Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models. Specifically, we investigate the impact of various discretization schemes, including Euler discretization, exponential integrators, and midpoint randomization methods. Our analysis provides the first quantitative comparison of these discrete approximations, emphasizing their influence on convergence behavior. Furthermore, we explore scenarios where Hessian information is available and propose an accelerated sampler based on the local linearization method. We establish the first Wasserstein convergence analysis for such a Hessian-based method, showing that it achieves an improved convergence rate of order eO( d/ε), which significantly outperforms the standard rate eO(d/ε2)of vanilla diffusion models.

Linear attention has attracted interest as a computationally efficient approximation to softmax attention, especially for long sequences. Recent studies have explored distilling softmax attention in pre-trained Transformers into linear attention. However, a critical challenge remains: how to choose the feature dimension that governs the approximation quality. Existing methods fix this dimension uniformly across all attention layers, overlooking the diverse roles and complexities of them. In this paper, we propose a principled method to automatically determine the feature dimension in linear attention using the concept of statistical degrees of freedom, which represent the effective dimensionality of the inputs. We provide a theoretical bound on the approximation error and show that the dimension chosen by our method achieves smaller errors under a fixed computational budget. Furthermore, we introduce an efficient layerwise training strategy to learn nonlinear features tailored to each layer. Experiments on multiple pre-trained transformers demonstrate that our method improves the performance of distilled models compared to baselines without increasing the inference cost. Our findings also provide insight into how the complexity of the attention mechanism evolves across layers.

Despite progress, deep neural networks still suffer performance declines under distribution shifts between training and test domains, leading to a substantial decrease in Quality of Experience (QoE) for applications. Existing test-time adaptation (TTA) methods are challenged by dynamic, multiple test distributions within batches. We observe that feature distributions across different domains inherently cluster into distinct groups with varying means and variances. This divergence reveals a critical limitation of previous global normalization strategies in TTA, which inevitably distort the original data characteristics. Based on this insight, we propose Feature-based Instance Neighbor Discovery (FIND), which comprises three key components: Layer-Wise Feature Disentanglement (LFD), Feature-Aware Batch Normalization (FABN) and Selective FABN (S-FABN). LFD stably captures features with similar distributions at each layer by constructing graph structures; while FABN optimally combines source statistics with test-time distribution-specific statistics for robust feature representation. Finally, S-FABN determines which layers require feature partitioning and which can remain unified, thus enhancing the efficiency of inference. Extensive experiments demonstrate that FIND significantly outperforms existing methods, achieving up to approximately 30% accuracy improvement in dynamic scenarios while maintaining computational efficiency. The source code is available at https://github.com/Peanut-255/

Deep neural networks trained to predict neural activity from visual input and behaviour have shown great potential to serve as digital twins of the visual cortex. Per-neuron embeddings derived from these models could potentially be used to map the functional landscape or identify cell types. However, state-of-the-art predictive models of mouse V1 do not generate functional embeddings that exhibit clear clustering patterns which would correspond to cell types. This raises the question whether the lack of clustered structure is due to limitations of current models or a true feature of the functional organization of mouse V1. In this work, we introduce DECEMber - Deep Embedding Clustering via Expectation Maximization-based refinement - an explicit inductive bias into predictive models that enhances clustering by adding an auxiliary t-distribution-inspired loss function that enforces structured organization among per-neuron embeddings.

Graph Transformers (GTs) have emerged as a powerful paradigm for graph representation learning due to their ability to model diverse node interactions. However, existing GTs often rely on intricate architectural designs tailored to specific interactions, limiting their flexibly. To address this, we propose a unified hierarchical mask framework that reveals an underlying equivalence between model architecture and attention mask construction. This framework enables a consistent modeling paradigm by capturing diverse interactions through carefully designed attention masks. Theoretical analysis under this framework demonstrates that the probability of correct classification positively correlates with the receptive field size and label consistency, leading to a fundamental design principle: An effective attention mask should ensure both a sufficiently large receptive field and a high level of label consistency.

In-silico prediction of protein mutant stability, measured by the difference in Gibbs free energy change ( G), is fundamental for protein engineering. Current sequence-to-label methods typically employ the two-stage pipeline: (i) encoding mutant sequences using neural networks (e.g., transformers), followed by (ii) the G regression from the latent representations. Although these methods have demonstrated promising performance, their dependence on specialized neural network encoders significantly increases the complexity. Additionally, the requirement to individually compute latent representations for each mutant site negatively impacts computational efficiency and poses the risk of overfitting. This work proposes the Venus-MAXWELL framework, which reformulates mutation G prediction as a sequence-to-landscape task. In Venus-MAXWELL, mutations of a protein and their corresponding Gvalues are organized into a landscape matrix, allowing our framework to learn the G landscape of a protein with a single forward and backward pass during training. Besides, to facilitate future works, we also curated a large-scale G dataset with strict controls on data leakage and redundancy to ensure robust evaluation. Venus-MAXWELL is compatible with multiple protein language models and enables these models for accurate and efficient G prediction. For example, when integrated with the ESM-IF, Venus-MAXWELL achieves higher accuracy than ThermoMPNN with 10 faster in inference speed (despite having 50 more parameters than ThermoMPNN).

We present a novel enhanced cyclic coordinate descent (ECCD) framework for solving generalized linear models with elastic net constraints that reduces training time in comparison to existing state-of-the-art methods. We redesign the CD method by performing a Taylor expansion around the current iterate to avoid nonlinear operations arising in the gradient computation. By introducing this approximation we are able to unroll the vector recurrences occurring in the CD method and reformulate the resulting computations into more efficient batched computations. We show empirically that the recurrence can be unrolled by a tunable integer parameter, s, such that s > 1 yields performance improvements without affecting convergence, whereas s= 1 yields the original CD method. A key advantage of ECCD is that it avoids the convergence delay and numerical instability exhibited by block coordinate descent. Finally, we implement our proposed method in C++ using Eigen to accelerate linear algebra computations. Comparison of our method against existing state-of-the-art solvers show consistent performance improvements of 3 in average for regularization path variant on diverse benchmark datasets. Our implementation is available at https://github.

Class imbalance in graph data presents a significant challenge for effective node classification, particularly in semi-supervised scenarios. In this work, we formally introduce the concept of geometric imbalance, which captures how message passing on class-imbalanced graphs leads to geometric ambiguity among minority-class nodes in the riemannian manifold embedding space. We provide a rigorous theoretical analysis of geometric imbalance on the riemannian manifold and propose a unified framework that explicitly mitigates it through pseudo-label alignment, node reordering, and ambiguity filtering. Extensive experiments on diverse benchmarks show that our approach consistently outperforms existing methods, especially under severe class imbalance. Our findings offer new theoretical insights and practical tools for robust semi-supervised node classification.

The estimation of average treatment effects (ATEs), defined as the difference in expected outcomes between treatment and control groups, is a central topic in causal inference. This study develops semiparametric efficient estimators for ATE in a setting where only a treatment group and an unlabeled group--consisting of units whose treatment status is unknown--are observed. This scenario constitutes a variant of learning from positive and unlabeled data (PU learning) and can be viewed as a special case of ATE estimation with missing data. For this setting, we derive the semiparametric efficiency bounds, which characterize the lowest achievable asymptotic variance for regular estimators. We then construct semiparametric efficient ATE estimators that attain these bounds. Our results contribute to the literature on causal inference with missing data and weakly supervised learning.

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