model merging, allowing us to adjust the merged model performance according to their deployment needs. We further propose a method for automatically constructing appropriate preference vectors by leveraging small amounts of target environment data and datasets from model training tasks, thereby eliminating the need for manual specification. The experimental result on CL benchmark tasks demonstrates that Tunable MAGMAX effectively controls task-wise performance and successfully adapts merged models to various target environments. The proposed Tunable MAGMAX achieves superior or comparable performance to baseline methods, making it a practical solution for deploying CL models to various environments where the preferences of each task performance differ.

Kei Hiroshima
Kento Uchida
Shinichi Shirakawa


Unlocking the Potential of Continual Model Merging: An ODE Perspective

Abstract: Continual Model Merging (CMM) enables rapid customization of foundation models by sequentially incorporating task-adapted models without repeated retraining. However, existing merging rules usually update the deployed model through fixed algebraic or projection-based operations, providing limited control over how much previously accumulated knowledge should be retained relative to the incoming task model. This limitation leads to unstable retention and performance degradation in long task streams, and becomes more pronounced when tasks have heterogeneous utilities. We propose ODE-driven Merging (ODE-M), a controllable framework that formulates each continual merge as a trajectory in parameter space rather than a one-step endpoint update. Motivated by mode connectivity, ODE-M constructs a barrier-aware trajectory using a rectified time-dependent velocity field, where lightweight first-order feedback from a small calibration set suppresses loss-increasing motion while preserving progress toward the incoming model. The next merged model is then obtained by selecting an operating point along this trajectory through a utility-aware time schedule, providing an explicit mechanism for balancing retained historical knowledge and incoming task expertise. Extensive experiments on standard CMM benchmarks show that ODE-M consistently improves over strong continual merging baselines across CLIP ViT backbones, stream lengths, and heterogeneous task-utility settings.


Distilling Linearized Behavior into Non-Linear Fine-Tuning for Effective Task Arithmetic

Abstract: Task vector composition has emerged as a promising paradigm for editing pre-trained models, enabling model merging through addition and unlearning through subtraction. Fine-tuning in the tangent space of a pre-trained model (linear fine-tuning) has proven effective, as it produces task vectors that are naturally disentangled and resistant to interference. However, linearized models suffer from limited expressivity during training and incur higher computational costs at inference time, which restrict their practical applicability. In this work, we bridge the gap between linear and standard non-linear fine-tuning. We show that linearity with respect to weight perturbations, a property defined in parameter space, can be enforced through constraints in activation space during training. Concretely, we distill hidden representations from a curvature-regularized linearized teacher into a non-linear student trained via conventional fine-tuning. We find that the resulting model inherits key properties of linearized models for task arithmetic, enabling effective composition of task vectors and achieving strong performance across vision and language benchmarks without incurring any inference-time overhead.

Thomas Sommariva
Francesca Morandi
Simone Calderara
Angelo Porrello


Dynamic Model Merging Made Slim

Abstract: Model merging enables the reuse of fine-tuned models without joint training or access to original data. Dynamic merging further improves flexibility by selectively activating task-relevant parameters and efficiently composing experts across multiple tasks. However, existing dynamic methods either maintain a full shared model with tiny experts or allocate excessive capacity to experts, leading to suboptimal accuracy--efficiency trade-offs. To address this, we propose DiDi-Merging, a slim dynamic merging framework that leverages differentiable rank allocation to balance shared and expert parameters. By formulating parameter budgeting as differentiable rank optimization in low-rank modules and introducing a data-free refinement step to recover task fidelity, DiDi-Merging matches prior dynamic baselines at only 1.24x the parameters of a single fine-tuned model and surpasses them at 1.4x, substantially more compact than methods requiring > 2x storage. DiDi-Merging applies across vision, language, and multimodal tasks.


E-PMQ: Expert-Guided Post-Merge Quantization with Merged-Weight Anchoring

Abstract: Low-resource deployment constraints have made model quantization essential for deploying neural networks while preserving performance. Meanwhile, model merging has become an increasingly practical low-resource strategy for integrating multiple task- or domain-specialized experts into a single model without joint training or multi-model serving. Together, quantization and model merging enable an efficient low-resource deployment pipeline by integrating multiple experts into one low-bit model. We formulate this setting as Post-Merge Quantization (PMQ). We show that directly applying post-training quantization (PTQ) to a merged model is unreliable because two distinct deviations are coupled: the quantization deviation introduced by low-bit reconstruction and the expert-relative merging deviation inherited from model merging. To mitigate these deviations, we propose E-PMQ, an expert-guided PMQ framework that uses source expert weights to provide expert- guided output targets during layer-wise calibration, together with merged-weight anchoring to stabilize the calibration and preserve the integrated behavior of the merged model. On CLIP-ViT-B/32 eight-task merging, E-PMQ improves 4-bit GPTQ from 65.0% to 73.6% under Task Arithmetic and from 69.1% to 74.8% under TIES-Merging. On harder settings, E-PMQ improves GPTQ from 34.8% to 76.7% on 20-task CLIP-ViT-L/14 and from 78.26% to 83.34% on FLAN-T5- base GLUE. These results demonstrate that E-PMQ enables effective post-merge quantization and low-bit deployment.

Wenjun Wang
Yanggan Gu
Shuo Cai
Yuanyi Wang
Pengkai Wang
Jianmin Wu
Hongxia Yang


Bayesian Model Merging

Abstract: Model merging aims to combine multiple task-specific expert models into a single model without joint retraining, offering a practical alternative to multi-task learning when data access or computational budget is limited. Existing methods, however, face two key limitations: (1) they overlook the valuable inductive bias of strong anchor models and estimate the merged weights from scratch, and (2) they rely on a shared hyperparameter setting across different modules of the network, lacking a global optimization strategy. This paper introduces Bayesian Model Merging (BMM), a plug-and-play bi-level optimization framework, where the inner level formulates the model merging as an activation-based Bayesian regression under a strong prior induced by an anchor model, yielding an efficient closed-form solution; and the outer level leverages a Bayesian optimization procedure to search module-specific hyperparameters globally based on a small validation set. Furthermore, we reveal a key alignment between activation statistics and task vectors, enabling us to derive a data-free variant of BMM that estimates the Gram matrix for regression without any auxiliary data. Across extensive benchmarks, including up to 20-task merging in vision and 5-task merging in language, BMM consistently outperforms all plug-and-play anchor baselines (e.g., TA, WUDI-Merging, and TSV). In particular, on the ViT-L/14 benchmark for 8-task merging, a single merged model reaches 95.1, closely matching the average performance of eight task-specific experts (95.8).


