Language Model Merging

The training-free integration of expert models via model merging has exposed significant security risks, enabling free-riders to combine specialized models without authorization. Recent works propose parameter-level defenses that employ linear parameter transformations to neutralize this threat. In this paper, we systematically analyze such defenses and reveal that their protected task vectors are inherently small in magnitude. Consequently, the protected weights remain overwhelmingly dominated by the pretrained model. Based on this observation, we designate the pretrained model as a static reference anchor and propose the Anchor-Guided Attack (AGA) to circumvent existing safeguards. Specifically, AGA aligns the protected model with this anchor to recover the transformation matrix analytically. Extensive evaluations validate that AGA consistently bypasses both individual and composite defenses under realistic defense-agnostic scenarios. Furthermore, we provide Anchor-Repulsive Fine-tuning (ARF), a defense method to mitigate the anchor dominance leveraged by AGA. Empirical results confirm that ARF effectively defeats the proposed attack. Our code is available at https://github.com/krumpguo/secure-merge-attack.

Fine-tuning Multimodal Large Language Models (MLLMs) on specialized tasks often leads to catastrophic forgetting of their general capabilities. Existing model merging methods to combat this are often heuristic or use sub-optimal objectives. We propose CurvatureGuided Mixing (CGM), a theoretically grounded framework that merges pre-trained and fine-tuned models. CGM formulates a joint optimization objective and uses a second-order (Hessian) approximation of the loss landscapes to analytically derive an optimal, closed-form "soft mixing" ratio. This ratio intelligently blends parameters based on their relative task-specific curvatures. We also introduce CGM$\dagger$, a robust "hard mixing" variant that performs sparse parameter selection guided by a novel, curvature-aware score. Experiments on LLaVA-1.5 and Qwen2.5VL across multiple downstream tasks show that CGM and CGM$\dagger$ consistently improve the trade-off between task specialization and general knowledge retention over existing methods. Code is available at github.com/zzsyjl/CGM-ECCV-2026.

Linear mode connectivity (LMC) provides a promising foundation for understanding and merging independently trained neural networks, but existing methods typically optimize the interpolation path from only one model endpoint, limiting their scalability and effectiveness for large pretrained transformers. We propose a novel and scalable framework for enabling LMC-based model merging to {\em billion-parameter pretrained transformers}. Our method applies properly parameterized functionality-preserving weight transformations to align functionally equivalent solutions, and introduces a dual learning procedure in which both models jointly learn their corresponding transformations toward a shared linear interpolation path. This bidirectional optimization substantially reduces interpolation barriers and enables more reliable merging across large-scale architectures. Empirically, we show that our approach achieves near-zero loss barriers on WikiText for language models with medium-sized parameters, representing, to our knowledge, the first demonstration of near-barrier-free linear connectivity at this scale. In the vision domain, ViT-L maintains above 69% ImageNet top-1 accuracy throughout the interpolation path, while modern billion-parameter LLMs exhibit only small loss barriers. These results suggest that properly resolving parameter symmetries enables large pretrained Transformers to be connected and merged through simple linear paths with substantially improved interpolation performance. Code: https://github.com/VILA-Lab/Dual-Learned-Matching .

Low-rank adaptation (LoRA) makes it cheap to train many domain- and task-specific language model adapters, but whether two adapters can be merged is usually discovered only after both have been fully trained and evaluated. This late feedback is costly: adapters that are strong in isolation can interfere destructively once their updates are combined. We ask whether this outcome can be anticipated. We formalize adapter mergeability as the degree to which an adapter preserves its single-task utility after merging, and show that it can be forecast from signals measured in the first few percent of training -- chiefly how the low-rank updates and their gradients align across tasks and how much they disturb shared representations. We package these signals into MergeProbe, a lightweight predictor that estimates pairwise and set-level retention and turns the estimate into a concrete decision: merge directly, reweight, prune, or route. On MERGE-PEFT, a five-domain benchmark spanning math, code, science, instruction following, and safety, MergeProbe attains the best average and worst-case retention among strong interference-aware merge baselines while adding far less deployment overhead than full task routing. This turns LoRA merging from a post-hoc engineering step into an anticipatory measurement problem.

