Daily Papers

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion. Many recent works focus on improving the integration schemes used when training HNNs. In this work, we propose to enhance HNNs with an estimation of a continuous-time trajectory of the modeled system using an additional neural network, called a deep hidden physics model in the literature. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.

Computing the numerical solution to high-dimensional tensor differential equations can lead to prohibitive computational costs and memory requirements. To reduce the memory and computational footprint, dynamical low-rank approximation (DLRA) has proven to be a promising approach. DLRA represents the solution as a low-rank tensor factorization and evolves the resulting low-rank factors in time. A central challenge in DLRA is to find time integration schemes that are robust to the arising small singular values. A robust parallel basis update & Galerkin integrator, which simultaneously evolves all low-rank factors, has recently been derived for matrix differential equations. This work extends the parallel low-rank matrix integrator to Tucker tensors and general tree tensor networks, yielding an algorithm in which all bases and connecting tensors are evolved in parallel over a time step. We formulate the algorithm, provide a robust error bound, and demonstrate the efficiency of the new integrators for problems in quantum many-body physics, uncertainty quantification, and radiative transfer.

Artificial Intelligence (AI) weather prediction (AIWP) models are powerful tools for medium-range forecasts but often lack physical consistency, leading to outputs that violate conservation laws. This study introduces a set of novel physics-based schemes designed to enforce the conservation of global dry air mass, moisture budget, and total atmospheric energy in AIWP models. The schemes are highly modular, allowing for seamless integration into a wide range of AI model architectures. Forecast experiments are conducted to demonstrate the benefit of conservation schemes using FuXi, an example AIWP model, modified and adapted for 1.0-degree grid spacing. Verification results show that the conservation schemes can guide the model in producing forecasts that obey conservation laws. The forecast skills of upper-air and surface variables are also improved, with longer forecast lead times receiving larger benefits. Notably, large performance gains are found in the total precipitation forecasts, owing to the reduction of drizzle bias. The proposed conservation schemes establish a foundation for implementing other physics-based schemes in the future. They also provide a new way to integrate atmospheric domain knowledge into the design and refinement of AIWP models.

Large language models (LLMs) excel at mathematical reasoning and logical problem-solving. The current popular training paradigms primarily use supervised fine-tuning (SFT) and reinforcement learning (RL) to enhance the models' reasoning abilities. However, when using SFT or RL alone, there are respective challenges: SFT may suffer from overfitting, while RL is prone to mode collapse. The state-of-the-art methods have proposed hybrid training schemes. However, static switching faces challenges such as poor generalization across different tasks and high dependence on data quality. In response to these challenges, inspired by the curriculum learning-quiz mechanism in human reasoning cultivation, We propose SASR, a step-wise adaptive hybrid training framework that theoretically unifies SFT and RL and dynamically balances the two throughout optimization. SASR uses SFT for initial warm-up to establish basic reasoning skills, and then uses an adaptive dynamic adjustment algorithm based on gradient norm and divergence relative to the original distribution to seamlessly integrate SFT with the online RL method GRPO. By monitoring the training status of LLMs and adjusting the training process in sequence, SASR ensures a smooth transition between training schemes, maintaining core reasoning abilities while exploring different paths. Experimental results demonstrate that SASR outperforms SFT, RL, and static hybrid training methods.

Millions of individuals' well-being are challenged by the harms of substance use. Harm reduction as a public health strategy is designed to improve their health outcomes and reduce safety risks. Some large language models (LLMs) have demonstrated a decent level of medical knowledge, promising to address the information needs of people who use drugs (PWUD). However, their performance in relevant tasks remains largely unexplored. We introduce HRIPBench, a benchmark designed to evaluate LLM's accuracy and safety risks in harm reduction information provision. The benchmark dataset HRIP-Basic has 2,160 question-answer-evidence pairs. The scope covers three tasks: checking safety boundaries, providing quantitative values, and inferring polysubstance use risks. We build the Instruction and RAG schemes to evaluate model behaviours based on their inherent knowledge and the integration of domain knowledge. Our results indicate that state-of-the-art LLMs still struggle to provide accurate harm reduction information, and sometimes, carry out severe safety risks to PWUD. The use of LLMs in harm reduction contexts should be cautiously constrained to avoid inducing negative health outcomes. WARNING: This paper contains illicit content that potentially induces harms.