FeatCal: Feature Calibration for Post-Merging Models

Abstract: Model merging combines task experts into one model and avoids joint training, retraining, or deploying many expert models, but the merged model often still underperforms task experts. We study this performance gap through feature drift, the difference between features produced by the merged model and by the expert on the same input. Our theory decomposes this drift into upstream propagation and local mismatch, tracks how it propagates and combines through later layers in forward order, and links final feature drift to output drift. This view motivates FeatCal, which uses a small calibration set to calibrate the merged model weights layer by layer in forward order, reducing feature drift while staying close to merged weights and preserving the benefits of model merging. FeatCal uses an efficient closed-form solution to update model weights, with no gradient descent, iterative optimization, or extra modules. On the main CLIP and GLUE benchmarks, FeatCal beats Surgery and ProbSurgery, the closest post-merging calibration baselines: 85.5% vs. 77.0%/78.8% on CLIP-ViT-B/32 Task Arithmetic (TA) and 85.2% vs. 83.7%/82.2% on FLAN-T5-base GLUE. On CLIP-ViT-B/32, 8 examples per task reach 82.9%, and 256 examples per task take 53 seconds, about 4x faster than both baselines, showing better sample efficiency and lower calibration cost.

Yanggan Gu
Shuo Cai
Zihao Wang
Wenjun Wang
Yuanyi Wang
Pengkai Wang
Sirui Huang
Su Lu
Jianmin Wu
Hongxia Yang


EHR-RAGp: Retrieval-Augmented Prototype-Guided Foundation Model for Electronic Health Records

Abstract: Electronic Health Records (EHR) contain rich longitudinal patient information and are widely used in predictive modeling applications. However, effectively leveraging historical data remains challenging due to long trajectories, heterogeneous events, temporal irregularity, and the varying relevance of past clinical context. Existing approaches often rely on fixed windows or uniform aggregation, which can obscure clinically important signals. In this work, we introduce EHR-RAGp, a retrieval-augmented foundation model that dynamically integrates the most relevant patient history across diverse clinical event types. We propose a prototype-guided retrieval module that acts as an alignment mechanism and estimates the relevance of retrieved historical chunks with respect to a given prediction task, guiding the model towards the most informative context. Across multiple clinical prediction tasks, EHR-RAGp consistently outperforms state-of-the-art EHR foundation models and transformer-based baselines. Furthermore, integrating EHR-RAGp with existing clinical foundation models yields substantial performance gains. Overall, EHR-RAGp provides a scalable and efficient framework for leveraging long-range clinical context to improve downstream performance.

Saeed Shurrab
Mariam Al-Omari
Dana El Samad
Farah E. Shamout


Revitalizing the Beginning: Avoiding Storage Dependency for Model Merging in Continual Learning

Abstract: Model merging provides a compelling paradigm for integrating specialized expertise into a unified multi-task model, a goal that aligns naturally with the sequential knowledge acquisition in continual learning (CL). However, the requirement for preserving diverse forms of previous knowledge conflicts with the storage limitations inherent to CL. In this paper, we systematically analyze existing model merging methods under the constraints of CL. We find that current methods prioritize global alignment, which often leads to the accumulation and amplification of task-specific errors within the continuous data stream; and the vanishing gradients at the onset of subsequent tasks frequently cause optimization to stagnate. These leave the merged model in a suboptimal state at the beginning of the next training phase. To address these challenges, we propose Trajectory Regularized Merging (TRM), a framework that reformulates the merging phase as an optimization process within an augmented trajectory subspace. Our framework integrates three synergistic objectives including task alignment, prediction consistency, and gradient responsiveness to concurrently preserve merged model's historical stability and re-activate optimization dynamics. Extensive experimental results demonstrate that our method achieves state-of-the-art performance across multiple benchmarks.


Abstract: In survival analysis, traditional models assume all individuals will eventually experience the event of interest. However, advances in therapeutics have led to multiple clinical contexts with potentially curative therapies, and in these contexts, certain individuals may never experience the event. Statisticians have developed cure models as a methodology to address this challenge. Nonetheless, despite significant statistical advances in cure models, we have seen more limited uptake in biomedical applications, and we hypothesize that this is caused by limited guidance in the appropriate application of cure models. Cure models require specific identifiability conditions for valid parameter estimation, and previous reports have demonstrated significant issues with the inappropriate application of cure models. Existing tutorials for cure models focus on model implementation and either assume or provide only limited guidance on whether cure modeling is appropriate for the given dataset. This tutorial addresses this gap by describing a systematic procedure that integrates clinical judgment, visual inspection of Kaplan-Meier curves, and quantitative evaluation. We provide a worked example using data from a randomized clinical trial in acute myeloid leukemia, and we also summarize findings from a series of other datasets of hematopoietic cell transplantation to suggest broad practical guidance for choosing to apply cure models. By systematically evaluating cure model appropriateness before fitting these models, researchers can achieve more reliable survival analysis and improved clinical decision-making.

A Tutorial for Evaluating Cure Model Appropriateness Geethanjalee Mudunkotuwa


Model Merging: Foundations and Algorithms

Abstract: Modern deep learning usually treats models as separate artifacts: trained independently, specialized for particular purposes, and replaced when improved versions appear. This thesis studies model merging as an alternative paradigm: combining independently trained neural networks directly in weight space, with little or no optimization and without requiring access to the original training data. The thesis considers two main regimes. In the single-task setting, where models share an objective but differ in initialization, we introduce C$^2$M$^3$, a cycle-consistent merging algorithm based on Frank-Wolfe optimization. C$^2$M$^3$ aligns multiple networks into a shared, reference-free parameter space, making weight averaging meaningful without privileging any individual model. In the multi-task setting, where models are fine-tuned for different downstream tasks from a common pretrained initialization, we first develop a theoretical account of task vectors as approximate gradients. This explains both the effectiveness and the limitations of task arithmetic. Building on this view, we show that task vectors inherit the low-rank structure of gradients and introduce Task Singular Vectors (TSV), a decomposition that enables compression and interference reduction through TSV-Merge. We then present MASS, an input-adaptive routing method that uses TSV geometry to select task-relevant subspaces at inference time. Finally, we introduce MERGE$^3$, an evolutionary merging framework that uses Item Response Theory to reduce evaluation costs by up to 50$\times$ while preserving solution quality. Together, these contributions provide theoretical and algorithmic foundations for model merging, supporting a paradigm in which learned capabilities can be composed, reused, and extended across models.


Auto-FlexSwitch: Efficient Dynamic Model Merging via Learnable Task Vector Compression

Abstract: Model merging has attracted attention as an effective path toward multi-task adaptation by integrating knowledge from multiple task-specific models. Among existing approaches, dynamic merging mitigates performance degradation caused by conflicting parameter updates across tasks by flexibly combining task-specific parameters at inference time, thereby maintaining high performance. However, these methods require storing independent parameters for each task, resulting in prohibitive storage overhead. To address this issue, we first experimentally demonstrate that the fine-tuned weight increments (referred to as task vectors) exhibit an impulse-like activation pattern and high robustness to low-bit representations. Driven by this insight, we propose T-Switch, which decomposes task vectors into three compact components: a binary sparse mask, a sign vector, and a scalar scaling factor, achieving high-fidelity approximation at high compression ratios. We then introduce Auto-Switch, a training-free merging scheme that automatically composes task vectors via feature similarity retrieval. Building on this, we develop Auto-Switch, a training-free merging scheme that automatically assembles task vectors through feature similarity retrieval. Furthermore, to transform task vector sparsification and quantization from static rules to adaptive learning, we propose FlexSwitch, a learnable framework which jointly optimizes the compression strategy for each model unit via Learnable Gating Sparsification (LGS) and Bit-width Adaptive Selection (BAS), while employing the Sparsity-Aware Storage Strategy (SASS) to select the optimal storage encoding structure. Finally, by incorporating a K-Nearest Neighbor (KNN) inference scheme with a learnable low-rank metric, we present Auto-FlexSwitch, a dynamic model merging approach that supports highly efficient task vector compression.