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.

Reinforcement Learning with Verifiable Reward (RLVR) has emerged as a powerful post-training paradigm that surpasses Supervised Fine-Tuning (SFT) in eliciting reasoning intelligence and resisting catastrophic forgetting. Recent studies further reveal that RLVR induces highly sparse and off-principal parameter updates compared to SFT. This naturally raises the question: does such sparsity make RLVR models more amenable to model merging? If so, model merging would offer a scalable, training-free path to aggregate diverse reasoning capabilities from independently trained RLVR models. Surprisingly, we find the opposite, uncovering a sparsity curse: the sparse RLVR updates are spread farther apart in parameter space, forming near-orthogonal shortcuts that make aggregation inherently fragile. This is likely rooted in the stochasticity of RL optimization and the diversity of emergent reasoning patterns. Unlike SFT models that converge to shared, flat basins and merge naturally, RLVR models suffer severe degradation under standard merging methods. Through systematic empirical analysis of the update geometry, we characterize the mechanisms behind this failure and propose Sensitivity-aware Resolving Merging (SAR-Merging), a merging recipe tailored for the unique structure of RLVR parameter spaces. SAR-Merging resolves conflicts in overlapping update regions via Fisher Information-based sensitivity arbitration, followed by magnitude-aware sparsification and rescaling to preserve fragile reasoning pathways. Experiments on mathematical and coding benchmarks demonstrate that SAR-Merging substantially outperforms existing merging methods on RLVR models, enabling both single-task enhancement and multi-capability fusion.

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/)

Access control in large language models (LLMs) requires modular mechanisms to enable domain-specific behavior without retraining or cross-domain interference. A common hypothesis is that interference during adapter composition arises from overlap in linear parameter updates, suggesting that enforcing orthogonality or directional independence should improve multi-domain performance. We test this hypothesis using DoRA-RBAC, a hierarchical adapter composition framework based on weight-decomposed low-rank adaptation. We compare conventional Euclidean merging with a geometry-aware Riemannian-inspired merging strategy that approximates the Frechet mean via normalized directional averaging across multiple QA benchmarks (GPQA, PubMedQA, SimpleQA, WMDP) on LLaMA-3.1-8B and Mistral-7B. Our results show that while single-domain performance matches LoRA, geometry-aware merging provides no consistent advantage over standard averaging in multi-domain settings.Diagnostic analysis further reveals that angular alignment and orthogonality of adapter updates are weak predictors of composition performance. These findings suggest that adapter interference is not governed primarily by parameter-space geometry, but is instead consistent with interactions in shared nonlinear representations.

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.

Model merging has emerged as a cost-effective approach for consolidating the capabilities of multiple LLMs without retraining. However, existing merging techniques, largely based on linear parameter arithmetic or optimization, struggle when applied to Mixture-of-Experts (MoE) architectures. We identify a critical failure mode in MoE merging, termed routing breakdown, in which the merged router fails to dispatch tokens to suitable experts. Routing breakdown stems from the sensitivity of the non-linear softmax and discrete Top-k routing mechanisms to parameter perturbations from merging, a sensitivity further amplified by load-balancing constraints imposed during MoE pretraining. Because fine-tuned experts exhibit distinct specializations, even modest misrouting can cause severe performance degradation. To address this issue, we propose Hessian-Aware Router Calibration (HARC), a training-free framework that leverages second-order curvature information to realign the merged router. This approach admits a closed-form solution that can be efficiently solved using a matrix-free conjugate gradient method. Experiments on mathematical reasoning and code generation tasks show that HARC effectively mitigates routing breakdown across diverse MoE merging baselines and leads to substantial performance improvements. Our code is available at https://github.com/huangcb01/HARC.

