Unsupervised skill discovery in reinforcement learning (RL) aims to learn diverse behaviors without relying on external rewards. However, current methods often overlook the periodic nature of learned skills, focusing instead on increasing the mutual dependence between states and skills or maximizing the distance traveled in latent space. Considering that many robotic tasks--particularly those involving locomotion--require periodic behaviors across varying timescales, the ability to discover diverse periodic skills is essential. Motivated by this, we propose Periodic Skill Discovery (PSD), a framework that discovers periodic behaviors in an unsupervised manner. The key idea of PSD is to train an encoder that maps states to a circular latent space, thereby naturally encoding periodicity in the latent representation. By capturing temporal distance, PSD can effectively learn skills with diverse periods in complex robotic tasks, even with pixel-based observations. We further show that these learned skills achieve high performance on downstream tasks such as hurdling. Moreover, integrating PSD with an existing skill discovery method offers more diverse behaviors, thus broadening the agent's repertoire. Our code and demos are available at https://jonghaepark.github.io/psd

Effective generalization in robotic manipulation requires representations that capture invariant patterns of interaction across environments and tasks. We present a self-supervised framework for learning hierarchical manipulation concepts that encode these invariant patterns through cross-modal sensory correlations and multilevel temporal abstractions without requiring human annotation. Our approach combines a cross-modal correlation network that identifies persistent patterns across sensory modalities with a multi-horizon predictor that organizes representations hierarchically across temporal scales. Manipulation concepts learned through this dual structure enable policies to focus on transferable relational patterns while maintaining awareness of both immediate actions and longer-term goals. Empirical evaluation across simulated benchmarks and real-world deployments demonstrates significant performance improvements with our concept-enhanced policies. Analysis reveals that the learned concepts resemble human-interpretable manipulation primitives despite receiving no semantic supervision. This work advances both the understanding of representation learning for manipulation and provides a practical approach to enhancing robotic performance in complex scenarios. Code is available at: https://github.com/zrllrz/HiMaCon.

Task-trained recurrent neural networks (RNNs) are widely used in neuroscience and machine learning to model dynamical computations. To gain mechanistic insight into how neural systems solve tasks, prior work often reverse-engineers individual trained networks. However, different RNNs trained on the same task and achieving similar performance can exhibit strikingly different internal solutions, a phenomenon known as solution degeneracy. Here, we develop a unified framework to systematically quantify and control solution degeneracy across three levels: behavior, neural dynamics, and weight space. We apply this framework to 3,400 RNNs trained on four neuroscience-relevant tasks: flip-flop memory, sine wave generation, delayed discrimination, and path integration, while systematically varying task complexity, learning regime, network size, and regularization. We find that higher task complexity and stronger feature learning reduce degeneracy in neural dynamics but increase it in weight space, with mixed effects on behavior. In contrast, larger networks and structural regularization reduce degeneracy at all three levels. These findings empirically validate the Contravariance Principle and provide practical guidance for researchers seeking to tune the variability of RNN solutions, either to uncover shared neural mechanisms or to model the individual variability observed in biological systems. This work provides a principled framework for quantifying and controlling solution degeneracy in task-trained RNNs, offering new tools for building more interpretable and biologically grounded models of neural computation.

Large Vision-Language Models (LVLMs) are susceptible to hallucinations, where generated responses seem semantically plausible yet exhibit little or no relevance to the input image. Previous studies reveal that this issue primarily stems from LVLMs' over-reliance on language priors while disregarding the visual information during decoding. To alleviate this issue, we introduce a novel Conditional Pointwise Mutual Information (C-PMI) calibrated decoding strategy, which adaptively strengthens the mutual dependency between generated texts and input images to mitigate hallucinations. Unlike existing methods solely focusing on text token sampling, we propose to jointly model the contributions of visual and textual tokens to C-PMI, formulating hallucination mitigation as a bi-level optimization problem aimed at maximizing mutual information. To solve it, we design a token purification mechanism that dynamically regulates the decoding process by sampling text tokens remaining maximally relevant to the given image, while simultaneously refining image tokens most pertinent to the generated response. Extensive experiments across various benchmarks reveal that the proposed method significantly reduces hallucinations in LVLMs while preserving decoding efficiency.

Humans and traditional computer vision methods rely on a diverse set of monocular cues to infer 3D structure from a single image, such as shading, texture, silhouette, etc. While recent deep generative models have dramatically advanced single-image 3D generation, it remains unclear which image cues these methods actually exploit. We introduce Cue3D, the first comprehensive, model-agnostic framework for quantifying the influence of individual image cues in single-image 3D generation. Our unified benchmark evaluates seven state-of-the-art methods, spanning regression-based, multi-view, and native 3D generative paradigms.

Modern Vision-Language Models (VLMs) can solve a wide range of tasks requiring visual reasoning. In real-world scenarios, desirable properties for VLMs include fast inference and controllable generation (e.g., constraining outputs to adhere to a desired format).

Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in mechanisms to enforce such constraints, and existing approaches based on regularization or projection are often limited to simple constraints, computationally expensive, or lack feasibility guarantees. This paper proposes a model-agnostic framework for enforcing input-dependent linear equality and inequality constraints on neural network outputs. The architecture combines a task network trained for prediction accuracy with a safe network trained using decision rules from the stochastic and robust optimization literature to ensure feasibility across the entire input space. The final prediction is a convex combination of the two subnetworks, guaranteeing constraint satisfaction during both training and inference without iterative procedures or runtime optimization. We prove that the architecture is a universal approximator of constrained functions and derive computationally tractable formulations based on linear decision rules. Empirical results on benchmark regression tasks show that our method consistently satisfies constraints while maintaining competitive accuracy and low inference latency.

We introduce the attention-indexed model (AIM), a theoretical framework for analyzing learning in deep attention layers. Inspired by multi-index models, AIM captures how token-level outputs emerge from layered bilinear interactions over high-dimensional embeddings. Unlike prior tractable attention models, AIM allows full-width key and query matrices, aligning more closely with practical transformers. Using tools from statistical mechanics and random matrix theory, we derive closed-form predictions for Bayes-optimal generalization error and identify sharp phase transitions as a function of sample complexity, model width, and sequence length. We propose a matching approximate message passing algorithm and show that gradient descent can reach optimal performance. AIM offers a solvable playground for understanding learning in self-attention layers, that are key components of modern architectures.

Simulated tempering is a widely used strategy for sampling from multimodal distributions. In this paper, we consider simulated tempering combined with an arbitrary local Markov chain Monte Carlo sampler and present a new decomposition theorem that provides a lower bound on the restricted spectral gap of the algorithm for sampling from mixture distributions. By working with the restricted spectral gap, the applicability of our results is extended to broader settings such as when the usual spectral gap is difficult to bound or becomes degenerate. We demonstrate the application of our theoretical results by analyzing simulated tempering combined with random walk Metropolis-Hastings for sampling from mixtures of Gaussian distributions. Our complexity bound scales polynomially with the separation between modes, logarithmically with 1/ε, where εdenotes the target accuracy in total variation distance, and exponentially with the dimension d.

We study population convergence guarantees of stochastic gradient descent (SGD) for smooth convex objectives in the interpolation regime, where the noise at optimum is zero or near zero. The behavior of the last iterate of SGD in this setting--particularly with large (constant) stepsizes--has received growing attention in recent years due to implications for the training of over-parameterized models, as well as to analyzing forgetting in continual learning and to understanding the convergence of the randomized Kaczmarz method for solving linear systems.