Junqi Gao
Dazhi Zhang
Zhichang Guo
Biqing Qi
Yi Ran
Wangmeng Zuo


Embedding Arithmetic: A Lightweight, Tuning-Free Framework for Post-hoc Bias Mitigation in Text-to-Image Models

Abstract: Modern text-to-image (T2I) models amplify harmful societal biases, challenging their ethical deployment. We introduce an inference-time method that reliably mitigates social bias while keeping prompt semantics and visual context (background, layout, and style) intact. This ensures context persistency and provides a controllable parameter to adjust mitigation strength, giving practitioners fine-grained control over fairness-coherence trade-offs. Using Embedding Arithmetic, we analyze how bias is structured in the embedding space and correct it without altering model weights, prompts, or datasets. Experiments on FLUX 1.0-Dev and Stable Diffusion 3.5-Large show that the conditional embedding space forms a complex, entangled manifold rather than a grid of disentangled concepts. To rigorously assess semantic preservation beyond the circularity and bias limitations of of CLIP scores, we propose the Concept Coherence Score (CCS). Evaluated against this robust metric, our lightweight, tuning-free method significantly outperforms existing baselines in improving diversity while maintaining high concept coherence, effectively resolving the critical fairness-coherence trade-off. By characterizing how models represent social concepts, we establish geometric understanding of latent space as a principled path toward more transparent, controllable, and fair image generation.

Venkatesh Thirugnana Sambandham
Torsten Schön


Understanding and Enforcing Weight Disentanglement in Task Arithmetic

Abstract: Task arithmetic provides an efficient, training-free way to edit pre-trained models, yet lacks a fundamental theoretical explanation for its success. The existing concept of ``weight disentanglement" describes the ideal outcome of non-interfering task composition but does not reveal its underlying cause. Crucially, what intrinsic properties of the pre-trained model ($θ_0$) or the task vectors ($τ_t$) enable this disentanglement remains underexplored. In this paper, we introduce Task-Feature Specialization (TFS), a model's ability to allocate distinct internal features to different tasks, as the fundamental principle. We first prove that TFS is a sufficient condition for weight disentanglement. More importantly, we find that TFS also gives rise to an observable geometric consequence: weight vector orthogonality. This positions TFS as the common cause for both the desired functional outcome (disentanglement) and a measurable geometric property (orthogonality). This relationship provides the key insight for our method: since the abstract TFS property is intractable to enforce directly, we can instead promote weight disentanglement by shaping its concrete geometric consequence, orthogonality. Therefore, we propose OrthoReg, a simple and effective regularization method that actively enforces an internal orthogonal structure on weight updates ($ΔW$) that constitute $τ_t$ during fine-tuning. And we theoretically prove that OrthoReg promotes disentanglement. Extensive experiments demonstrate that OrthoReg consistently and significantly enhances the performance of various task arithmetic methods. Code is available at \href{https://github.com/RL-MIND/OrthoReg}{https://github.com/RL-MIND/OrthoReg}.

Shangge Liu
Yuehan Yin
Lei Wang
Qi Fan
Yinghuan Shi
Wenbin Li
Yang Gao
Dacheng Tao


Task Alignment: A simple and effective proxy for model merging in computer vision

Abstract: Efficiently merging several models fine-tuned for different tasks, but stemming from the same pretrained base model, is of great practical interest. Despite extensive prior work, most evaluations of model merging in computer vision are restricted to image classification using CLIP, where different classification datasets define different tasks. In this work, our goal is to make model merging more practical and show its relevance on challenging scenarios beyond this specific setting. In most vision scenarios, different tasks rely on trainable and usually heterogeneous decoders. Differently from previous studies with frozen decoders, where merged models can be evaluated right away, the non-trivial cost of decoder training renders hyperparameter selection based on downstream performance impractical. To address this, we introduce the task alignment proxy, and show how it can be used to speed up hyperparameter selection by orders of magnitude while retaining performance. Equipped with the task alignment proxy, we extend the applicability of model merging to multi-task vision models beyond CLIP-based classification.

Pau de Jorge
César Roberto de Souza
Björn Michele
Mert Bülent Sarıyıldız
Philippe Weinzaepfel
Florent Perronnin
Diane Larlus
Yannis Kalantidis


One Model to Translate Them All? A Journey to Mount Doom for Multilingual Model Merging

Abstract: Weight-space model merging combines independently fine-tuned models without accessing original training data, offering a practical alternative to joint training. While merging succeeds in multitask settings, its behavior in multilingual contexts remains poorly understood. We systematically study weight-space merging for multilingual machine translation by fully fine-tuning language model on large-scale bilingual corpora and evaluating standard merging strategies. Our experiments reveal that merging degrades performance, especially when target languages differ. To explain this failure, we analyze internal representations using span-conditioned neuron selectivity and layer-wise centered kernel alignment. We find that language-specific neurons concentrate in embedding layers and upper transformer blocks, while intermediate layers remain largely shared across languages. Critically, fine-tuning redistributes rather than sharpens language selectivity: neurons for supervised and related languages become less exclusive, while those for unsupervised languages grow more isolated. This redistribution increases representational divergence in higher layers that govern generation. These findings suggest that multilingual fine-tuning may reshape geometry in ways that reduce compatibility with standard weight-space merging assumptions. Our work thus provides an explanation for why merging fails in multilingual translation scenarios.


Countering Catastrophic Forgetting of Large Language Models for Better Instruction Following via Weight-Space Model Merging

Abstract: Large language models have been adopted in the medical domain for clinical documentation to reduce clinician burden. However, studies have reported that LLMs often "forget" a significant amount of instruction-following ability when fine-tuned using a task-specific medical dataset, a critical challenge in adopting general-purpose LLMs for clinical applications. This study presents a model merging framework to efficiently adapt general-purpose LLMs to the medical domain by countering this forgetting issue. By merging a clinical foundation model (GatorTronLlama) with a general instruct model (Llama-3.1-8B-Instruct) via interpolation-based merge methods, we seek to derive a domain-adapted model with strong performance on clinical tasks while retaining instruction-following ability. Comprehensive evaluation across medical benchmarks and five clinical generation tasks (e.g., radiology and discharge summarization) shows that merged models can effectively mitigate catastrophic forgetting, preserve clinical domain expertise, and retain instruction-following ability. In addition, our model merging strategies demonstrate training efficiency, achieving performance on par with fully fine-tuned baselines under severely constrained supervision (e.g., 64-shot vs. 256-shot). Consequently, weight-space merging constitutes a highly scalable solution for adapting open-source LLMs to clinical applications, facilitating broader deployment in resource-constrained healthcare environments.