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.

Model merging offers a training-free way to combine multiple post-trained expert models, but merging experts obtained through reinforcement learning (RL) remains challenging. Existing spectral merging methods often assume that leading singular directions contain the main task signal, while lower-energy residual components can be compressed, selected, or attenuated to reduce interference. We find that this assumption does not hold for RL task vectors: after decomposing each task vector into a leading spectral head and a residual component, both parts can independently recover substantial behavior knowledge, while exhibiting different merging properties. The head is highly concentrated and informative but more prone to sharp cross-expert conflicts, whereas the residual component is more dispersed and provides a more stable basis for aggregation. Based on this observation, we propose ResMerge, a residual-based spectral merging framework for RL experts. ResMerge first constructs a stable residual backbone with Spherical Residual Consensus Adaptation, which estimates a reliability-weighted consensus direction on the Frobenius sphere. It then reintroduces leading-head information through a Lightweight Head Correction module gated by positive cross-expert agreement. Experiments across multiple RL expert groups and capability domains show that ResMerge better preserves expert capabilities than representative task-vector and spectral merging baselines. The implementation of ResMerge is publicly available at https://github.com/sunyd0303-cpu/ResMerge-release.

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.

Training strong large language models (LLMs) requires high-quality supervision, which is often scarce. Recent work shows that paired preference data from weak-weaker model pairs (e.g., Qwen3 4B over 1.7B), despite the limited quality of individual responses, can provide an effective supervision signal through relative quality deltas, which we term a "weak" signal. This motivates a key research question: can multiple "weak" signals be constructively aggregated for improving strong models (e.g., Qwen3 8B)? To this end, we propose Preference Delta Aggregation (PDA), the first framework that derives a preference delta from each weak-weaker model pair, instantiates it as a LoRA adapter learned through preference optimization, and aggregates the resulting deltas via LoRA merging. To further mitigate directional interference during LoRA merging, we introduce Geometric Alignment Merging (GAM), a geometry-aware merging method that aligns adapter subspaces before aggregation, enabling more robust composition of diverse deltas. Evaluations on knowledge reasoning and agentic search benchmarks show that aggregating multiple "weak" signals pushes performance beyond any single signal, with further gains as additional signals are incorporated. Correspondingly, PDA with GAM improves the strong model by 6.8 and 7.3 points on average for knowledge reasoning and agentic search, respectively. It outperforms all single-delta and multi-delta baselines, exceeding the best single-delta baseline by 2.1 and 4.3 points. Further analysis attributes these gains to the effective composition of complementary capabilities encoded across distinct preference deltas.

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.

Evolutionary model merging provides a powerful framework for the automated, training-free composition of LLMs through parameter-space search. However, existing methods predominantly rely on stochastic, hand-crafted operators that overlook the underlying performance landscape of the coefficient space. We propose Evolutionary Generative Merging (EvoGM), a framework that transcends manual heuristics by employing learnable generative modeling to optimize merging coefficients. Specifically, EvoGM features a dual-generator architecture with cycle-consistent learning to adaptively sample and refine promising merging candidates. By constructing winner-loser pairs from historical search trajectories, our framework effectively captures high-performance parameter distributions and maximizes data efficiency. This generative process is seamlessly integrated into a multi-round evolutionary pipeline, where elite merged models iteratively serve as new expert foundations. Extensive experiments across diverse benchmarks demonstrate that EvoGM significantly outperforms state-of-the-art baselines, exhibiting robust performance on both seen and unseen tasks. Code and data are available at https://github.com/JiangTao97/evogm.

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.

