Task Vector Merging

Model merging aims to build a multi-task model cheaply by combining the weights of individual task-specific models. To perform well across multiple tasks, most existing merging methods use an additional dataset to find the coefficients for the best linear combination of task-specific weight updates. However, we identify an implicit regularization in this standard practice: searching over coefficients restricts the candidate models to a subspace spanned by task-specific weight updates. In this work, we investigate whether this regularization is actually useful. Surprisingly, empirical results show that optimizing merged-model weights without this regularization significantly boosts the performance of common merging methods across multiple architectures, domains, and even in an extremely data-limited scenario where only one instance is available per class. Moreover, directly optimizing the pretrained model weights even outperforms some existing merging methods. Analysis shows that better multi-task weights exist outside the subspace and can be found using multiple methods. We study different strategies for using the additional dataset, discussing their practical use and implications for model merging. Overall, this work calls for revisiting the existing model-merging pipeline, motivating a broader exploration of the weight space and a reconsideration of the implicit regularization induced by task arithmetic.

Continual parameter-efficient fine-tuning for large language models (LLMs) must balance retention of previously acquired knowledge, adaptation to new tasks, and strict parameter budgets. We present \textbf{ChainLoRA}, a replay-free continual merging framework built on chain-updated task-vector geometry. From a parameter-merging perspective, we formulate a geometric view of forgetting through a measurable interaction between task updates, separating directional overlap from coefficient coupling. Building on this view, ChainLoRA combines chain-updated training with post-stream adaptive SVD merging. During training, initialization and a one-sided orthogonality proxy use only the last carrier, keeping their historical-state footprint and regularization overhead constant as the task stream grows. At merging time, Adaptive SVD extracts a shared carrier and aligns it to the latest task through Procrustes adaptation. Our theoretical analysis shows that Procrustes adaptation facilitates geometric approximate separation of shared and task-specific components. The one-sided proxy further bounds inter-task interference. An effective-rank penalty additionally promotes efficient utilization of the task subspace during continual learning. Experiments show that ChainLoRA achieves state-of-the-art performance among the evaluated replay-free methods on the Large and SuperNI benchmarks, while remaining competitive on Standard CL and attaining almost the closest average scores to the evaluated replay-based method across all three benchmarks.

Task vectors provide a simple mechanism for composing learned capabilities through model merging. However, the composability of task vectors produced by on-policy distillation (OPD) remains largely unexplored. OPD trains a student using teacher feedback on student-generated trajectories, yielding parameter updates that differ from those produced by the teacher model, usually by reinforcement learning (RL). We therefore ask whether OPD task vectors can complement their RL teacher updates and compose effectively across tasks. Across five domains and two model architectures, we find evidence for both forms of composability. Within a task, merging OPD and RL task vectors can outperform both constituent models, even when the OPD student is weaker than its RL teacher. Across tasks, OPD task-vector compositions achieve higher average scores than corresponding RL compositions in seven of eight backbone-merging-rule comparisons. Parameter-space analyses reveal substantial non-collinearity between OPD and RL updates. Experiment in CODE domain on SMOLLM3-3B shows that the combined direction outperforms either constituent direction at the tested global update norm, supporting directional complementarity in this configuration. Across tasks, OPD updates also show lower overlap among the top-10% feed-forward channels ranked by update energy. Together, these results show that weaker standalone performance does not imply weaker task-vector composability. OPD task vectors can complement stronger RL teacher updates and combine effectively across tasks, highlighting composability as a distinct property for understanding and evaluating post-training updates.

Merging pretrained models has emerged as an effective approach for consolidating diverse capabilities into a single unified model. However, prevailing merging methods typically treat each task vector as an indivisible merging unit, overlooking the heterogeneous geometric changes encoded within it. This treatment can induce cross-component coupling: when merging decisions are derived from statistics of the complete task vector, the geometric characteristics of one component may influence how another is selected, weighted, or combined, potentially degrading the quality of the merged model. To address this issue, we propose DiGA, a Disentangled Geometry-Aware model merging framework. Using the pretrained weights as a shared geometric reference, DiGA orthogonally decomposes each task vector into components corresponding to distinct geometric attributes. Rather than merging the task vectors as a whole, DiGA aggregates corresponding components independently within their respective subspaces and subsequently recombines them into a unified update. This component-wise formulation preserves the geometric identity of each component and prevents the characteristics of one component from interfering with the aggregation of another. Furthermore, DiGA can be incorporated into a broad range of existing model merging methods. Extensive experiments across diverse models, tasks, and merging methods demonstrate that DiGA improves merged-model performance and reduces capability degradation. Our repository is on https://github.com/wzj1718/DiGA.