Mengxian Lyu
Cheng Peng
Ziyi Chen
Mengyuan Zhang
Jieting Li Lu
Yonghui Wu


Yet Even Less Is Even Better For Agentic, Reasoning, and Coding LLMs

Abstract: Training effective software engineering agents requires large volumes of task-specific trajectories, incurring substantial data construction costs. Inspired by the "Less-Is-More" hypothesis in mathematical reasoning, we investigate its extension to agentic scenarios and propose an end-to-end training framework that achieves superior agentic capabilities with fewer but higher-quality training trajectories. This is achieved via STITCH (Sliding-memory Trajectory Inference and Task Chunking Heuristic), a coarse-to-fine mechanism that filters low-value noise and retains decision-critical tokens to maximize training signal quality. We conduct experiments across multiple agent frameworks (e.g., mini-SWE-agent, MSWE-agent), model scales (30B to 355B), and multilingual settings (Python, Java, and ArkTS). On SWE-bench Verified, models trained with STITCH achieve up to 63.16% relative improvement over base models. On Multi-SWE-bench (Java), MiniMax-M2.5-STITCH achieves 43.75% with our CodeArts Agent scaffold (+16.67%). On HarmonyOS (ArkTS), GLM-4.7-STITCH improves the compilation pass rate to 61.31% (+43.34%) with less than 1K training trajectories. Our results confirm that the "Less-Is-More" paradigm generalizes effectively to complex agentic tasks across diverse languages and model scales.

CodeArts Model Team
Yang Ye
Jingyuan Tan
Tianyue Jiang
Ruizhe Ye
Qiankun He
Jiarui Yang
Jian Dong
Sicong Liang
Chongjian Yue
Peibai Xu
Lufan Lu
Shiguan Pang
Taotao Qian
Junbao Hu
Yuechan Hao
Ensheng Shi
Qi Zhang
Yi Hao
Na Fan
Xin Tan
Shuai Yao
Zhiwei Shen
Zongchen Li
Yanlin Wang
Chong Chen
Yuchi Ma


Robust Language Identification for Romansh Varieties

Abstract: The Romansh language has several regional varieties, called idioms, which sometimes have limited mutual intelligibility. Despite this linguistic diversity, there has been a lack of documented efforts to build a language identification (LID) system that can distinguish between these idioms. Since Romansh LID should also be able to recognize Rumantsch Grischun, a supra-regional variety that combines elements of several idioms, this makes for a novel and interesting classification problem. In this paper, we present a LID system for Romansh idioms based on an SVM approach. We evaluate our model on a newly curated benchmark across two domains and find that it reaches an average in-domain accuracy of 97%, enabling applications such as idiom-aware spell checking or machine translation. Our classifier is publicly available.

Charlotte Model
Sina Ahmadi
Jannis Vamvas


Resolving Interference (RI): Disentangling Models for Improved Model Merging

Abstract: Model merging has shown that multitask models can be created by directly combining the parameters of different models that are each specialized on tasks of interest. However, models trained independently on distinct tasks often exhibit interference that degrades the merged model's performance. To solve this problem, we formally define the notion of Cross-Task Interference as the drift in the representation of the merged model relative to its constituent models. Reducing cross-task interference is key to improving merging performance. To address this issue, we propose our method, Resolving Interference (RI), a light-weight adaptation framework which disentangles expert models to be functionally orthogonal to the space of other tasks, thereby reducing cross-task interference. RI does this whilst using only unlabeled auxiliary data as input (i.e., no task-data is needed), allowing it to be applied in data-scarce scenarios. RI consistently improves the performance of state-of-the-art merging methods by up to 3.8% and generalization to unseen domains by up to 2.3%. We also find RI to be robust to the source of auxiliary input while being significantly less sensitive to tuning of merging hyperparameters. Our codebase is available at: https://github.com/pramesh39/resolving_interference

Pratik Ramesh
George Stoica
Arun Iyer
Leshem Choshen
Judy Hoffman


Mortgage Burnout and Selection Effects in Heterogeneous Cox Hazard Models

Abstract: We study the aggregate hazard rate of a heterogeneous population whose individual event intensities are modeled as Cox (doubly stochastic) processes. In the deterministic hazard setting, the observed pool hazard is the survival weighted mean of the individual hazards, and its time derivative equals the mean individual hazard drift minus a variance term. This yields a transparent structural explanation of burnout in mortgage pools. We extend this perspective to stochastic intensity models. The observed pool hazard remains a survival-weighted mean, but now evolves as an Ito process whose drift contains the mean drift of the individual hazards and a negative selection term driven by cross-sectional dispersion, together with a diffusion term inherited from the common factor. We formulate the general identity and discuss special cases relevant to mortgage prepayment modeling.


An Empirical Study and Theoretical Explanation on Task-Level Model-Merging Collapse

Abstract: Model merging unifies independently fine-tuned LLMs from the same base, enabling reuse and integration of parallel development efforts without retraining. However, in practice we observe that merging does not always succeed: certain combinations of task-specialist models suffer from catastrophic performance degradation after merging. We refer to this failure mode as merging collapse. Intuitively, collapse arises when the learned representations or parameter adjustments for different tasks are fundamentally incompatible, so that merging forces destructive interference rather than synergy. In this paper, we identify and characterize the phenomenon of task-level merging collapse, where certain task combinations consistently trigger huge performance degradation across all merging methods. Through extensive experiments and statistical analysis, we demonstrate that representational incompatibility between tasks is strongly correlated with merging collapse, while parameter-space conflict metrics show minimal correlation, challenging conventional wisdom in model merging literature. We provide a theoretical explanation on this phenomenon through rate-distortion theory with a dimension-dependent bound, establishing fundamental limits on task mergeability regardless of methodology.

Yuan Cao
Dezhi Ran
Yuzhe Guo
Mengzhou Wu
Simin Chen
Linyi Li
Wei Yang
Tao Xie


Model Merging in the Era of Large Language Models: Methods, Applications, and Future Directions

Abstract: Model merging combines the parameters of multiple neural networks into a single model without additional training. As fine-tuned large language models (LLMs) proliferate, merging offers a computationally efficient alternative to ensembles and full retraining, enabling practitioners to compose specialized capabilities at minimal cost. This survey examines model merging in the LLM era through the \textbf{FUSE} taxonomy, organized along \textbf{F}oundations, \textbf{U}nification Strategies, \textbf{S}cenarios, and \textbf{E}cosystem. We first establish the theoretical underpinnings of merging, including loss landscape geometry and mode connectivity, then systematically review the algorithmic space spanning weight averaging, task vector arithmetic, sparsification-enhanced methods, mixture-of-experts architectures, and evolutionary optimization. We further examine downstream applications across multi-task learning, safety alignment, domain specialization, and federated learning, and survey the supporting ecosystem of tools and evaluation benchmarks. Finally, we identify key open challenges and future directions, aiming to equip researchers and practitioners with a structured foundation for advancing model merging.