Composing autoregressive models remains a core challenge in understanding how large language models can combine behaviors or skills learned across tasks. We introduce a new and principled composition strategy for autoregressive systems, inspired by composition methods developed for diffusion models. Under a factorized-conditionals assumption, we show that the resulting composition is projective: each component model preserves control over its own designated subspace of the output distribution avoiding interference between models. This property is further preserved under smooth reparameterizations of the output space, yielding a feature-space theorem. Finally, we show that composition preserves length-generalizing behavior when the factorization assumptions and component guarantees hold uniformly at the target length. These results provide a principled understanding of when model composition and merging succeed in autoregressive systems and identify conditions under which their interactions remain stable.

Model merging has emerged as a lightweight paradigm for enhancing Large Language Models (LLMs), yet its underlying mechanisms remain poorly understood. In this work, we analyze late-stage pre-training trajectories and uncover a \textbf{Rank-1 Subspace} phenomenon: while raw optimization steps oscillate violently, consecutive \emph{merged} checkpoints collapse onto a stable, approximately one-dimensional linear manifold. We theoretically ground this observation in a \emph{river-valley} landscape analysis: averaging acts as a geometric low-pass filter that dampens high-curvature noise to reveal the optimal descent direction. Capitalizing on this insight, we propose \textbf{Extra-Merge}, a training-free strategy that extrapolates along this subspace to minimize loss without additional gradient updates. Extensive experiments across GPT-2 and LLaMA families (124M to 2B) demonstrate that Extra-Merge consistently outperforms standard merging baselines. Notably, it yields consistent zero-shot accuracy gains on Pythia-12B downstream tasks and generalizes effectively to the Muon optimizer \citep{jordan2024muon}.

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.

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.

Expanding Large Language Models~(LLMs) to new languages is a costly endeavor, demanding extensive Continued Pre-Training~(CPT) and data-intensive alignment. While recent data-free merging techniques attempt to bypass alignment by fusing a multilingual CPT-enhanced model with its instruct counterpart, they are plagued by a critical trade-off: mitigating parameter conflicts to preserve original abilities inevitably dilutes new language acquisition, and vice-versa. To resolve this conflict, we introduce \method, which upcycles a dense model into a Mixture-of-Experts~(MoE) architecture, allocating different experts to different languages. Alignment ability is then transferred by grafting a MoE-expanded parameter delta~($Δ_{\text{post}}$) to the CPT-enhanced base model, bypassing the complex alignment phase. Experiments demonstrate \method's superiority even against baselines with similar FLOPs or number of parameters; it improves performance on expanded languages while effectively preserving original capabilities. We further show our approach is highly applicable across different models and Post-training deltas.

We present Darwin Family, a framework for training-free evolutionary merging of large language models via gradient-free weight-space recombination. We ask whether frontier-level reasoning performance can be improved without additional training, by reorganizing latent capabilities already encoded in existing checkpoints. Darwin introduces three key ideas: (i) a 14-dimensional adaptive merge genome enabling fine-grained component- and block-level recombination; (ii) MRI-Trust Fusion, which adaptively balances diagnostic layer-importance signals with evolutionary search through a learnable trust parameter; and (iii) an Architecture Mapper that enables cross-architecture breeding between heterogeneous model families. Empirically, the flagship Darwin-27B-Opus achieves 86.9% on GPQA Diamond, ranking #6 among 1,252 evaluated models, and outperforming its fully trained foundation model without any gradient-based training. Across scales from 4B to 35B parameters, Darwin models consistently improve over their parents, support recursive multi-generation evolution, and enable a training-free evolutionary merge that combines Transformer- and Mamba-based components. Together, the Darwin Family demonstrates that diagnostic-guided evolutionary merging is a practical and reproducible alternative to costly post-training pipelines for reasoning-centric language models.