Model merging integrates task-specific fine-tuned models into a single multi-task model, but often suffers from parameter interference caused by conflicting task-vector updates. Existing methods typically mitigate conflicts by pruning task vectors based on weight magnitude or random heuristics, treating Transformers as unstructured ``bags of parameters'' and overlooking their inherent modularity. In this paper, we propose \textbf{C}ontribution-\textbf{A}ware \textbf{S}tructured \textbf{S}parsity (CASS), a unified framework that reduces parameter interference by identifying and preserving task-specific components. At the core of CASS is a contribution-aware structured mask that identifies task-relevant attention heads and FFN neurons. We instantiate this mask in two settings: CASS-Merging, the primary post-hoc setting where masks serve as a plug-and-play denoising filter for existing merging operators, and CASS-Tuning, an extension for scenarios with fine-tuning access where masks constrain gradients to reduce structural overlap between task vectors. Our analysis shows that task-relevant components are sparse and partially disjoint, supporting structured component-level filtering as an effective way to reduce merging interference. Extensive experiments across vision (ViT, 20 tasks) and language (RoBERTa, 8 tasks; Qwen2.5, 4 tasks) benchmarks demonstrate that CASS improves a range of representative merging baselines.

Model merging aims to combine multiple fine-tuned models derived from a common pretrained model into a single multi-task model without additional joint training. Recent spectral merging methods improve over simple weight averaging by exploiting low-rank structures of task-specific updates, but they commonly assign the same rank capacity to every task. This uniform allocation ignores that task vectors can have heterogeneous spectral complexity, causing the shared merging space to be used suboptimally. In this paper, we propose Spectral Energy-proportional Rank Allocation (SERA), a simple task-adaptive strategy that allocates ranks according to the singular-value energy structure of each task vector. By assigning richer spectral capacity to complex or isolated tasks and fewer directions to compact tasks, SERA extends SVD-based model merging from uniform-capacity merging to task-dependent capacity allocation. Experiments under standard vision model merging protocols show that SERA improves multi-task merging performance while preserving the same total rank budget as existing spectral merging methods. Further analysis demonstrates that task-level spectral concentration is closely related to the per-task effect of adaptive rank allocation, providing insight into when and why SERA is effective.

Task-arithmetic merging works until it doesn't, and the field diagnoses why by measuring interference inside the merged model. We take the most direct such measure, the exact layerwise activation cross-term of a factorial ledger, establish its causal anatomy, and then ask what it tracks. The anatomy is clean: each block mostly transports and amplifies the cross-term rather than generating it; erased, it is regenerated by the untouched marginal paths to 99% of its norm unless removed late; its output effect varies monotonically with the displacement's angle (orthogonal displacements make interference worse), and a two-assumption model derives the angle law and retro-dicts the dose curve (R^2 >= 0.99). What the measure tracks is not what the field assumes. Behavioural expert-likeness is decoupled from it across four instruments. Its cross-condition behaviour is denominator-dominated: an instruction template pins the main effect to within 1% while the absolute interaction grows 111x from two to six merged tasks, suppressing expressed interference at k=2 and amplifying it at k=6. And where merging actually collapses, the cross-term is a bystander, not the carrier: across two collapse parameterizations at two scales, even erased persistently at every position, removing it entirely repairs none of the collapse. There the output-side ratio carries no method information under a common counterfactual, while two state-space measures the field already uses rank methods correctly at both scales. All 81 predictions were frozen before their data; falsifications are reported as such. Output-side interference measurement reads the gate, the denominator, and the displacement budget, not the interference. What fails a merge is the carrier-bystander split: collapse rides in the marginal displacements while the cross-term merely accompanies it, and only state space sees the carrier.

Task vectors enable model merging without joint retraining. In practice, the subset of task vectors to be merged may vary, but many existing methods use scalar tuning for a particular subset, requiring repeated tuning across subsets and restricting task vector merging to linear rescaling. We therefore formulate merging across varying task subsets as a combinatorial correction problem and introduce HyperFix, a lightweight hypernetwork that predicts subset-conditioned nonlinear corrections in weight space. Trained once on singleton, pair, and triple subsets from a task bank, HyperFix generalizes to larger subsets without per-subset optimization. Our local perturbation analysis bounds the residual correction beyond linear merging and motivates learning it from small task updates. Experiments across diverse benchmarks show that HyperFix outperforms existing task vector merging methods while reducing tuning cost.