DC-Merge: Improving Model Merging with Directional Consistency

Abstract: Model merging aims to integrate multiple task-adapted models into a unified model that preserves the knowledge of each task. In this paper, we identify that the key to this knowledge retention lies in maintaining the directional consistency of singular spaces between merged multi-task vector and individual task vectors. However, this consistency is frequently compromised by two issues: i) an imbalanced energy distribution within task vectors, where a small fraction of singular values dominate the total energy, leading to the neglect of semantically important but weaker components upon merging, and ii) the geometric inconsistency of task vectors in parameter space, which causes direct merging to distort their underlying directional geometry. To address these challenges, we propose DC-Merge, a method for directional-consistent model merging. It first balances the energy distribution of each task vector by smoothing its singular values, ensuring all knowledge components are adequately represented. These energy-balanced vectors are then projected onto a shared orthogonal subspace to align their directional geometries with minimal reconstruction error. Finally, the aligned vectors are aggregated in the shared orthogonal subspace and projected back to the original parameter space. Extensive experiments on vision and vision-language benchmarks show that DC-Merge consistently achieves state-of-the-art performance in both full fine-tuning and LoRA settings. The implementation code is available at https://github.com/Tobeginwith/DC-Merge.

Han-Chen Zhang
Zi-Hao Zhou
Mao-Lin Luo
Shimin Di
Min-Ling Zhang
Tong Wei


Magic partition functions: Sign smoothing convolutions with Dirichlet invertible arithmetic functions

Abstract: Sign changes in sums of arithmetic functions and their inverses are a subtle topic with room to grow new results. Suppose that $S_f(x) := \sum_{n \leq x} f(n)$ is the summatory function of some arithmetic function $f$ such that $f(1) \neq 1$. There are known lower bounds on the limiting growth of $V(S_f, Y)$ -- the number of sign changes of $S_f(y)$ on the interval $y \in (0, Y]$ as $Y \rightarrow \infty$. We observe a partition theoretic sign smoothing by discrete convolution of the local oscillatory properties of the Dirichlet inverse of $f$, $S_{f^{-1}}(x)$. These so-called invertible ``magic partition function`` encodings lead to a sequence of convolution sums which have predictable sign properties provided the sequence of $f(n)$ ($f^{-1}(n)$, respectively) has reasonable asymptotic upper bounds with respect to $n$.


Bridging Domains through Subspace-Aware Model Merging

Abstract: Model merging integrates multiple task-specific models into a single consolidated one. Recent research has made progress in improving merging performance for in-distribution or multi-task scenarios, but domain generalization in model merging remains underexplored. We investigate how merging models fine-tuned on distinct domains affects generalization to unseen domains. Through an analysis of parameter competition in the task matrix using singular value decomposition, we show that merging models trained under different distribution shifts induces stronger conflicts between their subspaces compared to traditional multi-task settings. To mitigate this issue, we propose SCORE (Subspace COnflict-Resolving mErging), a method designed to alleviate such singular subspace conflicts. SCORE finds a shared orthogonal basis by computing the principal components of the concatenated leading singular vectors of all models. It then projects each task matrix into the shared basis, pruning off-diagonal components to remove conflicting singular directions. SCORE consistently outperforms, on average, existing model merging approaches in domain generalization settings across a variety of architectures and model scales, demonstrating its effectiveness and scalability.

Levy Chaves
Chao Zhou
Rebekka Burkholz
Eduardo Valle
Sandra Avila


Model Medicine: A Clinical Framework for Understanding, Diagnosing, and Treating AI Models

Abstract: Model Medicine is the science of understanding, diagnosing, treating, and preventing disorders in AI models, grounded in the principle that AI models -- like biological organisms -- have internal structures, dynamic processes, heritable traits, observable symptoms, classifiable conditions, and treatable states. This paper introduces Model Medicine as a research program, bridging the gap between current AI interpretability research (anatomical observation) and the systematic clinical practice that complex AI systems increasingly require. We present five contributions: (1) a discipline taxonomy organizing 15 subdisciplines across four divisions -- Basic Model Sciences, Clinical Model Sciences, Model Public Health, and Model Architectural Medicine; (2) the Four Shell Model (v3.3), a behavioral genetics framework empirically grounded in 720 agents and 24,923 decisions from the Agora-12 program, explaining how model behavior emerges from Core--Shell interaction; (3) Neural MRI (Model Resonance Imaging), a working open-source diagnostic tool mapping five medical neuroimaging modalities to AI interpretability techniques, validated through four clinical cases demonstrating imaging, comparison, localization, and predictive capability; (4) a five-layer diagnostic framework for comprehensive model assessment; and (5) clinical model sciences including the Model Temperament Index for behavioral profiling, Model Semiology for symptom description, and M-CARE for standardized case reporting. We additionally propose the Layered Core Hypothesis -- a biologically-inspired three-layer parameter architecture -- and a therapeutic framework connecting diagnosis to treatment.


BD-Merging: Bias-Aware Dynamic Model Merging with Evidence-Guided Contrastive Learning

Abstract: Model Merging (MM) has emerged as a scalable paradigm for multi-task learning (MTL), enabling multiple task-specific models to be integrated without revisiting the original training data. Despite recent progress, the reliability of MM under test-time distribution shift remains insufficiently understood. Most existing MM methods typically assume that test data are clean and distributionally aligned with both the training and auxiliary sources. However, this assumption rarely holds in practice, often resulting in biased predictions with degraded generalization. To address this issue, we present BD-Merging, a bias-aware unsupervised model merging framework that explicitly models uncertainty to achieve adaptive reliability under distribution shift. First, BD-Merging introduces a joint evidential head that learns uncertainty over a unified label space, capturing cross-task semantic dependencies in MM. Second, building upon this evidential foundation, we propose an Adjacency Discrepancy Score (ADS) that quantifies evidential alignment among neighboring samples. Third, guided by ADS, a discrepancy-aware contrastive learning mechanism refines the merged representation by aligning consistent samples and separating conflicting ones. Combined with general unsupervised learning, this process trains a debiased router that adaptively allocates task-specific or layer-specific weights on a per-sample basis, effectively mitigating the adverse effects of distribution shift. Extensive experiments across diverse tasks demonstrate that BD-Merging achieves superior effectiveness and robustness compared to state-of-the-art MM baselines.


ACE-Merging: Data-Free Model Merging with Adaptive Covariance Estimation

Abstract: Model merging aims to combine multiple task-specific expert models into a single model while preserving generalization across diverse tasks. However, interference among experts, especially when they are trained on different objectives, often leads to significant performance degradation. Despite recent progress, resolving this interference without data access, retraining, or architectural modification remains a fundamental challenge. This paper provides a theoretical analysis demonstrating that the input covariance of each task, which is a key factor for optimal merging, can be implicitly estimated from the parameter differences of its fine-tuned model, even in a fully data-free setting. Building on this insight, we introduce \acem, an Adaptive Covariance Estimation framework that effectively mitigates inter-task interference. Our approach features a principled, closed-form solution that contrasts with prior iterative or heuristic methods. Extensive experiments on both vision and language benchmarks demonstrate that \acem sets a new state-of-the-art among data-free methods. It consistently outperforms existing baselines; for example, \acem achieves an average absolute improvement of 4\% over the previous methods across seven tasks on GPT-2. Owing to its efficient closed-form formulation, \acem delivers superior performance with a modest computational cost, providing a practical and theoretically grounded solution for model merging.

