Graph coarsening aims to diminish the size of a graph to lighten its memory footprint, and has numerous applications in graph signal processing and machine learning. It is usually defined using a reduction matrix and a lifting matrix, which, respectively, allows to project a graph signal from the original graph to the coarsened one and back. This results in a loss of information measured by the so-called Restricted Spectral Approximation (RSA). Most coarsening frameworks impose a fixed relationship between the reduction and lifting matrices, generally as pseudoinverses of each other, and seek to define a coarsening that minimizes the RSA. In this paper, we remark that the roles of these two matrices are not entirely symmetric: indeed, putting constraints on the lifting matrix alone ensures the existence of important objects such as the coarsened graph's adjacency matrix or Laplacian.

Linear TD(λ) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold in many practical scenarios. This paper instead establishes the first L2 convergence rates for linear TD(λ) operating under arbitrary features, without making any algorithmic modification or additional assumptions. Our results apply to both the discounted and average-reward settings. To address the potential non-uniqueness of solutions resulting from arbitrary features, we develop a novel stochastic approximation result featuring convergence rates to the solution set instead of a single point.

Tri-plane-like representations have been widely adopted in 3D-aware GANs for head image synthesis and other 3D object/scene modeling tasks due to their efficiency. However, querying features via Cartesian coordinate projection often leads to feature entanglement, which results in mirroring artifacts. A recent work, SphereHead, attempted to address this issue by introducing spherical tri-planes based on a spherical coordinate system. While it successfully mitigates feature entanglement, SphereHead suffers from uneven mapping between the square feature maps and the spherical planes, leading to inefficient feature map utilization during rendering and difficulties in generating fine image details. Moreover, both tri-plane and spherical tri-plane representations share a subtle yet persistent issue: feature penetration across convolutional channels can cause interference between planes, particularly when one plane dominates the others (see Figure 1). These challenges collectively prevent tri-plane-based methods from reaching their full potential. In this paper, we systematically analyze these problems for the first time and propose innovative solutions to address them. Specifically, we introduce a novel hybrid-plane (hy-plane for short) representation that combines the strengths of both planar and spherical planes while avoiding their respective drawbacks. We further enhance the spherical plane by replacing the conventional theta-phi warping with a novel near-equal-area warping strategy, which maximizes the effective utilization of the square feature map.

Encoding models using word embeddings or artificial neural network (ANN) features reliably predict brain responses to naturalistic stimuli, yet interpreting these models remains challenging. A central limitation is superposition: distinct semantic features become entangled along correlated directions in dense embeddings when latent features outnumber embedding dimensions. This entanglement renders regression weights non-identifiable--different combinations of semantic directions can produce identical predictions, precluding principled interpretation of voxel selectivity. To address this, we introduce the Sparse Concept Encoding Model, which transforms dense embeddings into a higher-dimensional, sparse, non-negative space of learned concept atoms.

We address the problem of looking into the water from the air, where we seek to remove image distortions caused by refractions at the water surface. Our approach is based on modeling the different water surface structures at various points in time, assuming the underlying image is constant. To this end, we propose a model that consists of two neural-field networks. The first network predicts the height of the water surface at each spatial position and time, and the second network predicts the image color at each position. Using both networks, we reconstruct the observed sequence of images and can therefore use unsupervised training.

Low-Rank Adaptation (LoRA) is a popular method for parameter-efficient finetuning (PEFT) of generative models, valued for its simplicity and effectiveness. Despite recent enhancements, LoRA still suffers from a fundamental limitation: overfitting when the bottleneck is widened. It performs best at ranks 32-64, yet its accuracy stagnates or declines at higher ranks, still falling short of full fine-tuning (FFT) performance. We identify the root cause as LoRA's structural bottleneck, which introduces gradient entanglement to the unrelated input channels and distorts gradient propagation. To address this, we introduce a novel structure, Granular Low-Rank Adaptation (GraLoRA) that partitions weight matrices into sub-blocks, each with its own low-rank adapter. With negligible computational or storage cost, GraLoRA overcomes LoRA's limitations, effectively increases the representational capacity, and more closely approximates FFT behavior. Experiments on code generation, commonsense reasoning, mathematical reasoning, general language understanding, and image generation benchmarks show that GraLoRA consistently outperforms LoRA and other baselines, achieving up to +8.5% absolute gain in Pass@1 on HumanEval+. These improvements hold across model sizes and rank settings, making GraLoRA a scalable and robust solution for PEFT.

Extensive research has produced robust methods for unsupervised data visualization. Yet supervised visualization--where expert labels guide representations--remains underexplored, as most supervised approaches prioritize classification over visualization. Recently, RF-PHATE, a diffusion-based manifold learning method leveraging random forests and information geometry, marked significant progress in supervised visualization.

As language models scale, their performance improves dramatically across a wide range of tasks, but so does their tendency to memorize and regurgitate parts of their training data verbatim. This tradeoff poses serious legal, ethical, and safety concerns, especially in real-world deployments. Existing mitigation techniques, such as differential privacy or model unlearning, often require retraining or access to internal weights making them impractical for most users. In this work, we introduce TOKENSWAP, a lightweight, post-hoc defense designed for realistic settings where the user can only access token-level outputs. Our key insight is that while large models are necessary for high task performance, small models (e.g., DistilGPT-2) are often sufficient to assign fluent, grammatically plausible probabilities to common function words - and crucially, they memorize far less. By selectively swapping token probabilities between models, TOKENSWAP preserves the capabilities of large models while reducing their propensity for verbatim reproduction.

Recent Graphical User Interface (GUI) agents replicate the R1-Zero paradigm, coupling online Reinforcement Learning (RL) with explicit chain-of-thought reasoning prior to object grounding and thereby achieving substantial performance gains.

Retrieval-Augmented Generation (RAG) based on knowledge graphs (KGs) enhances large language models (LLMs) with structural and textual external knowledge. Yet, existing KG-based RAG methods struggle to retrieve accurate and diverse information when handling complex queries. By modeling KG-based retrieval as a multi-step decision process, Process Reward Models (PRMs) offer a promising solution to align the retrieval behavior with the query-specific knowledge requirements. However, PRMs heavily rely on process-level supervision signals that are expensive and hard to obtain on KGs. To address this challenge, we propose GraphFlow, a framework that efficiently retrieves accurate and diverse knowledge required for complex queries from text-rich KGs. GraphFlow employs a detailed balance objective with local exploration to jointly optimize a retrieval policy and a flow estimator.