Instruction tuning improves the ability of large language models (LLMs) to follow diverse human instructions, but achieving strong performance on specific target tasks remains challenging. A critical bottleneck is selecting the most relevant data to maximize task-specific performance. Existing data selection approaches include unstable influence-based methods and more stable distribution alignment methods, the latter of which critically rely on the underlying sample representation. In practice, most distribution alignment methods, from shallow features (e.g., BM25) to neural embeddings (e.g., BGE, LLM2Vec), may fail to capture how the model internally processes samples. To bridge this gap, we adopt a model-centric strategy in which each sample is represented by its neuronal activation pattern in the model, directly reflecting internal computation. However, directly using raw neuron activations leads to spurious similarity between unrelated samples due to neuron polysemanticity, where a single neuron may respond to multiple, unrelated concepts. To address this, we employ sparse autoencoders to disentangle polysemantic activations into sparse, monosemantic representations, and introduce a dedicated similarity metric for this space to better identify task-relevant data. Comprehensive experiments across multiple instruction datasets, models, tasks, and selection ratios show that our approach consistently outperforms existing data selection baselines in both stability and task-specific performance2.

Learning-to-learn or meta-learning focuses on developing algorithms that leverage prior experience to quickly acquire new skills or adapt to novel environments. A crucial component of meta-learning is representation learning, which aims to construct data representations capable of transferring knowledge across multiple tasks--a critical advantage in data-scarce settings. We study how representation learning can improve the efficiency of bandit problems. We consider T d-dimensional linear bandits that share a common low-dimensional linear representation. We provide provably fast, sample-efficient algorithms to address the two key problems in meta-learning: (1) learning a common set of features from multiple related bandit tasks and (2) transferring this knowledge to new, unseen bandit tasks.

Large Language Models (LLMs) have shown remarkable capabilities, with optimizing their input prompts playing a pivotal role in maximizing their performance. However, while LLM prompts consist of both the task-agnostic system prompts and task-specific user prompts, existing work on prompt optimization has focused on user prompts specific to individual queries or tasks, and largely overlooked the system prompt that is, once optimized, applicable across different tasks and domains. Motivated by this, we introduce the novel problem of bilevel system prompt optimization, whose objective is to design system prompts that are robust to diverse user prompts and transferable to unseen tasks. To tackle this problem, we then propose a meta-learning framework, which meta-learns the system prompt by optimizing it over various user prompts across multiple datasets, while simultaneously updating the user prompts in an iterative manner to ensure synergy between them. We conduct experiments on 14 unseen datasets spanning 5 different domains, on which we show that our approach produces system prompts that generalize effectively to diverse user prompts. Also, our findings reveal that the optimized system prompt enables rapid adaptation even to unseen tasks, requiring fewer optimization steps for test-time user prompts while achieving improved performance.

Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target problems by inferring compositional rules from context examples, which are composed of basic components structured by underlying rules. However, some of these tasks remain challenging for Transformers, which are not inherently designed to handle compositional tasks and offer limited structural inductive bias. In this work, inspired by the principle of sparse coding, we propose a reformulation of the attention to enhance its capability for compositional tasks. In sparse coding, data are represented as sparse combinations of dictionary atoms with coefficients that capture their compositional rules.

Multi-source transfer learning provides an effective solution to data scarcity in realworld supervised learning scenarios by leveraging multiple source tasks. In this field, existing works typically use all available samples from sources in training, which constrains their training efficiency and may lead to suboptimal results. To address this, we propose a theoretical framework that answers the question: what is the optimal quantity of source samples needed from each source task to jointly train the target model? Specifically, we introduce a generalization error measure based on K-L divergence, and minimize it based on high-dimensional statistical analysis to determine the optimal transfer quantity for each source task. Additionally, we develop an architecture-agnostic and data-efficient algorithm OTQMS to implement our theoretical results for target model training in multisource transfer learning. Experimental studies on diverse architectures and two real-world benchmark datasets show that our proposed algorithm significantly outperforms state-of-the-art approaches in both accuracy and data efficiency. The code is available at https://github.com/zqy0126/OTQMS.

