We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory, physics and economics. While traditional numerical methods suffer from the curse of dimensionality and become computationally intractable in high dimensions, more recent neural network-based approaches scale better, but have mostly been studied with the aim of solving optimal transport problems and require the solution of complicated optimization or max-min problems. Using an implicit Fenchel formulation of convex conjugation, our approach facilitates an efficient gradient-based framework for the minimization of approximation errors and, as a byproduct, also provides a posteriori estimates of the approximation accuracy. Numerical experiments demonstrate our method's ability to deliver accurate results across different high-dimensional examples. Moreover, by employing symbolic regression with Kolmogorov-Arnold networks, it is able to obtain the exact convex conjugates of specific convex functions.

The ability to actively acquire information is essential for open-world planning under partial observability and incomplete knowledge. However, most existing embodied AI systems either assume a known object category or rely on passive perception strategies that exhaustively gather object and relational information from the environment. Such a strategy becomes insufficient in visually complex open-world settings. For instance, a typical household may contain thousands of novel and uniquely configured objects, most of which are irrelevant to the agent's current task. Consequently, open-world agents must be capable of actively identifying and prioritizing task-relevant objects to enable efficient and goal-directed knowledge acquisition. In this work, we introduce ActiveVOO, a novel zero-shot framework for open-world embodied planning that emphasizes object-centric active knowledge acquisition. ActiveVOO employs lifted regression to generate compact, first-order subgoal descriptions that identify task-relevant objects, and provides a principled mechanism to quantify the utility of sensing actions based on commonsense priors derived from LLMs and VLMs. We evaluate ActiveVOO on the visual ALFWorld benchmark, where it achieves substantial improvements over existing LLMand VLM-based planning approaches, notably outperforming VLMs fine-tuned on ALFWorld data. This work establishes a principled foundation for developing embodied agents capable of actively and efficiently acquiring knowledge to plan and act in open-world environments.

Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability simplex. Despite the constant injection of noise and the non-convexity of the underlying optimization problem, one can rigorously prove that the considered Hebbian learning dynamic identifies the presynaptic neuron with the highest activity and that the convergence is exponentially fast in the number of iterations. This is non-standard and surprising as typically noisy gradient descent with fixed noise level only converges to a stationary regime where the noise causes the dynamic to fluctuate around a minimiser.

The rapid increase in AI-generated images (AIGIs) underscores the need for detection methods. Existing detectors are often trained on biased datasets, leading to overfitting on spurious correlations between non-causal image attributes and real/synthetic labels. While these biased features enhance performance on the training data, they result in substantial performance degradation when tested on unbiased datasets. A common solution is to perform data alignment through generative reconstruction, matching the content between real and synthetic images. However, we find that pixel-level alignment alone is inadequate, as the reconstructed images still suffer from frequency-level misalignment, perpetuating spurious correlations.

We consider the problem of recovering a mental target (e.g., an image of a face) that a participant has in mind from paired EEG (i.e., brain responses) and image (i.e., perceived faces) data collected during interactive sessions without access to labeled information. The problem has been previously explored with labeled data but not via self-calibration, where labeled data is unavailable. Here, we present the first framework and an algorithm, CURSOR, that learns to recover unknown mental targets without access to labeled data or pre-trained decoders. Our experiments on naturalistic images of faces demonstrate that CURSOR can (1) predict image similarity scores that correlate with human perceptual judgments without any label information, (2) use these scores to rank stimuli against an unknown mental target, and (3) generate new stimuli indistinguishable from the unknown mental target (validated via a user study, N=53). We release the brain response data set (N=29), associated face images used as stimuli data, and a codebase to initiate further research on this novel task.