We consider cross-silo federated linear contextual bandit (LCB) problem under differential privacy, where multiple silos (agents) interact with the local users and communicate via a central server to realize collaboration while without sacrificing each user's privacy. We identify three issues in the state-of-the-art: (i) failure of claimed privacy protection and (ii) incorrect regret bound due to noise miscalculation and (iii) ungrounded communication cost. To resolve these issues, we take a two-step principled approach. First, we design an algorithmic framework consisting of a generic federated LCB algorithm and flexible privacy protocols. Then, leveraging the proposed framework, we study federated LCBs under two different privacy constraints. We first establish privacy and regret guarantees under silo-level local differential privacy, which fix the issues present in state-of-the-art algorithm. To further improve the regret performance, we next consider shuffle model of differential privacy, under which we show that our algorithm can achieve nearly ``optimal'' regret without a trusted server. We accomplish this via two different schemes -- one relies on a new result on privacy amplification via shuffling for DP mechanisms and another one leverages the integration of a shuffle protocol for vector sum into the tree-based mechanism, both of which might be of independent interest. Finally, we support our theoretical results with numerical evaluations over contextual bandit instances generated from both synthetic and real-life data.

We present FreeBird, an extensible Julia-based platform for computational studies of phase equilibria at generic interfaces. The package supports a range of system configurations, from atomistic solid surfaces to coarse-grained lattice-gas models, with energies evaluated using classical interatomic potentials or lattice Hamiltonians. Both atomistic and lattice systems accommodate single- or multi-component mixtures with flexibly definable surface and lattice geometries. Implemented sampling algorithms include nested sampling, Wang-Landau sampling, Metropolis Monte Carlo, and, for tractable lattice systems, exact enumeration. Leveraging Julia's type hierarchies and multiple dispatch, FreeBird provides a modular interface that allows seamless integration of system definitions, energy evaluators, and sampling schemes. Designed for flexibility, extensibility, and performance, FreeBird offers a versatile framework for exploring the thermodynamics of interfacial phenomena.

This paper presents an experimental study regarding the use of OpenAI's ChatGPT for robotics applications. We outline a strategy that combines design principles for prompt engineering and the creation of a high-level function library which allows ChatGPT to adapt to different robotics tasks, simulators, and form factors. We focus our evaluations on the effectiveness of different prompt engineering techniques and dialog strategies towards the execution of various types of robotics tasks. We explore ChatGPT's ability to use free-form dialog, parse XML tags, and to synthesize code, in addition to the use of task-specific prompting functions and closed-loop reasoning through dialogues. Our study encompasses a range of tasks within the robotics domain, from basic logical, geometrical, and mathematical reasoning all the way to complex domains such as aerial navigation, manipulation, and embodied agents. We show that ChatGPT can be effective at solving several of such tasks, while allowing users to interact with it primarily via natural language instructions. In addition to these studies, we introduce an open-sourced research tool called PromptCraft, which contains a platform where researchers can collaboratively upload and vote on examples of good prompting schemes for robotics applications, as well as a sample robotics simulator with ChatGPT integration, making it easier for users to get started with using ChatGPT for robotics.

The integration of Multimodal Large Language Models (MLLMs) into chemistry promises to revolutionize scientific discovery, yet their ability to comprehend the dense, graphical language of reactions within authentic literature remains underexplored. Here, we introduce RxnBench, a multi-tiered benchmark designed to rigorously evaluate MLLMs on chemical reaction understanding from scientific PDFs. RxnBench comprises two tasks: Single-Figure QA (SF-QA), which tests fine-grained visual perception and mechanistic reasoning using 1,525 questions derived from 305 curated reaction schemes, and Full-Document QA (FD-QA), which challenges models to synthesize information from 108 articles, requiring cross-modal integration of text, schemes, and tables. Our evaluation of MLLMs reveals a critical capability gap: while models excel at extracting explicit text, they struggle with deep chemical logic and precise structural recognition. Notably, models with inference-time reasoning significantly outperform standard architectures, yet none achieve 50\% accuracy on FD-QA. These findings underscore the urgent need for domain-specific visual encoders and stronger reasoning engines to advance autonomous AI chemists.

Named entity disambiguation (NED), which involves mapping textual mentions to structured entities, is particularly challenging in the medical domain due to the presence of rare entities. Existing approaches are limited by the presence of coarse-grained structural resources in biomedical knowledge bases as well as the use of training datasets that provide low coverage over uncommon resources. In this work, we address these issues by proposing a cross-domain data integration method that transfers structural knowledge from a general text knowledge base to the medical domain. We utilize our integration scheme to augment structural resources and generate a large biomedical NED dataset for pretraining. Our pretrained model with injected structural knowledge achieves state-of-the-art performance on two benchmark medical NED datasets: MedMentions and BC5CDR. Furthermore, we improve disambiguation of rare entities by up to 57 accuracy points.