Multilingual knowledge editing (MKE) remains challenging because language-specific edits interfere with one another, even when locate-then-edit methods work well in monolingual settings. This paper focuses on three issues: the effectiveness of vector merging methods for MKE, the extent to which Task Singular Vectors for Merging (TSVM) can reduce multilingual interference, and the influence of the weight scaling factor and rank compression ratio on performance. We evaluate six merging variants with two popular backbone large language models, two base knowledge editing methods, and 12 languages on the MzsRE benchmark under a large-scale batch-editing setting. Our results show that vector summation with shared covariance is the most reliable overall strategy, whereas simple summation without shared covariance performs poorly. TSVM improves performance in some settings, but its ability to mitigate multilingual interference is limited. We also find that performance is sensitive to both weight scale and rank ratio, with larger-than-default scaling and relatively low rank often yielding better results. These findings clarify the practical strengths and limits of current vector merging methods for MKE and provide guidance for future multilingual knowledge editing research.

Towards more general and human-like intelligence, large language models should seamlessly integrate both multilingual and multimodal capabilities; however, extending an existing multimodal model to many languages typically requires expensive multilingual multimodal data construction and repeated end-to-end retraining. We study a training-free alternative: injecting multilingual capability into an existing multimodal model by composing residual updates in the shared language model backbone. The key challenge is that multilingual and multimodal updates are heterogeneous, reflecting different functional roles in the shared model. To address this, we propose Direction- and Magnitude-aware Multilingual Multimodal merging (DiM3), which selectively composes the two updates at each parameter dimension while preserving the original vision encoder and multimodal projector. Experiments on multilingual benchmarks in both text-only and vision-language settings, covering 57 languages across LLaVA- and Qwen-based backbones, show that DiM3 consistently outperforms existing merging baselines, substantially improves multilingual performance over the original multimodal model, and remains competitive with dedicated multilingual multimodal fine-tuning while largely retaining general multimodal ability. We further show that DiM3 can be directly applied to already trained multilingual multimodal models and still yield additional gains. Further interpretability analysis shows that DiM3 primarily reshapes intermediate-layer semantic representations, strengthening cross-lingual alignment under both text-only and multimodal inputs while preserving higher-layer task-sensitive structure. Our repository is on https://github.com/wzj1718/DiM3.

Model merging has emerged as a cost-effective paradigm for combining capabilities of multiple large language models (LLMs) without additional training. Among existing approaches, Data Flow Space (DFS) merging operates by selectively activating parameter groups across model layers, offering greater flexibility than naive parameter averaging. However, the optimization challenges underlying DFS merging remain poorly understood. In this paper, we formally characterize the DFS merging problem as a mixed binary-continuous black-box optimization problem, identifying three fundamental challenges: (1) mixed binary-continuous variable types, (2) high-dimensional search spaces with up to 291 parameter groups, and (3) conditional variable dependencies corresponding to Type-I interaction as characterized by Akimoto et al. [1]. We demonstrate that this characterization directly motivates the application of evolutionary algorithms designed for mixed-variable optimization. Empirically, we evaluate Structured DFS with CMA-ES against Parameter Space (PS) merging, Unstructured DFS, TIES-Merging, DARE, and DELLA on Mistral-7B models across official GSM8K (1,319 questions) and MMLU (14,042 questions, 57 subjects) benchmarks. Our structured approach achieves a 49.5% reduction in effective search space while maintaining competitive performance. Results reveal that standard parameter space methods (TIES: 30.48%, DELLA: 26.93% on full MMLU) perform significantly worse than optimization-aware approaches, while also identifying an important tension between task-specific reasoning performance and general knowledge preservation.

A promising paradigm for adapting instruction-tuned language models is to learn task-specific updates on a pretrained base model and subsequently merge them into the instruction-tuned model. However, existing approaches typically treat the instruction-tuned model as a passive target that is only involved at the final merging stage, without guiding the training process. We propose GIFT (Guided Fine-Tuning and Transfer), a simple and efficient framework that incorporates guidance from the instruction model into task adaptation. GIFT fine-tunes a low-rank adapter on the pretrained base model using confidence signals derived from the instruction-tuned model. The learned adapter is then merged into the instruction-tuned model, yielding task-specialized models that preserve general instruction-following behavior. We evaluate GIFT on mathematical and knowledge-intensive benchmarks across multiple model families and scales. Results show that GIFT consistently outperforms direct fine-tuning and representative transfer-based baselines, while maintaining robust generalization and favorable test-time scaling behavior.

