Standard Retrieval-Augmented Generation (RAG) relies on chunk-based retrieval, whereas GraphRAG advances this approach by graph-based knowledge representation. However, existing graph-based RAG approaches are constrained by binary relations, as each edge in an ordinary graph connects only two entities, limiting their ability to represent the n-ary relations (n >= 2) in real-world knowledge. In this work, we propose HyperGraphRAG, the first hypergraph-based RAG method that represents n-ary relational facts via hyperedges. HyperGraphRAG consists of a comprehensive pipeline, including knowledge hypergraph construction, retrieval, and generation. Experiments across medicine, agriculture, computer science, and law demonstrate that HyperGraphRAG outperforms both standard RAG and previous graph-based RAG methods in answer accuracy, retrieval efficiency, and generation quality.

Organisms constantly pivot between tasks such as evading predators, foraging, traversing rugged terrain, and socializing, often within milliseconds. Remarkably, they preserve knowledge of once-learned environments sans catastrophic forgetting, a phenomenon neuroscientists hypothesize, is due to a singular neural circuitry dynamically overlayed by neuromodulatory agents such as dopamine and acetylcholine. In parallel, deep learning research addresses analogous challenges via domain generalization ($\textbf{DG}$) and continual learning ($\textbf{CL}$), yet these methods remain siloed, despite the brain's ability to perform them seamlessly. In particular, prior work has not explored architectures involving associative memories ($\textbf{AM}$s), which are an integral part of biological systems, to jointly address these tasks. We propose Memory-Integrated Reconfigurable Adapters ($\textbf{MIRA}$), a unified framework that integrates Hopfield-style associative memory modules atop a shared backbone. These memory modules store adapter-weight updates as values and retrieve them via learned keys. Associative memory keys are learned post-hoc to index and retrieve an affine combination of stored adapter updates for any given task or domain on a per-sample basis. By varying only the task-specific objectives, we demonstrate that $\textbf{MIRA}$ seamlessly accommodates domain shifts and sequential task exposures under one roof. Empirical evaluations on standard benchmarks confirm that our $\textbf{AM}$-augmented architecture significantly enhances adaptability and retention: in $\textbf{DG}$, $\textbf{MIRA}$ achieves SoTA out-of-distribution accuracy, and in incremental learning settings, it outperforms architectures explicitly designed to handle catastrophic forgetting using generic $\textbf{CL}$ algorithms.

We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data, including images, point clouds, graphs, meshes, and topological manifolds. While deep learning has profoundly impacted domains ranging from digital assistants to autonomous systems, the principled design of neural architectures tailored to specific tasks and data types remains one of the field's most persistent open challenges. CTNNs address this gap by formulating model design in the language of copresheaves, a concept from algebraic topology that generalizes most practical deep learning models in use today. This abstract yet constructive formulation yields a rich design space from which theoretically sound and practically effective solutions can be derived to tackle core challenges in representation learning, such as long-range dependencies, oversmoothing, heterophily, and non-Euclidean domains. Our empirical results on structured data benchmarks demonstrate that CTNNs consistently outperform conventional baselines, particularly in tasks requiring hierarchical or localized sensitivity. These results establish CTNNs as a principled multi-scale foundation for the next generation of deep learning architectures.

Transformers have driven remarkable breakthroughs in natural language processing and computer vision, yet their standard attention mechanism still imposes $O(N^2)$ complexity, hindering scalability to longer sequences. We introduce Circular-convolutional ATtention (CAT), a Fourier-based approach that efficiently applies circular convolutions to reduce complexity without sacrificing representational power. CAT achieves $O(N \log N)$ computations, requires fewer learnable parameters by streamlining fully connected layers, and introduces no heavier operations, resulting in consistent accuracy improvements and about a 10\% speedup in naive PyTorch implementations. Based on the engineering-isomorphic transformer framework, CAT's design not only offers practical efficiency and ease of implementation, but also provides insights to guide the development of future high-performance Transformer architectures. Finally, our ablation studies highlight the key conditions underlying CAT's success, shedding light on broader principles for scalable attention mechanisms.

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parameterizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that treats the residual of the generated PINN as delta PDE and performs another forward pass to generate a corrective PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves a > 100 lower $L_2$ loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems. The code and model weights are publicly available at https://github.com/rbischof/hypino.