Convolutions (Convs) and multi-head self-attentions (MHSAs) are typically considered alternatives to each other for building vision backbones. Although some works try to integrate both, they apply the two operators simultaneously at the finest pixel granularity. With Convs responsible for per-pixel feature extraction already, the question is whether we still need to include the heavy MHSAs at such a fine-grained level. In fact, this is the root cause of the scalability issue w.r.t. the input resolution for vision transformers. To address this important problem, we propose in this work to use MSHAs and Convs in parallel at different granularity levels instead. Specifically, in each layer, we use two different ways to represent an image: a fine-grained regular grid and a coarse-grained set of semantic slots. We apply different operations to these two representations: Convs to the grid for local features, and MHSAs to the slots for global features. A pair of fully differentiable soft clustering and dispatching modules is introduced to bridge the grid and set representations, thus enabling local-global fusion. Through extensive experiments on various vision tasks, we empirically verify the potential of the proposed integration scheme, named GLMix: by offloading the burden of fine-grained features to light-weight Convs, it is sufficient to use MHSAs in a few (e.g., 64) semantic slots to match the performance of recent state-of-the-art backbones, while being more efficient. Our visualization results also demonstrate that the soft clustering module produces a meaningful semantic grouping effect with only IN1k classification supervision, which may induce better interpretability and inspire new weakly-supervised semantic segmentation approaches. Code will be available at https://github.com/rayleizhu/GLMix.

Most existing sandstorm image enhancement methods are based on traditional theory and prior knowledge, which often restrict their applicability in real-world scenarios. In addition, these approaches often adopt a strategy of color correction followed by dust removal, which makes the algorithm structure too complex. To solve the issue, we introduce a novel image restoration model, named all-in-one sandstorm removal network (AOSR-Net). This model is developed based on a re-formulated sandstorm scattering model, which directly establishes the image mapping relationship by integrating intermediate parameters. Such integration scheme effectively addresses the problems of over-enhancement and weak generalization in the field of sand dust image enhancement. Experimental results on synthetic and real-world sandstorm images demonstrate the superiority of the proposed AOSR-Net over state-of-the-art (SOTA) algorithms.

There is an emerging effort to combine the two popular 3D frameworks using Multi-View Stereo (MVS) and Neural Implicit Surfaces (NIS) with a specific focus on the few-shot / sparse view setting. In this paper, we introduce a novel integration scheme that combines the multi-view stereo with neural signed distance function representations, which potentially overcomes the limitations of both methods. MVS uses per-view depth estimation and cross-view fusion to generate accurate surfaces, while NIS relies on a common coordinate volume. Based on this strategy, we propose to construct per-view cost frustum for finer geometry estimation, and then fuse cross-view frustums and estimate the implicit signed distance functions to tackle artifacts that are due to noise and holes in the produced surface reconstruction. We further apply a cascade frustum fusion strategy to effectively captures global-local information and structural consistency. Finally, we apply cascade sampling and a pseudo-geometric loss to foster stronger integration between the two architectures. Extensive experiments demonstrate that our method reconstructs robust surfaces and outperforms existing state-of-the-art methods.

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical scheme is based on a generalized Scharfetter-Gummel discretization of the nonlocal flux term. For merely integrable kernel functions, the scheme preserves the positivity, total mass, and entropy structure. The existence of a discrete solution and its convergence to a solution to the continuous problem, as the mesh size tends to zero, are shown. A key difficulty is the degeneracy of the generalized Bernoulli function in the Scharfetter-Gummel approximation. This issue is overcome by proving a uniform estimate for the discrete Fisher information, which requires both the Boltzmann and Rao entropy inequalities. Numerical simulations illustrate the features of the scheme in one and two space dimensions.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

We give explicit low-rank bilinear non-commutative schemes for multiplying structured n times n matrices with 2 leq n leq 5, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic complexity. Our schemes are discovered over F_2 or F_3 and lifted to Z or Q. Using a flip graph search over tensor decompositions, we derive schemes for general, upper-triangular, lower-triangular, symmetric, and skew-symmetric inputs, as well as products of a structured matrix with its transpose. In particular, we obtain 4 times 4 rank-34 schemes: (i) multiplying a general matrix by its transpose using 10 recursive calls, improving the factor from 26/41 (0.634) to 8/13 (0.615); and (ii) multiplying an upper-triangular matrix by a general matrix using 12 recursive calls, improving the factor from 8/13 (0.615) to 22/37 (0.595). Additionally, using F_3 flip graphs, we discover schemes over Q that fundamentally require the inverse of 2, including a 2 times 2 symmetric-symmetric multiplication of rank 5 and a 3 times 3 skew-symmetric-general multiplication of rank 14 (improving upon AlphaTensor's 15).