Information-Theoretic Requirements for Gradient-Based Task Affinity Estimation in Multi-Task Learning

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 $Δ$ from validation residual correlations, showing that clustered LoRA substantially reduces $\widehatΔ$, outperforms size-matched random partitions, and results in statistically significant gains with multi-seed confidence intervals.

A fundamental problem in multi-task learning (MTL) is identifying groups of tasks that should be learned together. Since training MTL models for all possible combinations of tasks is prohibitively expensive for large task sets, a crucial component of efficient and effective task grouping is predicting whether a group of tasks would benefit from learning together, measured as per-task performance gain over single-task learning. In this paper, we propose ETAP (Ensemble Task Affinity Predictor), a scalable framework that integrates principled and data-driven estimators to predict MTL performance gains. First, we consider the gradient-based updates of shared parameters in an MTL model to measure the affinity between a pair of tasks as the similarity between the parameter updates based on these tasks. This linear estimator, which we call affinity score, naturally extends to estimating affinity within a group of tasks. Second, to refine these estimates, we train predictors that apply non-linear transformations and correct residual errors, capturing complex and non-linear task relationships. We train these predictors on a limited number of task groups for which we obtain ground-truth gain values via multi-task learning for each group. We demonstrate on benchmark datasets that ETAP improves MTL gain prediction and enables more effective task grouping, outperforming state-of-the-art baselines across diverse application domains.

Existing multi-task active learning (MTL-AL) methods predominantly rely on linear scalarization of heterogeneous objectives such as uncertainty, diversity, and gradient conflict. We argue that this entangled formulation is fundamentally limited, as linear combination fails to capture Pareto-optimal trade-offs under conflicting objectives. We propose a shift from combination to deconstruction and introduce a principled framework that rethinks MTL-AL along three orthogonal dimensions. First, we identify the Conflict Paradox: although the optimization literature treats gradient conflict as interference to be suppressed, penalizing conflict when ranking candidates is measurably worse than not scoring it at all. We therefore decouple the two concerns: the acquisition function does not score conflict, and the resulting interference is resolved by gradient surgery during training. Second, we introduce Orthogonal Decomposition, separating acquisition into Informativeness and Exploration. This two-stage process, informativeness filtering followed by coverage maximization, prevents "diversity dilution" by excluding uninformative outliers before enforcing diversity. Third, we propose Cross-Task Mutual Information (CTMI), a covariance-based statistic of cross-task dependency computed from MC-dropout task entropies. Extensive experiments on COCO, Cityscapes, and NYUv2, including comparisons against recent MTL-AL and data-selection baselines, demonstrate consistent improvements over state-of-the-art methods, highlighting that structural rethinking of acquisition yields larger gains than incremental heuristic design. Code is available at https://github.com/Juho-Jung/multitask_active_learning_official.