Medicinal chemists often optimize drugs considering their 3D structures and designing structurally distinct molecules that retain key features, such as shapes, pharmacophores, or chemical properties. Previous deep learning approaches address this through supervised tasks like molecule inpainting or property-guided optimization. In this work, we propose a flexible zero-shot molecule manipulation method by navigating in a shared latent space of 3D molecules. We introduce a Variational AutoEncoder (VAE) for 3D molecules, named MolFLAE, which learns a fixed-dimensional, E(3)-equivariant latent space independent of atom counts. MolFLAE encodes 3D molecules using an E(3)-equivariant neural network into fixed number of latent nodes, distinguished by learned embeddings. The latent space is regularized, and molecular structures are reconstructed via a Bayesian Flow Network (BFN) conditioned on the encoder's latent output. MolFLAE achieves competitive performance on standard unconditional 3D molecule generation benchmarks. Moreover, the latent space of MolFLAE enables zero-shot molecule manipulation, including atom number editing, structure reconstruction, and coordinated latent interpolation for both structure and properties. We further demonstrate our approach on a drug optimization task for the human glucocorticoid receptor, generating molecules with improved hydrophilicity while preserving key interactions, under computational evaluations.

Recent multimodal image generators such as GPT-4o, Gemini 2.0 Flash, and Gemini 2.5 Pro excel at following complex instructions, editing images and maintaining concept consistency. However, they are still evaluated by disjoint toolkits: text-to-image (T2I) benchmarks that lacks multi-modal conditioning, and customized image generation benchmarks that overlook compositional semantics and common knowledge.

Physics Informed Neural Networks (PINNs) often exhibit "failure modes" in which the PDE residual loss converges while the solution error stays large, a phenomenon traditionally blamed on local optima separated from the true solution by steep loss barriers. We challenge this understanding by demonstrate that the real culprit is insufficient arithmetic precision: with standard FP32, the L BFGS optimizer prematurely satisfies its convergence test, freezing the network in a spurious failure phase. Simply upgrading to FP64 rescues optimization, enabling vanilla PINNs to solve PDEs without any failure modes. These results reframe PINN failure modes as precision induced stalls rather than inescapable local minima and expose a three stage training dynamic--un converged, failure, success--whose boundaries shift with numerical precision. Our findings emphasize that rigorous arithmetic precision is the key to dependable PDE solving with neural networks. Our code is available at Supplementary Material.

Despite their many successes, transformer-based large language models (LLMs) continue to struggle with tasks that require complex reasoning over large parts of their input. We argue that these failures arise due to capacity limits on the accurate flow of information within LLMs. To formalize this issue, we introduce the bounded attention prefix oracle (BAPO) model, a new computational framework that models bandwidth constraints on attention heads, the mechanism for internal communication in LLMs. We show that several important reasoning problems like graph reachability require high communication bandwidth for BAPOs to solve; we call these problems BAPO-hard. Our experiments corroborate our theoretical predictions: GPT-4o, Claude, and Gemini succeed on BAPO-easy tasks and fail even on relatively small BAPO-hard tasks. BAPOs also reveal another benefit of chain of thought (CoT): we prove that breaking down a task using CoT can turn any BAPO-hard problem into a BAPO-easy one. Our results offer principled explanations for key LLM failures and suggest directions for architectures and inference methods that mitigate bandwidth limits.

Obtaining a generalizable reward model is crucial in Reinforcement Learning from Human Feedback (RLHF) as it enables correctly evaluating unseen prompt-response pairs. However, existing reward models lack this ability, as they are typically trained by increasing the reward gap between chosen and rejected responses, while overlooking the prompts that the responses are conditioned on. Consequently, when the trained reward model is evaluated on prompt-response pairs that lie outside the data distribution, neglecting the effect of prompts may result in poor generalization of the reward model. To address this issue, we decompose the reward value into two independent components: prompt-free reward and prompt-related reward. Prompt-free reward represents the evaluation that is determined only by responses, while the prompt-related reward reflects the reward that derives from both the prompt and the response. We extract these two components from an information theoretical perspective, which requires no extra models.. Subsequently, we propose a new reward learning algorithm by prioritizing data samples based on their prompt-free reward values. Through toy examples, we demonstrate that the extracted prompt-free and prompt-related rewards effectively characterize two parts of the reward model. Further, standard evaluations show that our method improves both the alignment performance and the generalization capability of the reward model.