Dense expert merging combines domain-specialized language models into one single checkpoint, typically by admitting task-vector support in weight space. However, this admission is governed by three decisions that existing methods answer only partially: where to open layer capacity from cross-expert conflict, who should occupy that capacity based on domain demand, and how to admit the resulting support without relying on costly recipe search. To tackle these issues, we propose SigMerge (Signature-Guided Capacity Occupancy), a structured capacity assignment framework for dense expert merging. Starting from a dense base merge, conflict signatures set each layer's capacity from cross-expert conflict, positive base-merge deficits set each domain's share of that capacity, and a sequential occupancy rule admits each expert delta up to the resulting layer-domain budget. Across 21 paired settings spanning seven dense base merges and three model pools, SigMerge improves every one (by 15.0% on average) and achieves the best average rank (1.67) among six merging methods, outperforming three categories of merging baselines.

Model merging is often used to combine capabilities from separately fine-tuned models without additional training, but it is unclear whether standard merging methods preserve multiple safety-relevant behaviors simultaneously. We study this question through a controlled case study using two Gemma-3-1B-IT finetunes on two complementary safety objectives: CARES harm-level classification and WildJailbreak adversarial refusal. We merge the two fine-tunes using Linear, SLERP, TIES, and DARE-TIES, and evaluate the merged models on classification accuracy, attack resistance, and benign compliance. Across all four methods, attack resistance transfers significantly more than classification accuracy: merged models retain 81-85% jailbreak refusal rates while CARES accuracy falls to at most 12.9%. Weight-space measurements suggest that this asymmetry is not caused by strongly opposing task-vector directions: the two task vectors are nearly orthogonal (cosine similarity 0.011). Instead, the refusal fine-tune induces consistently larger per-layer task-vector magnitudes, causing magnitude-sensitive methods to favor refusal updates. These results show that standard model merging can collapse safety recognition into broad refusal when safety-relevant task vectors differ substantially in scale.

Model merging is promoted as a substitute for joint multi-task training, yet in the reinforcement-learning setting this substitution is essentially never tested against the baseline it claims to replace: methods merge independently released agents precisely because a joint model is unavailable. We build the missing comparison. Training difficulty-1 and difficulty-2 Qwen3-8B specialists on the AppWorld agent benchmark with LOOP, we merge them (TIES, RAM+) and pit the result against a jointly trained model on the same data. On task-goal completion, merging matches joint RL -- and every merge variant is statistically indistinguishable. To explain why merge method does not matter here, we measure the geometry of the specialists' task vectors, which carries no task-sampling noise: they are near-orthogonal (cosine 0.06 - 0.10) despite ~65% support overlap, a small, shared direction that grows over training and that we calibrate against a random-init floor and a same-run ceiling to confirm it reflects learning, not the low-rank parameterization. Because direction and support are decoupled, support and sign-based merging (RAM, TIES) collapse to near-uniform averaging. We release all code and statistics.

Adapting a multilingual encoder to a new language \emph{and} a new task with only a few hundred gold examples is a common low-resource NLP setting, yet the two axes are usually fused via an expensive language--task fine-tuning run. We ask whether they can instead be trained separately and recombined in weight space. \DeltaMergeLowRes{} learns a language delta $Δ_L$ from unlabeled monolingual text and a task delta $Δ_T$ from labeled English data, then composes them at inference under one of four rules: additive, activation-guided, sparsity-aware, and a novel \emph{cross-axis TIES}. The new rule adapts the TIES-Merging steps of trimming, sign election, and merging to the language and task axes rather than to two task axes. Holding $(Δ_L,Δ_T)$ fixed across rules on four task families and four African languages ($158$ evaluated cells, $10{,}000$-sample paired bootstrap per cell), we find: (i) cross-axis TIES wins summarisation on $3/4$ languages by $+4$ to $+7$ chrF (chrF $18.59$ vs.\ $13.80$ task-only); (ii) it improves QA F1 by $+2.32$ and EM by $+2.91$; and (iii) sparsity-aware merging cuts classification ECE by $36\%$ at parity macro-F1. The composition rule materially changes what the merged model preserves, suppresses, and calibrates. We release all JSON traces and a claim ledger.