Bo Xu
Haotian Wu
Hehai Lin
Weiquan Huang
Beier Zhu
Yao Shu
Chengwei Qin


Leveraging Model Soups to Classify Intangible Cultural Heritage Images from the Mekong Delta

Abstract: The classification of Intangible Cultural Heritage (ICH) images in the Mekong Delta poses unique challenges due to limited annotated data, high visual similarity among classes, and domain heterogeneity. In such low-resource settings, conventional deep learning models often suffer from high variance or overfit to spurious correlations, leading to poor generalization. To address these limitations, we propose a robust framework that integrates the hybrid CoAtNet architecture with model soups, a lightweight weight-space ensembling technique that averages checkpoints from a single training trajectory without increasing inference cost. CoAtNet captures both local and global patterns through stage-wise fusion of convolution and self-attention. We apply two ensembling strategies - greedy and uniform soup - to selectively combine diverse checkpoints into a final model. Beyond performance improvements, we analyze the ensembling effect through the lens of bias-variance decomposition. Our findings show that model soups reduces variance by stabilizing predictions across diverse model snapshots, while introducing minimal additional bias. Furthermore, using cross-entropy-based distance metrics and Multidimensional Scaling (MDS), we show that model soups selects geometrically diverse checkpoints, unlike Soft Voting, which blends redundant models centered in output space. Evaluated on the ICH-17 dataset (7,406 images across 17 classes), our approach achieves state-of-the-art results with 72.36% top-1 accuracy and 69.28% macro F1-score, outperforming strong baselines including ResNet-50, DenseNet-121, and ViT. These results underscore that diversity-aware checkpoint averaging provides a principled and efficient way to reduce variance and enhance generalization in culturally rich, data-scarce classification tasks.

Quoc-Khang Tran
Minh-Thien Nguyen
Nguyen-Khang Pham


Model Merging in the Essential Subspace

Abstract: Model merging aims to integrate multiple task-specific fine-tuned models derived from a shared pre-trained checkpoint into a single multi-task model without additional training. Despite extensive research, task interference remains a major obstacle that often undermines the performance of merged models. In this paper, we propose ESM (Essential Subspace Merging) , a robust framework for effective model merging. We begin by performing Principal Component Analysis (PCA) on feature shifts induced by parameter updates. The resulting principal directions span an essential subspace that dominantly influences feature representations. Each task's parameter update matrix is projected onto its respective essential subspace for low-rank decomposition before merging. This methodology mitigates inter-task interference while preserving core task-specific functionality. Furthermore, we introduce a multi-level polarized scaling strategy that amplifies parameters containing critical knowledge and suppresses redundant ones, preventing essential knowledge from being overwhelmed during fusion. Extensive experiments across multiple task sets and model scales demonstrate that our method achieves state-of-the-art performance in multi-task model merging.


Interpolation in Proof Theory

Abstract: This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion are two foundational techniques: Maehara's method for Craig interpolation and Pitts' method for uniform interpolation. The chapter demonstrates how these methods lead to results on the existence of well-behaved proof systems in the contemporary framework of universal proof theory and how they provide a road map for constructing interpolation proofs using modern proof formalisms. The emphasis of the chapter is on constructive, modular, and syntax-driven techniques that illuminate deeper connections between interpolation properties and proof systems.

Iris van der Giessen
Raheleh Jalali
Roman Kuznets


Beyond Parameter Arithmetic: Sparse Complementary Fusion for Distribution-Aware Model Merging

Abstract: Model merging has emerged as a promising paradigm for composing the capabilities of large language models by directly operating in weight space, enabling the integration of specialized models without costly retraining. However, existing merging methods largely rely on parameter-space heuristics, which often introduce severe interference, leading to degraded generalization and unstable generation behaviors such as repetition and incoherent outputs. In this work, we propose Sparse Complementary Fusion with reverse KL (SCF-RKL), a novel model merging framework that explicitly controls functional interference through sparse, distribution-aware updates. Instead of assuming linear additivity in parameter space, SCF-RKL measures the functional divergence between models using reverse Kullback-Leibler divergence and selectively incorporates complementary parameters. This mode-seeking, sparsity-inducing design effectively preserves stable representations while integrating new capabilities. We evaluate SCF-RKL across a wide range of model scales and architectures, covering both reasoning-focused and instruction-tuned models. Extensive experiments on 24 benchmarks spanning advanced reasoning, general reasoning and knowledge, instruction following, and safety demonstrate, vision classification that SCF-RKL consistently outperforms existing model merging methods while maintaining strong generalization and generation stability.

Weihong Lin
Lin Sun
Qilong Shi
Aomufei Yuan
Yuxuan Tian
Zhengyang Wang
Guangxiang Zhao
Xiangzheng Zhang
Tong Yang


Craig Interpolation in Program Verification

Abstract: Craig interpolation is used in program verification for automating key tasks such as the inference of loop invariants and the computation of program abstractions. This chapter covers some of the most important techniques that have been developed in this context over the last years, focusing on two aspects: the derivation of Craig interpolants modulo the theories and data types used in verification and the basic design of verification algorithms applying interpolation.


M-Loss: Quantifying Model Merging Compatibility with Limited Unlabeled Data

Abstract: Training of large-scale models is both computationally intensive and often constrained by the availability of labeled data. Model merging offers a compelling alternative by directly integrating the weights of multiple source models without requiring additional data or extensive training. However, conventional model merging techniques, such as parameter averaging, often suffer from the unintended combination of non-generalizable features, especially when source models exhibit significant weight disparities. Comparatively, model ensembling generally provides more stable and superior performance that aggregates multiple models by averaging outputs. However, it incurs higher inference costs and increased storage requirements. While previous studies experimentally showed the similarities between model merging and ensembling, theoretical evidence and evaluation metrics remain lacking. To address this gap, we introduce Merging-ensembling loss (M-Loss), a novel evaluation metric that quantifies the compatibility of merging source models using very limited unlabeled data. By measuring the discrepancy between parameter averaging and model ensembling at layer and node levels, M-Loss facilitates more effective merging strategies. Specifically, M-Loss serves both as a quantitative criterion of the theoretical feasibility of model merging, and a guide for parameter significance in model pruning. Our theoretical analysis and empirical evaluations demonstrate that incorporating M-Loss into the merging process significantly improves the alignment between merged models and model ensembling, providing a scalable and efficient framework for accurate model consolidation.

Tiantong Wang
Yiyang Duan
Haoyu Chen
Tiantong Wu
Wei Yang Bryan Lim

AAAI Conference on Artificial Intelligence


Definability and Interpolation in Philosophy

Abstract: This paper is a historical tour of occurrences of the Craig interpolation theorem and the Beth definability theorem in philosophy since the 1950s. We identify the notion of dependence as one major red thread behind these, and include some new technical results, in particular, on logical system translations and generalized definability


Fine-Grained Model Merging via Modular Expert Recombination

Abstract: Model merging constructs versatile models by integrating task-specific models without requiring labeled data or expensive joint retraining. Although recent methods improve adaptability to heterogeneous tasks by generating customized merged models for each instance, they face two critical limitations. First, the instance-specific merged models lack reusability, restricting the exploitation of high-quality merging configurations and efficient batch inference. Second, these methods treat each task-specific model as a monolithic whole, overlooking the diverse mergeability of homologous components such as attention and multilayer perceptron layers, and the differing merging sensitivities across components. To address these limitations, we propose MERGE (\underline{M}odular \underline{E}xpert \underline{R}ecombination for fine-\underline{G}rained m\underline{E}rging), a method that enables component-wise model merging and input-aware, on-demand module recombination at inference. MERGE formulates component-wise merging as a bi-objective optimization problem that balances cross-task performance and storage efficiency, and develops a surrogate-assisted evolutionary algorithm to efficiently identify Pareto-optimal merging configurations. These high-quality configurations underpin a reusable modular expert library, from which a lightweight routing network dynamically activates and recombines modular experts to assemble input-specific models and enable efficient inference under storage constraints. Extensive experiments across various model scales, task types, and fine-tuning strategies demonstrate that MERGE consistently outperforms strong baselines and generalizes effectively.