Sparse-reward reinforcement learning (RL) can model a wide range of highly complex tasks. Solving sparse-reward tasks is RL's core premise--requiring efficient exploration coupled with long-horizon credit assignment--and overcoming these challenges is key for building self-improving agents with superhuman ability. Prior work commonly explores with the objective of solving many sparse-reward tasks, making exploration of individual high-dimensional, long-horizon tasks intractable. We argue that solving such challenging tasks requires solving simpler tasks that are relevant to the target task, i.e., whose achieval will teach the agent skills required for solving the target task. We demonstrate that this sense of direction, necessary for effective exploration, can be extracted from existing RL algorithms, without leveraging any prior information. To this end, we propose a method for directed sparse-reward goal-conditioned very long-horizon RL (DISCOVER), which selects exploratory goals in the direction of the target task. We connect DISCOVER to principled exploration in bandits, formally bounding the time until the target task becomes achievable in terms of the agent's initial distance to the target, but independent of the volume of the space of all tasks. We then perform a thorough evaluation in high-dimensional environments. We find that the directed goal selection of DISCOVER solves exploration problems that are beyond the reach of prior state-of-the-art exploration methods in RL.

Sparse-reward reinforcement learning (RL) can model a wide range of highly complex tasks. Solving sparse-reward tasks is RL's core premise -- requiring efficient exploration coupled with long-horizon credit assignment -- and overcoming these challenges is key for building self-improving agents with superhuman ability. We argue that solving complex and high-dimensional tasks requires solving simpler tasks that are to the target task. In contrast, most prior work designs strategies for selecting exploratory tasks with the objective of solving task, making exploration of challenging high-dimensional, long-horizon tasks intractable. We find that the sense of direction, necessary for effective exploration, can be extracted from existing reinforcement learning algorithms, without needing any prior information.

Modern learning systems excel at interpolation but struggle to generalize to unseen tasks outside the training distribution's support. This failure occurs even in simple settings, such as handling task parameters beyond the training range, and persists despite advances in foundation models. To this end, we develop the Relational Task Extrapolator (RTE), an algorithm designed to enable systematic extrapolation to novel tasks. The key observation is that extrapolation is inherently relational: extrapolating to unseen tasks requires learning how tasks transform into one another. If a model learns the transformation between tasks A and B during training, it can apply that same transformation to relate known tasks to unseen ones at test time. RTE operationalizes this idea by decomposing each target task into a known anchor task and a transformation linking the anchor and target. It then learns a relational operator, mapping an anchor-transformation pair to predictions for the target task. We instantiate RTE across multiple task extrapolation regimes in function prediction, e.g. where target tasks use out-of-range parameters (parameter extrapolation), have greater compositional depth (length extrapolation), and/or recombine function primitives in unseen ways (compositional extrapolation). We further extend RTE to sequence prediction, integrating it into fine-tuning algorithms for foundation models. Across empirical studies, we find that RTE substantially outperforms existing approaches on extrapolation to novel, unseen tasks.

Representation learning based on multi-task pretraining has become a powerful approach in many domains. In particular, task-aware representation learning aims to learn an optimal representation for a specific target task by sampling data from a set of source tasks, while task-agnostic representation learning seeks to learn a universal representation for a class of tasks. In this paper, we propose a general and versatile algorithmic and theoretic framework for active representation learning, where the learner optimally chooses which source tasks to sample from. This framework, along with a tractable meta algorithm, allows most arbitrary target and source task spaces (from discrete to continuous), covers both task-aware and task-agnostic settings, and is compatible with deep representation learning practices. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. In the bilinear case, by leveraging the non-uniform spectrum of the task representation and the calibrated source-target relevance, we prove that the sample complexity to achieve ε-excess risk on target scales with (k)2 v 22ε 2 where k is the effective dimension of the target and v 22 (0,1] represents the connection between source and target space. Compared to the passive one, this can save up to 1dW of sample complexity, where dW is the task space dimension. Finally, we demonstrate different instantiations of our meta algorithm in synthetic datasets and robotics problems, from pendulum simulations to real-world drone flight datasets. On average, our algorithms outperform baselines by 20% 70%. 1