Deep neural networks are starting to show their potential for solving partial differential equations (PDEs)inavarietyofproblemdomains,includingturbulentflow,heattransfer,elastodynamics,and many more [1, 2, 3, 4, 5]. Thanks to their smooth and analytically-differentiable nature, implicit neural representations with periodic activation functions are emerging as a particularly attractive and powerful option in this context [4].

Large vision-language models (LVLMs) have recently achieved rapid progress, exhibiting great perception and reasoning abilities concerning visual information. However, when faced with prompts in different sizes of solution spaces, LVLMs fail to always give consistent answers regarding the same knowledge point. This inconsistency of answers between different solution spaces is prevalent in LVLMs and erodes trust. To this end, we provide a multi-modal benchmark ConBench, to intuitively analyze how LVLMs perform when the solution space of a prompt revolves around a knowledge point. Based on the ConBench tool, we are the first to reveal the tapestry and get the following findings: (1) In the discriminate realm, the larger the solution space of the prompt, the lower the accuracy of the answers.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space.On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates.In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space.

Federated reinforcement learning (FRL) enables distributed learning of optimal policies while preserving local data privacy through gradient sharing.However, FRL faces the risk of data privacy leaks, where attackers exploit shared gradients to reconstruct local training data.Compared to traditional supervised federated learning, successful reconstruction in FRL requires the generated data not only to match the shared gradients but also to align with real transition dynamics of the environment (i.e., aligning with the real data transition distribution).To address this issue, we propose a novel attack method called Regularization Gradient Inversion Attack (RGIA), which enforces prior-knowledge-based regularization on states, rewards, and transition dynamics during the optimization process to ensure that the reconstructed data remain close to the true transition distribution.Theoretically, we prove that the prior-knowledge-based regularization term narrows the solution space from a broad set containing spurious solutions to a constrained subset that satisfies both gradient matching and true transition dynamics.Extensive experiments on control tasks and autonomous driving tasks demonstrate that RGIA can effectively constrain reconstructed data transition distributions and thus successfully reconstruct local private data.

Reasoning based on Large Language Models (LLMs) has garnered increasing attention due to outstanding performance of these models in mathematical and complex logical tasks. Beginning with the Chain-of-Thought (CoT) prompting technique, numerous reasoning methods have emerged that decompose problems into smaller, sequential steps (or thoughts). However, existing reasoning models focus on conventional problem-solving and do not necessarily generate creative solutions by ``creative reasoning''. In domains where the solution space is expansive and conventional solutions are suboptimal, such as drug discovery or business strategization, creative reasoning to discover innovative solutions is crucial. To address this gap, first we introduce a computational framework for creative reasoning inspired by established cognitive science principles. With this framework, we propose three core creative reasoning paradigms, namely, \textit{combinational}, \textit{exploratory}, and \textit{transformative} reasoning, where each offers specific directions for systematic exploration of the universe of thoughts to generate creative solutions. Next, to materialize this framework using LLMs, we introduce the \textit{Universe of Thoughts} (or \textit{UoT}, for short), a novel set of methods to implement the aforementioned three creative processes. Finally, we introduce three novel tasks that necessitate creative problem-solving, along with an evaluation benchmark to assess creativity from three orthogonal perspectives: feasibility as constraint, and utility and novelty as metrics. With a comparative analysis against the state-of-the-art (SOTA) reasoning techniques as well as representative commercial models with reasoning capability, we show that UoT demonstrates superior performance in creative reasoning.

In this work, we consider the problem of planning for temporal logic tasks in large robot environments. When full task compliance is unattainable, we aim to achieve the best possible task satisfaction by integrating user preferences for relaxation into the planning process. Utilizing the automata-based representations for temporal logic goals and user preferences, we propose an A*-based planning framework. This approach effectively tackles large-scale problems while generating near-optimal high-level trajectories. To facilitate this, we propose a simple, efficient heuristic that allows for planning over large robot environments in a fraction of time and search memory as compared to uninformed search algorithms. We present extensive case studies to demonstrate the scalability, runtime analysis as well as empirical bounds on the suboptimality of the proposed heuristic.