Haiyun Qiu
Xingyu Wu
Liang Feng
Kay Chen Tan


Orthogonal Model Merging

Abstract: Merging finetuned Large Language Models (LLMs) has become increasingly important for integrating diverse capabilities into a single unified model. However, prevailing model merging methods rely on linear arithmetic in Euclidean space, which often destroys the intrinsic geometric properties of pretrained weights, such as hyperspherical energy. To address this, we propose Orthogonal Model Merging (OrthoMerge), a method that performs merging operations on the Riemannian manifold formed by the orthogonal group to preserve the geometric structure of the model's weights. By mapping task-specific orthogonal matrices learned by Orthogonal Finetuning (OFT) to the Lie algebra, OrthoMerge enables a principled yet efficient integration that takes into account both the direction and intensity of adaptations. In addition to directly leveraging orthogonal matrices obtained by OFT, we further extend this approach to general models finetuned with non-OFT methods (i.e., low-rank finetuning, full finetuning) via an Orthogonal-Residual Decoupling strategy. This technique extracts the orthogonal components of expert models by solving the orthogonal Procrustes problem, which are then merged on the manifold of the orthogonal group, while the remaining linear residuals are processed through standard additive merging. Extensive empirical results demonstrate the effectiveness of OrthoMerge in mitigating catastrophic forgetting and maintaining model performance across diverse tasks.


When Shared Knowledge Hurts: Spectral Over-Accumulation in Model Merging

Abstract: Model merging combines multiple fine-tuned models into a single model by adding their weight updates, providing a lightweight alternative to retraining. Existing methods primarily target resolving conflicts between task updates, leaving the failure mode of over-counting shared knowledge unaddressed. We show that when tasks share aligned spectral directions (i.e., overlapping singular vectors), a simple linear combination repeatedly accumulates these directions, inflating the singular values and biasing the merged model toward shared subspaces. To mitigate this issue, we propose Singular Value Calibration (SVC), a training-free and data-free post-processing method that quantifies subspace overlap and rescales inflated singular values to restore a balanced spectrum. Across vision and language benchmarks, SVC consistently improves strong merging baselines and achieves state-of-the-art performance. Furthermore, by modifying only the singular values, SVC improves the performance of Task Arithmetic by 13.0%. Code is available at https://github.com/lyymuwu/SVC.

Yayuan Li
Ze Peng
Jian Zhang
Jintao Guo
Yue Duan
Yinghuan Shi


Model-Dowser: Data-Free Importance Probing to Mitigate Catastrophic Forgetting in Multimodal Large Language Models

Abstract: Fine-tuning Multimodal Large Language Models (MLLMs) on task-specific data is an effective way to improve performance on downstream applications. However, such adaptation often leads to a degradation in generalization on pretrained tasks, a phenomenon known as Catastrophic Forgetting. Existing methods that aim to mitigate this issue either become ineffective when fine-tuning deeper layers of the language decoder or scale poorly with increasing model size. To address these limitations, we propose Model-Dowser, a novel sparse fine-tuning approach for MLLMs. Model-Dowser measures a principled importance score for each model parameter with respect to pretrained generalization (prior to downstream adaptation) by jointly considering weight magnitudes, input activations, and output sensitivities. During fine-tuning, Model-Dowser selectively preserves high-importance parameters and updates the remaining. Comprehensive experiments on two representative MLLMs, LLaVA and NVILA, demonstrate that Model-Dowser effectively mitigates catastrophic forgetting and consistently outperforms prior methods, while remaining resource-efficient and scalable to multi-billion-parameter models.

Hyeontaek Hwang
Nguyen Dinh Son
Daeyoung Kim


Self-Soupervision: Cooking Model Soups without Labels

Abstract: Model soups are strange and strangely effective combinations of parameters. They take a model (the stock), fine-tune it into multiple models (the ingredients), and then mix their parameters back into one model (the soup) to improve predictions. While all known soups require supervised learning, and optimize the same loss on labeled data, our recipes for Self-Soupervision generalize soups to self-supervised learning (SSL). Our Self-Souping lets us flavor ingredients on new data sources, e.g. from unlabeled data from a task for transfer or from a shift for robustness. We show that Self-Souping on corrupted test data, then fine-tuning back on uncorrupted train data, boosts robustness by +3.5% (ImageNet-C) and +7% (LAION-C). Self-Soupervision also unlocks countless SSL algorithms to cook the diverse ingredients needed for more robust soups. We show for the first time that ingredients can differ in their SSL hyperparameters -- and more surprisingly, in their SSL algorithms. We cook soups of MAE, MoCoV3, MMCR, and LeJEPA ingredients that are more accurate than any single SSL ingredient.

Anthony Fuller
James R. Green
Evan Shelhamer


AutoMerge: Search-Based Model Merging Framework for Effective Model Reuse

Abstract: Software reuse has long been recognized as a critical and widely studied topic in software engineering, offering substantial benefits in reducing development costs, improving software quality, and enhancing operational efficiency. This paradigm extends into deep learning through model reuse. Recently, model merging has emerged in the domain of large language models (LLMs) as a training-free approach that takes multiple task-specific models with the same architecture as source models and merges them without retraining, enhancing model reuse within LLMs. However, no prior work has systematically investigated whether such an approach can be effectively applied to other deep learning models with different architectures across domains. To bridge this gap, we present the first systematic study that evaluates five model merging techniques on three distinct model architectures across three domains: LLMs, image classification, and autonomous driving. Our findings reveal that directly applying existing model merging techniques leads to highly inconsistent results and falls notably short of their success within LLMs. Moreover, a single model merging technique often fails to handle the heterogeneous structural properties within a model, limiting its applicability to different model architectures across domains. Furthermore, the effectiveness of model merging techniques is highly sensitive to hyperparameter configurations, thereby constraining their potential for broader adoption. Inspired by these insights, we propose AutoMerge, a novel search-based model merging framework that first segments complex models into multiple heterogeneous blocks and then systematically explores the merging space to identify the merging technique and its hyperparameter configuration.

