A Capacity--Redundancy (CR) identity is investigated that decomposes the sum of per-task predictive informations into joint predictive information that includes label redundancy defined via total correlation (TC), and a residual coupling term that quantifies interference left unresolved by the shared representation.
Abstract
In multi-task learning (MTL) negative transfer is often considered as an optimization artifact, but it can also be viewed as a consequence of limited shared capacity and weak task redundancy. We investigate this effect through a Capacity--Redundancy (CR) identity that decomposes the sum of per-task predictive informations into joint predictive information that includes label redundancy defined via total correlation (TC), and a residual coupling term that quantifies interference left unresolved by the shared representation. Additionally, we show two key results: (i) a clustering-gap decomposition that gives a necessary and sufficient condition for clustered sharing to outperform global sharing, and (ii) a gradient--TC bridge in a Gaussian multi-task model that formally justifies gradient cosine similarity as a proxy for redundancy ordering. Empirically, we estimate the residual coupling $\Delta$ from validation residual correlations, showing that clustered LoRA substantially reduces $\widehat{\Delta}$, outperforms size-matched random partitions, and results in statistically significant gains with multi-seed confidence intervals.
Model merging provides an efficient way to construct multi-task generalist models without additional training, but its performance often degrades under severe task interference. Task interference in model merging primarily stems from \textit{superposition}, where task-specific features become entangled within the parameter space. This entanglement renders conventional decomposition methods insufficient for effectively isolating useful task directions from interfering components. In this paper, we propose a sparse-representation-based merging framework that uses Sparse Autoencoders (SAEs) to project task vectors into a high-dimensional sparse feature space, enabling feature-level disentanglement before fusion. To reduce computational overhead, we further introduce a lightweight Group-Ranked Zeroth-Order Optimizer (GR-ZOO) to identify task-critical layers for selective merging. Experiments on both Qwen2.5-1.5B and Qwen2.5-7B demonstrate that our method consistently outperforms representative baselines, including Task Arithmetic, TIES-Merge, DARE, Fisher-Merge,and several recent training-free merging methods, across mathematical reasoning, code generation, instruction following, and general knowledge tasks. In a highly conflicting four-task setting on Qwen2.5-1.5B, our method further achieves a 2.78\% improvement over the strongest baseline.
Yi-Hang Zhang, Shengen Sun, Junbo Wen et al.· 0 citations
Vision foundation backbones provide strong representations for dense prediction, yet a single shared feature still needs to support tasks with different, image-dependent adaptation requirements. We propose MemMTL, a multi-task dense prediction framework that estimates a compact task state from global visual context and refines it through a learnable task-state prototype memory. The refined state is converted into task-conditioned expert logits and combined with token-level logits before sparse top-$k$ selection over a local expert bank shared by all tasks. A separate task-agnostic residual bank provides a common adaptation path, and both paths are added once to the backbone feature before task-specific prediction. We specify a matched evaluation protocol on NYUD-v2 and PASCAL-Context with SAM 3 and ViT-L backbones to measure predictive quality, computational cost, and the contributions of task-state conditioning, prototype retrieval, and sparse routing. The numerical record in the present working draft predates this canonical implementation and must be regenerated before it can support empirical claims.
Yangyang Xu, Haobo Yuan, Yuzhu Wang et al.· 0 citations
By eliminating routers entirely, CD-LoRA employs a consistency-driven alignment mechanism to enforce representation congruence across tasks in a shared low-rank space, which fosters robust, task-agnostic features without explicit partitioning overhead.
Viewing OC as a last-layer ensemble also organizes detectors into a two-axis taxonomy and exposes the OC score as a magnitude, motivating a scale-invariant, label-free direction score that repairs its near-OOD failure.
H. M. Gillis, Isaac Xu, Gabriel Spadon et al.· arXiv.org· 0 citations
Experiments show that FiUni can effectively infer latent batch-level task affiliations and achieve competitive performance against advanced task-aware CL methods with fewer trainable parameters.
Dezheng Han, Anlan Zhang, Zhiwu Zhu et al.· 0 citations
Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) exhibit fundamentally different behaviors in enhancing multi-task reasoning for large language models (LLMs). Our preliminary experiments revealed a phenomenon: SFT suffers from severe task conflicts under multi-stage training, whereas RL enables stable coexistence across diverse tasks. Empirically, we trace this to the parameter level, observing that RL induces sparse and approximately orthogonal updates across tasks. We provide a theoretical explanation for this mechanism by analyzing multi-task gradient interference. Our results reveal a distinction: interference in SFT is norm-limited, scaling with the absolute gradient magnitude, whereas interference in RL is variance-limited, bounded by the gradient variance induced by advantage normalization and on-policy optimization. This small variance bound yields near-orthogonal optimization directions across tasks. Leveraging this insight, we propose Parallel-RL, a paradigm that decouples multi-task training, significantly improving efficiency and flexibility.
Kejian Zhu, Zhuoran Jin, Shangqing Tu et al.· 0 citations
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