Length generalization, the ability of sequence models to generalize to sequences longer than those encountered during training, remains a key challenge for transformers, especially in tasks requiring algorithmic reasoning. Existing theoretical understanding of length generalization is limited, often providing only asymptotic results or focusing on specific problem classes or architectural variants, while empirical approaches frequently rely on ad hoc and often fragile techniques. In this work we introduce a novel framework for analyzing and proving length generalization bounds under specified, verifiable assumptions. A key outcome of the theory is the identification of a natural set of auxiliary tasks, intricately related to the primary task structure, such that strong performance on these auxiliary tasks, alongside the primary task, provably guarantees length generalization within the framework. This motivates a multi-task training procedure that explicitly optimizes performance on both the primary and the identified auxiliary tasks. Empirical evaluations on a variety of synthetic benchmarks known to be challenging for length generalization, including sequence sorting, and reversal, demonstrate that our proposed method yields significant improvements in generalization to substantially longer sequences.

Recent studies in Machine Learning (ML) for biological research focus on investigating molecular properties to accelerate drug discovery. However, limited labeled molecular data often hampers the performance of ML models. A common strategy to mitigate data scarcity is leveraging auxiliary learning tasks to provide additional supervision, but selecting effective auxiliary tasks requires substantial domain expertise and manual effort, and their inclusion does not always guarantee performance gains. To overcome these challenges, we introduce Automatic Auxiliary Task Selection (AUTAUT), a fully automated framework that seamlessly retrieves auxiliary tasks using large language models and adaptively integrates them through a novel gradient alignment weighting mechanism. By automatically emphasizing auxiliary tasks aligned with the primary objective, AUTAUT significantly enhances predictive accuracy while reducing negative impacts from irrelevant tasks. Extensive evaluations demonstrate that AUTAUT outperforms 10 auxiliary task-based approaches and 18 advanced molecular property prediction models.

Recent studies in (ML) for biological research focus on investigating molecular properties to accelerate drug discovery. However, limited labeled molecular data often hampers the performance of ML models. A common strategy to mitigate data scarcity is leveraging auxiliary learning tasks to provide additional supervision, but selecting effective auxiliary tasks requires substantial domain expertise and manual effort, and their inclusion does not always guarantee performance gains. To overcome these challenges, we introduce (AutAuT), a fully automated framework that seamlessly retrieves auxiliary tasks using large language models and adaptively integrates them through a novel weighting mechanism. By automatically emphasizing auxiliary tasks aligned with the primary objective, AutAuT significantly enhances predictive accuracy while reducing negative impacts from irrelevant tasks. Extensive evaluations demonstrate that AutAuT outperforms auxiliary task-based approaches and advanced molecular property prediction models.

Our main contribution in this work is an empirical finding that random General Value Functions (GVFs), i.e., deep action-conditional predictions--random both in what feature of observations they predict as well as in the sequence of actions the predictions are conditioned upon--form good auxiliary tasks for reinforcement learning (RL) problems. In particular, we show that random deep action-conditional predictions when used as auxiliary tasks yield state representations that produce control performance competitive with state-of-the-art hand-crafted auxiliary tasks like value prediction, pixel control, and CURL in both Atari and DeepMind Lab tasks. In another set of experiments we stop the gradients from the RL part of the network to the state representation learning part of the network and show, perhaps surprisingly, that the auxiliary tasks alone are sufficient to learn state representations good enough to outperform an end-to-end trained actor-critic baseline.

In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this issue in two canonical linear settings: ordinary least squares regression and under-parameterized linear neural networks. For linear regression, we derive exact closed-form expressions for the expected generalization error with bias-variance decomposition, yielding necessary and sufficient conditions for auxiliary tasks to improve generalization on the main task. We also derive globally optimal task weights as outputs of solvable optimization programs, with consistency guarantees for empirical estimates. For linear neural networks with shared representations of width $q \leq K$, where $K$ is the number of auxiliary tasks, we derive a non-asymptotic expectation bound on the generalization error, yielding the first non-vacuous sufficient condition for beneficial auxiliary learning in this setting, as well as principled directions for task weight curation. We achieve this by proving a new column-wise low-rank perturbation bound for random matrices, which improves upon existing bounds by preserving fine-grained column structures. Our results are verified on synthetic data simulated with controlled parameters.

Multi-Task Learning (MTL) is appealing for deep learning regularization. In this paper, we tackle a specific MTL context denoted as primary MTL, where the ultimate goal is to improve the performance of a given primary task by leveraging several other auxiliary tasks. Our main methodological contribution is to introduce ROCK, a new generic multi-modal fusion block for deep learning tailored to the primary MTL context. ROCK architecture is based on a residual connection, which makes forward prediction explicitly impacted by the intermediate auxiliary representations. The auxiliary predictor's architecture is also specifically designed to our primary MTL context, by incorporating intensive pooling operators for maximizing complementarity of intermediate representations. Extensive experiments on NYUv2 dataset (object detection with scene classification, depth prediction, and surface normal estimation as auxiliary tasks) validate the relevance of the approach and its superiority to flat MTL approaches. Our method outperforms state-of-the-art object detection models on NYUv2 dataset by a large margin, and is also able to handle large-scale heterogeneous inputs (real and synthetic images) with missing annotation modalities.

Supervised learning requires a large amount of training data, limiting its application where labeled data is scarce. To compensate for data scarcity, one possible method is to utilize auxiliary tasks to provide additional supervision for the main task. Assigning and optimizing the importance weights for different auxiliary tasks remains an crucial and largely understudied research question. In this work, we propose a method to automatically reweight auxiliary tasks in order to reduce the data requirement on the main task. Specifically, we formulate the weighted likelihood function of auxiliary tasks as a surrogate prior for the main task. By adjusting the auxiliary task weights to minimize the divergence between the surrogate prior and the true prior ofthe main task, we obtain amore accurate prior estimation, achieving the goal of minimizing the required amount of training data for the main task and avoiding a costly grid search.