Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging

Zijing Wang; Yongkang Liu; Mingyang Wang; Ercong Nie; Mengjie Zhao; Yunpu Ma; Kang Liu; Zihan Wang; Shi Feng; Daling Wang; Hinrich Schütze

arXiv · 2609.37564

Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging

Zijing Wang·Yongkang Liu·Mingyang Wang·Ercong Nie·Mengjie Zhao·Yunpu Ma·Kang Liu·Zihan Wang·Shi Feng·Daling Wang·Hinrich Schütze

View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cs.CL

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Zijing Wang, Yongkang Liu, Mingyang Wang, Ercong Nie, Mengjie Zhao, Yunpu Ma, Kang Liu, Zihan Wang, Shi Feng, Daling Wang, Hinrich Schütze. 2026-09-29. Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging. https://arxiv.org/abs/2609.37564

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

NMIXX: Domain-Adapted Neural Embeddings for Cross-Lingual eXploration of Finance

Financial text embeddings must distinguish changes in event status, perspective, and obligations even when passages share similar wording. NMIXX adapts existing encoders through 18.8k source-linked triplets: paraphrases and Korean-English translations preserve meaning, while targeted financial rewrites introduce semantic contrasts. We examine this recipe across seven backbones on English and Korean financial and general-domain semantic textual similarity (STS), and analyze the composition and passage lengths of KorFinSTS. BGE-M3 attains the highest adapted financial correlations in this comparison, improving from 0.1969 to 0.2967 on FinSTS and from 0.0512 to 0.2732 on KorFinSTS. Its general English and Korean correlations decrease by 0.0391 and 0.0463. Across the seven models, five improve their mean financial correlation, but all reduce their mean general-domain correlation. Per-language comparisons and benchmark-weight sensitivity analysis reveal differences obscured by a single aggregate score. The study contributes a finance-specific supervision design and evidence for evaluating adaptation jointly with retained general semantic capability; direct cross-language retrieval remains outside its evaluation scope.

cs.CL↗

arXiv2026

Sequential Bayesian Evaluation of Large Language Model Behavior

It is increasingly important to evaluate the characteristics of systems based on large language models (LLMs). Evaluations in this context often rely on a curated benchmark set of input prompts provided to the LLM, where the output for each prompt may be assigned a binary or ordinal score and the aggregation of scores across prompts is then used as a summary evaluation. In this paper, we develop a Bayesian approach for quantifying the uncertainty that arises in such evaluation metrics as a result of the stochasticity of the LLM-based systems; the same prompt may exhibit different outcomes on repeated runs. Our framework leads naturally to a sequential evaluation, in which we leverage the Bayesian model to preferentially select which prompts in the benchmark to use next, enabling more cost-effective LLM evaluations. We demonstrate this approach through four case studies: pairwise LLM preferences in interactive dialogue (MT-Bench), refusal rates on adversarial inputs (JailbreakBench), embodied agentic reasoning (ALFWorld), and agentic web-search Q&A (GAIA). Our results illustrate how a Bayesian approach can provide insightful uncertainty quantification about the behavior of blackbox LLM-based systems in a manner that is not accessible via deterministic or single-run evaluations.

cs.CL↗

arXiv2026

ResidualKV: Residual-Based KV Cache Compression for Efficient Long-Context Inference

Efficient long-context inference faces two coupled bottlenecks: KV-cache memory grows linearly with context length, while attention computation grows quadratically. Existing approaches typically address one at the expense of irreversible token eviction, full-cache retention, or full-history reconstruction, limiting their effectiveness for multi-turn interaction and long-form reasoning. Motivated by two empirical properties, Long-Range Inter-Token Similarity and Smooth Residual Distribution, we propose ResidualKV, which factorizes the KV cache into a sparse set of globally retrieved references and compact, quantized residual codes for the remaining tokens. This representation preserves token-specific information without permanent eviction and, when combined with sparse attention, reconstructs only the selected states on demand. Dynamic-stride scheduling further reduces reference growth from linear to approximately logarithmic at ultra-long contexts. Across Llama, Qwen, LLaVA-OV, and Qwen3-VL backbones, ResidualKV maintains near-full-cache performance using only 13%-16% KV storage and 30% attention computation on LongBench, and 8%-10% storage and 10% computation in matched-budget multimodal evaluation. It also accelerates decoding by up to $1.5\times$ with KV-cache quantization and $3.4\times$ without it. These results show that global cross-token redundancy supports accurate, memory-efficient, and computation-efficient long-context inference. The source code is available at https://github.com/CURRENTF/ResidualKV.

cs.CL↗