You Lu
Jiyang Zhang
Bihuan Chen
Chaofeng Sha
Dingji Wang
Xin Peng


Per-parameter Task Arithmetic for Unlearning in Large Language Models

Abstract: In large language model (LLM) unlearning, private information is required to be removed. Task arithmetic unlearns by subtracting a specific task vector (TV)--defined as the parameter difference between a privacy-information-tuned model and the original model. While efficient, it can cause over-forgetting by disrupting parameters essential for retaining other information. Motivated by the observation that each parameter exhibits different importance for forgetting versus retention, we propose a per-parameter task arithmetic (PerTA) mechanism to rescale the TV, allowing per-parameter adjustment. These weights quantify the relative importance of each parameter for forgetting versus retention, estimated via gradients (i.e., PerTA-grad) or the diagonal Fisher information approximation (i.e., PerTA-fisher). Moreover, we discuss the effectiveness of PerTA, extend it to a more general form, and provide further analysis. Extensive experiments demonstrate that PerTA consistently improves upon standard TV, and in many cases surpasses widely used training-based unlearning methods in both forgetting effectiveness and overall model utility. By retaining the efficiency of task arithmetic while mitigating over-forgetting, PerTA offers a principled and practical framework for LLM unlearning.

Chengyi Cai
Zesheng Ye
Jiangchao Yao
Jianzhong Qi
Bo Han
Xiaolu Zhang
Feng Liu
Jun Zhou


SOUP: Token-level Single-sample Mix-policy Reinforcement Learning for Large Language Models

Abstract: On-policy reinforcement learning (RL) methods widely used for language model post-training, like Group Relative Policy Optimization (GRPO), often suffer from limited exploration and early saturation due to low sampling diversity. While off-policy data can help, current approaches that mix entire trajectories cause significant policy mismatch and instability. In this work, we propose the $\textbf{S}$ingle-sample Mix-p$\textbf{O}$licy $\textbf{U}$nified $\textbf{P}$aradigm (SOUP), a framework that unifies off- and on-policy learning within individual samples at the token level. It confines off-policy influence to the prefix of a generated sequence sampled from historical policies, while the continuation is generated on-policy. Through token-level importance ratios, SOUP effectively leverages off-policy information while preserving training stability. Extensive experiments demonstrate that SOUP consistently outperforms standard on-policy training and existing off-policy extensions. Our further analysis clarifies how our fine-grained, single-sample mix-policy training can improve both exploration and final performance in LLM RL.

Lei Yang
Wei Bi
Chenxi Sun
Renren Jin
Deyi Xiong


Multi-task Code LLMs: Data Mix or Model Merge?

Abstract: Recent research advocates deploying smaller, specialized code LLMs in agentic frameworks alongside frontier models, sparking interest in efficient strategies for multi-task learning that balance performance, constraints, and costs. We compare two approaches for creating small, multi-task code LLMs: data mixing versus model merging. We conduct extensive experiments across two model families (Qwen Coder and DeepSeek Coder) at two scales (2B and 7B parameters), fine-tuning them for code generation and code summarization tasks. Our evaluation on HumanEval, MBPP, and CodeXGlue benchmarks reveals that model merging achieves the best overall performance at larger scale across model families, retaining 96% of specialized model performance on code generation tasks while maintaining summarization capabilities. Notably, merged models can even surpass individually fine-tuned models, with our best configuration of Qwen Coder 2.5 7B model achieving 92.7% Pass@1 on HumanEval compared to 90.9% for its task-specific fine-tuned equivalent. At a smaller scale we find instead data mixing to be a preferred strategy. We further introduce a weight analysis technique to understand how different tasks affect model parameters and their implications for merging strategies. The results suggest that careful merging and mixing strategies can effectively combine task-specific capabilities without significant performance degradation, making them ideal for resource-constrained deployment scenarios.

Mingzhi Zhu
Boris Sobolev
Rahul Krishna
Raju Pavuluri
Stacy Patterson
Michele Merler


Behavior Knowledge Merge in Reinforced Agentic Models

Abstract: Reinforcement learning (RL) is central to post-training, particularly for agentic models that require specialized reasoning behaviors. In this setting, model merging offers a practical mechanism for integrating multiple RL-trained agents from different tasks into a single generalist model. However, existing merging methods are designed for supervised fine-tuning (SFT), and they are suboptimal to preserve task-specific capabilities on RL-trained agentic models. The root is a task-vector mismatch between RL and SFT: on-policy RL induces task vectors that are highly sparse and heterogeneous, whereas SFT-style merging implicitly assumes dense and globally comparable task vectors. When standard global averaging is applied under this mismatch, RL's non-overlapping task vectors that encode critical task-specific behaviors are reduced and parameter updates are diluted. To address this issue, we propose Reinforced Agent Merging (RAM), a distribution-aware merging framework explicitly designed for RL-trained agentic models. RAM disentangles shared and task-specific unique parameter updates, averaging shared components while selectively preserving and rescaling unique ones to counteract parameter update dilution. Experiments across multiple agent domains and model architectures demonstrate that RAM not only surpasses merging baselines, but also unlocks synergistic potential among agents to achieve performance superior to that of specialized agents in their domains.

Xiangchi Yuan
Dachuan Shi
Chunhui Zhang
Zheyuan Liu
Shenglong Yao
Soroush Vosoughi
Wenke Lee


Will it Merge? On The Causes of Model Mergeability

Abstract: Model merging has emerged as a promising technique for combining multiple fine-tuned models into a single multitask model without retraining. However, the factors that determine whether merging will succeed or fail remain poorly understood. In this work, we investigate why specific models are merged better than others. To do so, we propose a concrete, measurable definition of mergeability. We investigate several potential causes for high or low mergeability, highlighting the base model knowledge as a dominant factor: Models fine-tuned on instances that the base model knows better are more mergeable than models fine-tuned on instances that the base model struggles with. Based on our mergeability definition, we explore a simple weighted merging technique that better preserves weak knowledge in the base model.

Adir Rahamim
Asaf Yehudai
Boaz Carmeli
Leshem Choshen
Yosi Mass
Yonatan Belinkov


Model Merging via Multi-Teacher Knowledge Distillation

Abstract: Model merging has emerged as a lightweight alternative to joint multi-task learning (MTL), yet the generalization properties of merged models remain largely unexplored. Establishing such theoretical guarantees is non-trivial, as the merging process typically forbids access to the original training data and involves combining fine-tuned models trained on fundamentally heterogeneous data distributions. Without a principled understanding of these dynamics, current methods often rely on heuristics to approximate the optimal combination of parameters. This dependence is most critical in coefficient scaling, the weighting factors that modulate the magnitude of each fine-tuned model's contribution to the shared parameter. However, without a principled objective to guide their selection, these methods lead to brittle performance and are highly sensitive to scaling initialization. We address this gap by (i) establishing a novel flatness-aware PAC-Bayes generalization bound specifically for the model merging setting. This analysis introduces a "cross-task heterogeneity" term that formally captures the mismatch between diverse fine-tuned model priors and the target multi-task distributions. Guided by this theoretical insight, (ii) we frame model merging as multi-teacher knowledge distillation on scarce, unlabeled data. We formally demonstrate that minimizing the student-teacher Kullback-Leibler divergence directly tightens the upper bound on the merged model's excess risk. Guided by the flatness-aware bound derived, (iii) we operationalize this objective via SAMerging, a method that employs Sharpness-Aware Minimization (SAM) to find flat minima. Empirically, SAMerging establishes a new state of the art across vision and NLP benchmarks, achieving remarkable performance. The code is available at https://github.com/arshandalili/SAMerging.