Pre-training has proven effective in addressing data scarcity and performance limitations in solving PDE problems with neural operators. However, challenges remain due to the heterogeneity of PDE datasets in equation types, which leads to high errors in mixed training. Additionally, dense pre-training models that scale parameters by increasing network width or depth incur significant inference costs. To tackle these challenges, we propose a novel Mixture-of-Experts Pre-training Operator Transformer (MoE-POT), a sparse-activated architecture that scales parameters efficiently while controlling inference costs. Specifically, our model adopts a layer-wise router-gating network to dynamically select 4 routed experts from 16 expert networks during inference, enabling the model to focus on equationspecific features. Meanwhile, we also integrate 2 shared experts, aiming to capture common properties of PDE and reduce redundancy among routed experts. The final output is computed as the weighted average of the results from all activated experts.

Monocular depth estimation has advanced significantly with foundation models like Depth Anything, leveraging large-scale transformer architectures for the superior generalization. However, the deployment on resource-constrained devices remains challenging due to the high computation and memory requirement. Existing quantization methods, such as post-training quantization (PTQ) and quantization-aware training (QAT), often face trade-offs between efficiency and accuracy, or require extensive labeled data for retraining. To address these limitations, we propose Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation (QSCA), a novel framework for 4-bit post-training quantization of Monocular depth estimation models. Our method integrates a lightweight Self-Compensating Auxiliary (SCA) module into both transformer encoder and decoder blocks, enabling the quantized model to recover from performance degradation without requiring ground truth. This design enables fast adaptation while preserving structural and spatial consistency in predicted depth maps. To our knowledge, this is the first framework to successfully apply 4-bit quantization across all layers of large-scale monocular depth estimation models. Experimental results demonstrate that QSCA significantly improves quantized depth estimation performance. On the NYUv2 dataset, it achieves an 11% improvement in δ1 accuracy over existing post-training quantization methods.

Diffusion-based models have shown great promise in molecular generation but often require a large number of sampling steps to generate valid samples. In this paper, we introduce a novel Straight-Line Diffusion Model (SLDM) to tackle this problem, by formulating the diffusion process to follow a linear trajectory. The proposed process aligns well with the noise sensitivity characteristic of molecular structures and uniformly distributes reconstruction effort across the generative process, thus enhancing learning efficiency and efficacy. Consequently, SLDM achieves state-of-the-art performance on 3D molecule generation benchmarks, delivering a 100-fold improvement in sampling efficiency.1

Neural networks trained with ERM (empirical risk minimization) sometimes learn unintended decision rules, in particular when their training data is biased, i.e., when training labels are strongly correlated with undesirable features. To prevent a network from learning such features, recent methods augment training data such that examples displaying spurious correlations (i.e., bias-aligned examples) become a minority, whereas the other, bias-conflicting examples become prevalent. However, these approaches are sometimes difficult to train and scale to real-world data because they rely on generative models or disentangled representations. We propose an alternative based on mixup, a popular augmentation that creates convex combinations of training examples. Our method, coined SelecMix, applies mixup to contradicting pairs of examples, defined as showing either (i) the same label but dissimilar biased features, or (ii) different labels but similar biased features. Identifying such pairs requires comparing examples with respect to unknown biased features. For this, we utilize an auxiliary contrastive model with the popular heuristic that biased features are learned preferentially during training. Experiments on standard benchmarks demonstrate the effectiveness of the method, in particular when label noise complicates the identification of bias-conflicting examples.

Molecular Relational Learning (MRL) is a rapidly growing field that focuses on understanding the interaction dynamics between molecules, which is crucial for applications ranging from catalyst engineering to drug discovery. Despite recent progress, ture of molecules, earlier MRL as obtaining approaches the are 3D limited interaction to using geometry only the remains 2D topological prohibiti strucvely expensive. This paper introduces a novel 3D geometric pre-training strategy for MRL (3DMRL) that incorporates a 3D virtual interaction environment, overcoming the the constructe limitations d of 3D costly virtual tradit interaction ional quantum environment, mechanical 3DMRL calculation trains 2D methods. MRL model With to learn the global and local 3D geometric information of molecular interaction. Extensive experiments on various tasks using real-world datasets, including out-ofdistribution and extrapolation scenarios, demonstrate the effectiveness of 3DMRL, sho publicly wing a up vailable to a 24.93% at https://github.com/

Despite substantial efforts in safety alignment, recent research indicates that Large Language Models (LLMs) remain highly susceptible to jailbreak attacks.

Designing neural networks within a Hamiltonian framework offers a principled way to ensure that conservation laws are respected in physical systems. While promising, these capabilities have been largely limited to discrete, analytically solvable systems. In contrast, many physical phenomena are governed by PDEs, which govern infinite-dimensional fields through Hamiltonian functionals and their functional derivatives. Building on prior work, we represent the Hamiltonian functional as a kernel integral parameterized by a neural field, enabling learnable function-to-scalar mappings and the use of automatic differentiation to calculate functional derivatives. This allows for an extension of Hamiltonian mechanics to neural PDE solvers by predicting a functional and learning in the gradient domain. We show that the resulting Hamiltonian Neural Solver (HNS) can be an effective surrogate model through improved stability and conserving energy-like quantities across 1D and 2DPDEs. This ability to respect conservation laws also allows HNS models to better generalize to longer time horizons or unseen initial conditions.

We study metric distortion in distributed voting, where nvoters are partitioned into k groups, each selecting a local representative, and a final winner is chosen from these representatives (or from the entire set of candidates). This setting models systems like U.S. presidential elections, where state-level decisions determine the national outcome. We focus on four cost objectives from Anshelevich et al. [1]: avg-avg, avg-max, max-avg, and max-max. We present improved distortion bounds for both deterministic and randomized mechanisms, offering a near-complete characterization of distortion in this model. For deterministic mechanisms, we reduce the upper bound for avg-max from 11 to 7, establish a tight lower bound of 5 for max-avg (improving on 2+ 5), and tighten the upper bound for max-max from 5 to 3. For randomized mechanisms, we consider two settings: (i) only the second stage is randomized, and (ii) both stages may be randomized. In case (i), we prove tight bounds: 5 2/k for avg-avg, 3for avg-max and max-max, and 5for max-avg. In case (ii), we show tight bounds of 3 for max-avg and max-max, and nearly tight bounds for avg-avg and avg-max within [3 2/n, 3 2/(kn)]and [3 2/n, 3], respectively, where n denotes the largest group size.

We study the problem of computing an optimal large language model (LLM) policy for the constrained alignment problem, where the goal is to maximize a primary reward objective while satisfying constraints on secondary utilities. Despite the popularity of Lagrangian-based LLM policy search in constrained alignment, iterative primal-dual methods often fail to converge, and non-iterative dual-based methods do not achieve optimality in the LLM parameter space. To address these challenges, we employ Lagrangian duality to develop an iterative dual-based alignment method that alternates between updating the LLM policy via Lagrangian maximization and updating the dual variable via dual descent. In theory, we characterize the primal-dual gap between the primal value in the distribution space and the dual value in the LLM parameter space. We further quantify the optimality gap of the learned LLM policies at near-optimal dual variables with respect to both the objective and the constraint functions. These results prove that dual-based alignment methods can find an optimal constrained LLM policy, up to an LLM parametrization gap. We demonstrate the effectiveness and merits of our approach through extensive experiments conducted on the PKU-SafeRLHF and Anthropic HH-RLHF datasets.

Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.