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The rapid growth of digital pathology and advances in self-supervised deep learning have enabled the development of foundational models for various pathology tasks across diverse diseases. While multimodal approaches integrating diverse data sources have emerged, a critical gap remains in the comprehensive integration of whole-slide images (WSIs) with spatial tran-scriptomics (ST), which is crucial for capturing critical molecular heterogeneity beyond standard hematoxylin & eosin (H&E) staining. We introduce SPADE, a foundation model that integrates histopathology with ST data to guide image representation learning within a unified framework, in effect creating an ST-informed latent space. These authors contributed equally to this work. Pre-trained on the comprehensive HEST-1k dataset, SPADE is evaluated on 20 downstream tasks, demonstrating significantly superior few-shot performance compared to baseline models, highlighting the benefits of integrating morphological and molecular information into one latent space. Introduction High-resolution whole slide images (WSIs) have propelled the development of powerful deep learning foundation models in computational pathology, demonstrating robust performance across diverse tissue types and tasks [1, 2, 3, 4]. These models are typically trained using self-supervision, enabling learning from large unlabeled datasets and producing embeddings robust to institutional variations, including differences in staining procedures and other image-quality factors [5, 6, 7, 8]. By visually capturing cellular arrangement, WSIs enable the study of spatial organization and disorganization of cells in tissues, characterizations that are especially relevant in cancer research [9, 10]. In clinical settings, WSIs are commonly stained with hematoxylin & eosin (H&E), a two-color stain that highlights nuclei and cytoplasm but offers a limited view of molecular-level heterogeneity [11]. As tumor tissues are known to exhibit high variability within and across patients, deciphering the heterogeneity at the molecular level is critical for improving deep learning applications that can more precisely inform diagnosis, treatment, and prognosis [12, 13]. While H&E provides crucial morphological insights, its inability to capture molecular heterogeneity limits its utility in fully characterizing tissue complexity. Spatial transcriptomics addresses this gap by providing spatially resolved gene expression data, allowing for additional molecular context for a given tissue specimen. Although both ST and H&E data have independently proven useful in various applications, their combined potential for creating a more comprehensive representation learning framework remains unexplored. To this end, we introduce SPADE, a vision-ST foundation model that uses a mixture of experts, each trained via contrastive learning, to unify ST data and H&E images to produce slide representations that encompass both modalities.

The rapid advancement of large language models (LLMs) has inspired researchers to integrate them extensively into the academic workflow, potentially reshaping how research is practiced and reviewed. While previous studies highlight the potential of LLMs in supporting research and peer review, their dual roles in the academic workflow and the complex interplay between research and review bring new risks that remain largely underexplored. In this study, we focus on how the deep integration of LLMs into both peer-review and research processes may influence scholarly fairness, examining the potential risks of using LLMs as reviewers by simulation. This simulation incorporates a research agent, which generates papers and revises, alongside a review agent, which assesses the submissions. Based on the simulation results, we conduct human annotations and identify pronounced misalignment between LLM-based reviews and human judgments: (1) LLM reviewers systematically inflate scores for LLM-authored papers, assigning them markedly higher scores than human-authored ones; (2) LLM reviewers persistently underrate human-authored papers with critical statements (e.g., risk, fairness), even after multiple revisions. Our analysis reveals that these stem from two primary biases in LLM reviewers: a linguistic feature bias favoring LLM-generated writing styles, and an aversion toward critical statements. These results highlight the risks and equity concerns posed to human authors and academic research if LLMs are deployed in the peer review cycle without adequate caution. On the other hand, revisions guided by LLM reviews yield quality gains in both LLM-based and human evaluations, illustrating the potential of the LLMs-as-reviewers for early-stage researchers and enhancing low-quality papers.

We introduce Cautious Weight Decay (CWD), a one-line, optimizer-agnostic modification that applies weight decay only to parameter coordinates whose signs align with the optimizer update. Unlike standard decoupled decay, which implicitly optimizes a regularized or constrained objective, CWD preserves the original loss and admits a bilevel interpretation: it induces sliding-mode behavior upon reaching the stationary manifold, allowing it to search for locally Pareto-optimal stationary points of the unmodified objective. In practice, CWD is a drop-in change for optimizers such as AdamW, Lion, and Muon, requiring no new hyperparameters or additional tuning. For language model pre-training and ImageNet classification, CWD consistently improves final loss and accuracy at million- to billion-parameter scales.