SFT and RLVR represent two fundamental yet distinct paradigms for LLM post-training, each excelling in distinct dimensions. SFT expands knowledge breadth while RLVR enhances reasoning depth. Yet integrating these complementary strengths remains a formidable challenge. Sequential training can cause catastrophic forgetting, and joint optimization often suffers from severe gradient conflicts. We analyze SFT and RLVR through the lens of task vectors and reveal three structural properties behind these failures: a 30* magnitude disparity, 45* sign interference, and heterogeneous module-wise update distributions. These findings show SFT and RLVR are difficult to integrate directly, but they also suggest that the two paradigms modify partly complementary components of the model. Motivated by these observations, we propose Decoupled Test-time Synthesis (DoTS), a post-hoc framework allows SFT and RLVR checkpoints to be trained independently and synthesizes their capabilities only at inference time via task vector arithmetic, without updating model parameters. To reduce interference, DOTS applies selective sparsification with norm-preserving rescaling. It then uses Bayesian optimization on a small set of unlabeled queries to search for combination coefficients on the Pareto frontier of consistency and perplexity. Empirically, \ours matches or exceeds the performance of training-based SFT--RLVR integration methods across multiple mathematical reasoning benchmarks, incurring only $\sim$3% of the computational cost. When applied to stronger post-trained checkpoints, DOTS surpasses SOTA models and generalizes to out-of-domain benchmarks without re-tuning. Code is available at https://github.com/chaohaoyuan/DoTS.

This paper narrows the performance gap between small, specialized models and significantly larger general-purpose models through domain adaptation via continual pre-training and merging. We address the scarcity of specialized non-English data by constructing a high-quality German medical corpus (FineMed-de) from FineWeb2. This corpus is used to continually pre-train and merge three well-known LLMs (ranging from $7B$ to $24B$ parameters), creating the DeFineMed model family. A comprehensive evaluation confirms that specialization dramatically enhances $7B$ model performance on German medical benchmarks. Furthermore, the pairwise win-rate analysis of the Qwen2.5-based models demonstrates an approximately $3.5$-fold increase in the win-rate against the much larger Mistral-Small-24B-Instruct through domain adaptation. This evidence positions specialized $7B$ models as a competitive, resource-efficient solution for complex medical instruction-following tasks. While model merging successfully restores instruction-following abilities, a subsequent failure mode analysis reveals inherent trade-offs, including the introduction of language mixing and increased verbosity, highlighting the need for more targeted fine-tuning in future work. This research provides a robust, compliant methodology for developing specialized LLMs, serving as the foundation for practical use in German-speaking healthcare contexts.

Merging multiple Low-Rank Adaptation (LoRA) experts into a single backbone is a promising approach for efficient multi-task deployment. While existing methods strive to alleviate interference via weight interpolation or subspace alignment, they rest upon the implicit assumption that all LoRA matrices contribute constructively to the merged model. In this paper, we uncover a critical bottleneck in current merging paradigms: the existence of $\textit{negative modules}$ -- specific LoRA layers that inherently degrade global performance upon merging. We propose $\textbf{E}$volutionary $\textbf{N}$egative $\textbf{M}$odule $\textbf{P}$runing ($\textbf{ENMP}$), a plug-and-play LoRA pruning method to locate and exclude these detrimental modules prior to merging. By leveraging an evolutionary search strategy, ENMP effectively navigates the discrete, non-differentiable landscape of module selection to identify optimal pruning configurations. Extensive evaluations demonstrate that ENMP consistently boosts the performance of existing merging algorithms, achieving a new state-of-the-art across both language and vision domains. Code is available at https://github.com/CaoAnda/ENMP-LoRAMerging.