Ever since the advent of foundation models and the pre-training-finetuning paradigm, there have been numerous efforts to merge multiple task-specific experts into a single multi-task model. Prior work largely focuses on finding a single merged model, but it often underperforms individual experts due to parameter interference. To resolve this, dynamic model merging employs routing to activate task-relevant parameters per input. However, existing routers typically require either additional training with abundant labeled datasets or assume the access to task IDs of each input at inference time. In this work, we aim to close the gap to expert performance without additional training or task-ID-access assumption. To this end, we formulate routing as training-free task classification for each test input. Using singular value decomposition (SVD)-based low-rank manifold approximations for each task, SiM scores tasks by the projection residual of the test input feature onto each task manifold and routes accordingly. The task manifolds are pre-computable offline from a pretrained backbone using a small per-task support set (e.g., 32 examples per task) prior to merging process, requiring no router training and no data during the merging process. Moreover, SiM integrates seamlessly with subspace-/mask-based merging that represents task-expert via lightweight compressed task vectors, avoiding the need to store full expert parameters. Experiments across computer vision and natural language processing benchmarks under task-unknown inference demonstrate that SiM substantially improves merged-model performance and consistently narrows the gap to individual task experts.

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.

Stereo matching has advanced through foundation models trained on large-scale datasets, yet this paradigm suffers from a scalability bottleneck: incorporating new data requires costly joint retraining. Model merging offers a scalable post-hoc alternative by integrating knowledge from specialized models after source checkpoints are available. However, existing merging methods typically retain all available models or rely on greedy inclusion, which can preserve harmful task-vector interference. We propose StereoFactory, a coarse-to-fine evolutionary framework for adaptive model merging. Stage1 employs a genetic algorithm to search the combinatorial space of model subsets, determining which models should participate. Stage2 addresses module-level knowledge specialization (different functional modules exhibit distinct preferences for knowledge sources) through CMA-ES optimization of architecture-adaptive routing over the selected task vectors, with optional module-level scaling. Experiments across two architectures and four benchmarks demonstrate that StereoFactory consistently achieves the best four-benchmark average under the same checkpoint pool, reducing the average error from 3.80 to 3.30 on NMRF and from 2.88 to 2.19 on FoundationStereo relative to the strongest controlled baseline. The post-hoc search requires only 2.7--3.7% of the corresponding joint-retraining wall-clock time. Analysis reveals that knowledge contributions are inherently module-specific, and selected subsets can transfer across architectures with minimal degradation. Code will be publicly released upon acceptance at: https://github.com/XiandaGuo/StereoFactory.

Omni-modal retrieval promises a single embedding space for text, image, video, document, and audio inputs, but building such a unified retriever is difficult since these modalities differ in data distribution, architecture, and optimization dynamics. In this work, we present Conan-embedding-v3, a decouple--fuse--recover framework for omni-modal retrieval. Conan-embedding-v3 first trains modality specialists independently and fuses their task vectors into a single dense backbone, a strategy we call Decoupled Specialist Fusion. We show that this fusion composes visual, video, and document retrieval capabilities, but also exposes a failure mode for projector-based modalities: when audio is attached through an external encoder and projector, fusing the backbone leaves the projector calibrated to the audio-specialist backbone, causing a large audio retrieval regression despite copying all audio-specific modules unchanged. We call this failure Projector Drift. To repair it, Conan-embedding-v3 applies Projector Recovery (i.e., full-parameter fine-tuning of the projector while keeping the backbone frozen) followed by balanced multi-modal rehearsal. The resulting model supports these retrieval pathways in one backbone, achieving 74.9 scores on MMEB while obtaining 55.61 on the 30-task MAEB audio suite.

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.

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.

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.

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.

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.

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.

Merging separately trained LoRA adapters is a practical alternative to joint multi-task training, but it often hurts performance. Existing methods usually treat the LoRA update $ΔW = BA$ as a single object and do not distinguish the two LoRA matrices. We show that the main source of LoRA merge interference comes from the output-side matrix $B$. Across tasks, $B$ repeatedly uses a small set of shared directions, while $A$ remains much more task-specific. As a result, the merged adapter overemphasizes these shared directions, and task-specific information is lost. We propose Pico (Pre-merge interference calibration in output-space), a data-free method that calibrates $B$ before merge by downscaling over-shared directions and then rescaling the merged update. Pico plugs directly into existing merging methods such as Task Arithmetic, TIES, and TSV-M. Across eight different benchmarks from math, coding, finance, and medical domains, Pico improves average accuracy by 3.4-8.3 points over the corresponding base method and achieves the best overall average performance. Pico also enables merged adapters to outperform the LoRA trained with all task data. These results show that LoRA merging works better when the two LoRA matrices are treated separately.