We present CuMPerLay, a novel differentiable vectorization layer that enables the integration of Cubical Multiparameter Persistence (CMP) into deep learning pipelines. While CMP presents a natural and powerful way to topologically work with images, its use is hindered by the complexity of multifiltration structures as well as the vectorization of CMP. In face of these challenges, we introduce a new algorithm for vectorizing MP homologies of cubical complexes. Our CuMPerLay decomposes the CMP into a combination of individual, learnable single-parameter persistence, where the bifiltration functions are jointly learned. Thanks to the differentiability, its robust topological feature vectors can be seamlessly used within state-of-the-art architectures such as Swin Transformers. We establish theoretical guarantees for the stability of our vectorization under generalized Wasserstein metrics. Our experiments on benchmark medical imaging and computer vision datasets show the benefit CuMPerLay on classification and segmentation performance, particularly in limited-data scenarios. Overall, CuMPerLay offers a promising direction for integrating global structural information into deep networks for structured image analysis.

Recent experiments reveal that task-relevant variables are often encoded in approximately orthogonal subspaces of the neural activity space. These disentangled low-dimensional representations are observed in multiple brain areas and across different species, and are typically the result of a process of abstraction that supports simple forms of out-of-distribution generalization. The mechanisms by which such geometries emerge remain poorly understood, and the mechanisms that have been investigated are typically unsupervised (e.g., based on variational auto-encoders). Here, we show mathematically that abstract representations of latent variables are guaranteed to appear in the last hidden layer of feedforward nonlinear networks when they are trained on tasks that depend directly on these latent variables. These abstract representations reflect the structure of the desired outputs or the semantics of the input stimuli. To investigate the neural representations that emerge in these networks, we develop an analytical framework that maps the optimization over the network weights into a mean-field problem over the distribution of neural preactivations. Applying this framework to a finite-width ReLU network, we find that its hidden layer exhibits an abstract representation at all global minima of the task objective. We further extend these analyses to two broad families of activation functions and deep feedforward architectures, demonstrating that abstract representations naturally arise in all these scenarios. Together, these results provide an explanation for the widely observed abstract representations in both the brain and artificial neural networks, as well as a mathematically tractable toolkit for understanding the emergence of different kinds of representations in task-optimized, feature-learning network models.

We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm. Finally, we demonstrate the empirical effectiveness of our method on synthetic and image datasets.

This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the network. Mainly, we investigate how the Fiedler partition of the dual graph and show that it appears to correlate with the decision boundary -- in the case of binary classification. Additionally, we compute the homology of the cellular decomposition -- in a regression task -- to draw similar patterns in behavior between the training loss and polyhedral cell-count, as the model is trained.

As sixth generation (6G) wireless networks evolve, accurate signal-to-interference-noise ratio (SINR) maps are becoming increasingly critical for effective resource management and optimization. However, acquiring such maps at high resolution is often cost-prohibitive, creating a severe data scarcity challenge. This necessitates machine learning (ML) approaches capable of robustly reconstructing the full map from extremely sparse measurements. To address this, we introduce a novel reconstruction framework based on Group Equivariant Non-Expansive Operators (GENEOs). Unlike data-hungry ML models, GENEOs are low-complexity operators that embed domain-specific geometric priors, such as translation invariance, directly into their structure. This provides a strong inductive bias, enabling effective reconstruction from very few samples. Our key insight is that for network management, preserving the topological structure of the SINR map, such as the geometry of coverage holes and interference patterns, is often more critical than minimizing pixel-wise error. We validate our approach on realistic ray-tracing-based urban scenarios, evaluating performance with both traditional statistical metrics (mean squared error (MSE)) and, crucially, a topological metric (1-Wasserstein distance). Results show that while maintaining competitive MSE, our method dramatically outperforms established ML baselines in topological fidelity. This demonstrates the practical advantage of GENEOs for creating structurally accurate SINR maps that are more reliable for downstream network optimization tasks.

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation in each training step. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, the forward computational graphs of all MC samples need to be retained for the gradient computation of non-linear terms in the RL objective, resulting in significant memory overhead. This constraint restricts feasible sample sizes, leading to imprecise likelihood approximations and ultimately distorting the RL objective. To overcome this limitation, we propose \emph{Boundary-Guided Policy Optimization} (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is formulated in a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, resulting in more accurate likelihood approximations and improved RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks. Our codes and models are available at \href{https://github.com/THU-KEG/BGPO}{https://github.com/THU-KEG/BGPO}.