Direct Preference Optimization (DPO) is a powerful paradigm to align language models with human preferences using pairwise comparisons. However, its binary win-or-loss supervision often proves insufficient for training small models with limited capacity. Prior works attempt to distill information from large teacher models using behavior cloning or KL divergence. These methods often focus on mimicking current behavior and overlook distilling reward modeling. To address this issue, we propose \textit{Teacher Value-based Knowledge Distillation} (TVKD), which introduces an auxiliary reward from the value function of the teacher model to provide a soft guide. This auxiliary reward is formulated to satisfy potential-based reward shaping, ensuring that the global reward structure and optimal policy of DPO are preserved. TVKD can be integrated into the standard DPO training framework and does not require additional rollouts. Our experimental results show that TVKD consistently improves performance across various benchmarks and model sizes.

Uncertainty quantification for Large Language Models (LLMs) encompasses a diverse range of approaches, with two major families being particularly prominent: (i) information-based, which estimate model confidence from token-level probabilities, and (ii) consistency-based, which assess the semantic agreement among multiple outputs generated using repeated sampling. While several recent methods have sought to combine these two paradigms to improve uncertainty quantification performance, they often fail to consistently outperform simpler baselines. In this work, we revisit the foundations of uncertainty estimation through the lens of Minimum Bayes Risk decoding, establishing a direct link between uncertainty and the optimal decision-making process of LLMs. Building on these findings, we propose CoCoA, a unified framework that integrates model confidence with output consistency, yielding a family of efficient and robust uncertainty quantification methods. We evaluate CoCoA across diverse tasks, including question answering, abstractive text summarization, and machine translation, and demonstrate sizable improvements over state-of-the-art uncertainty quantification approaches.

Preference optimization for diffusion models aims to align them with human preferences for images. Previous methods typically use Vision-Language Models (VLMs) as pixel-level reward models to approximate human preferences. However, when used for step-level preference optimization, these models face challenges in handling noisy images of different timesteps and require complex transformations into pixel space. In this work, we show that pre-trained diffusion models are naturally suited for step-level reward modeling in the noisy latent space, as they are explicitly designed to process latent images at various noise levels.

Despite significant advances in Vision Language Models (VLMs), they remain constrained by the complexity and redundancy of visual input. When images contain large amounts of irrelevant information, VLMs are susceptible to interference, thus generating excessive task-irrelevant reasoning processes or even hallucinations. This limitation stems from their inability to discover and process the required regions during reasoning precisely. To address this limitation, we present the Chain of Foresight-Focus Thought (CoFFT), a novel training-free approach that enhances VLMs' visual reasoning by emulating human visual cognition. Each Foresight-Focus Thought consists of three stages: (1) Diverse Sample Generation: generates diverse reasoning samples to explore potential reasoning paths, where each sample contains several reasoning steps; (2) Dual Foresight Decoding: rigorously evaluates these samples based on both visual focus and reasoning progression, adding the first step of optimal sample to the reasoning process; (3) Visual Focus Adjustment: precisely adjust visual focus toward regions most beneficial for future reasoning, before returning to stage (1) to generate subsequent reasoning samples until reaching the final answer. These stages function iteratively, creating an interdependent cycle where reasoning guides visual focus and visual focus informs subsequent reasoning.

Langevin Dynamics (LD) and its discrete proposal have been widely applied in the field of Combinatorial Optimization (CO). Both sampling-based and data-driven approaches have benefited significantly from these methods. However, LD's reliance on Gaussian noise limits its ability to escape narrow local optima, requires costly parallel chains, and performs poorly in rugged landscapes or with non-strict constraints. These challenges have impeded the development of more advanced approaches. To address these issues, we introduce Fractional Langevin Dynamics (FLD) for CO, replacing Gaussian noise with $\alpha$-stable L\'evy noise. FLD can escape from local optima more readily via L\'evy flights, and in multiple-peak CO problems with high potential barriers it exhibits a polynomial escape time that outperforms the exponential escape time of LD. Moreover, FLD coincides with LD when $\alpha = 2$, and by tuning $\alpha$ it can be adapted to a wider range of complex scenarios in the CO fields. We provide theoretical proof that our method offers enhanced exploration capabilities and improved convergence. Experimental results on the Maximum Independent Set, Maximum Clique, and Maximum Cut problems demonstrate that incorporating FLD advances both sampling-based and data-driven approaches, achieving state-of-the-art (SOTA) performance in most of the experiments.