Topological Neural Operators: operator learning on cell complexes via Discrete Exterior Calculus
Researchers introduce Topological Neural Operators (TNOs), a framework that extends neural operators from point/edge functions to general topological domains (cell complexes) using Discrete Exterior Calculus. The design decouples fixed topological information flow from learned transformations, enabling models that respect geometric structure and conservation laws. A hierarchical variant (HTNOs) adds learned coarse complexes for long-range propagation. TNOs subsume existing neural operators as a special case and show accuracy improvements on PDE benchmarks including irregular-geometry flow problems.
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Topo-Omni: Topographic multimodal model discovers functionally selective brain regions consistent with human neuroimaging
Researchers introduce Topo-Omni, a topographic multimodal model that jointly represents visual, auditory, and language/cognitive processing on a single contiguous in-silico cortical sheet, built by fine-tuning a pretrained foundation model with a spatial smoothness objective. The model develops clusters consistent with human neuroimaging data, and driving or suppressing clusters selectively biases or impairs perception in ways that parallel human intervention studies. The authors use the model to screen for novel cortical networks in-silico and validate discoveries — including natural landscape and animal networks — in human neuroimaging data. The work bridges deep learning architectures and computational neuroscience, offering testable hypotheses about cortical organization.
Functional Attention: Reinterpreting Attention as Functional Correspondences for Operator Learning
This paper introduces Functional Attention, a novel attention mechanism for operator learning that replaces standard softmax token-wise affinities with structured linear operators inspired by geometric functional maps. The approach treats attention as a correspondence between adaptive bases rather than discrete tokens, yielding a resolution-invariant, globally-aware representation. Experiments show competitive or state-of-the-art performance on PDE solving, 3D segmentation, and regression tasks, with robustness to varying discretizations.
P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for spatiotemporal super-resolution
Researchers propose P-K-GCN, a framework combining graph convolutional networks, Koopman operator theory, and physics-informed loss functions for spatiotemporal super-resolution on irregular geometries. The method linearizes nonlinear dynamics in a latent space and enforces physical constraints to improve reconstruction fidelity. Theoretical analysis claims guaranteed error reduction via Rademacher complexity bounds. The framework is evaluated on reconstructing high-resolution cardiac electrodynamics from sparse 3D heart geometry measurements.
NF-CoT: Latent reasoning with normalizing flows preserves autoregressive LLM advantages
Researchers propose NF-CoT, a latent reasoning framework that replaces discrete chain-of-thought token streams with continuous intermediate states modeled by normalizing flows embedded inside an LLM backbone. The approach uses a TARFlow-style normalizing flow head alongside the standard language model head, enabling exact likelihoods, KV-cache-compatible left-to-right decoding, and policy-gradient optimization in latent space. On code-generation benchmarks, NF-CoT improves pass rates over both explicit CoT and prior latent-reasoning baselines while reducing intermediate reasoning cost. The work addresses a key limitation of existing latent reasoning methods, which typically sacrifice probabilistic tractability or autoregressive compatibility.
NeSyCat Torch: Differentiable tensor framework unifying neurosymbolic semantics via monadic abstraction
NeSyCat Torch extends the NeSyCat/ULLER neurosymbolic framework with neural network support for predicates and functions, implemented via probabilistic programming and tensor backends (HaskTorch, JAX, PyTorch). The key technical contribution is a lazy log-tensor monad over the log-semiring enabling numerically stable, differentiable training, alongside a batch monad for efficient batched inference. On MNIST addition benchmarks, the implementations outperform LTN and DeepProbLog in speed and accuracy while remaining within a uniform categorical framework that generalizes across first-order neurosymbolic approaches. The work positions itself as a unifying foundation for classical, fuzzy, probabilistic, and neural truth semantics.
COGENT: Continuous graph emulator with Neural ODEs for long-term physical forecasting on irregular meshes
COGENT is a new architecture combining graph neural networks with Neural Ordinary Differential Equations for continuous-time physical forecasting on irregular geospatial meshes. The model encodes historical system states and forcings into latent dynamics that can be queried at arbitrary future times, avoiding the error accumulation of autoregressive rollout. Evaluated on ice-sheet simulations from the Ice-sheet and Sea-level System Model, COGENT shows improved long-range stability over autoregressive graph baselines. The work introduces training stabilization strategies including rollout-horizon sampling and progressive scheduling.
AdamO optimizer and dynamical isometry regularization preserve plasticity in continual learning
A new arXiv preprint connects plasticity loss in continual learning to the empirical Neural Tangent Kernel and identifies dynamical isometry—keeping layer-wise Jacobian singular values near one—as a key mechanism for maintaining learning capacity under non-stationarity. The authors propose an isometry-promoting regularization scheme that can reactivate dormant ReLU units and introduce AdamO, an Adam-style optimizer that decouples isometry regularization from gradient updates analogously to AdamW. The methods are evaluated on supervised and reinforcement-learning continual-learning benchmarks, consistently matching or outperforming prior approaches. The work also reinterprets existing plasticity-preserving methods as targeting only partial isometry measures.
Training-Free Looped Transformers: Inference-Time Recurrence via ODE-Motivated Layer Reapplication
The paper introduces a method to retrofit recurrence onto frozen pretrained transformer checkpoints at inference time by looping a contiguous mid-stack block of layers without any fine-tuning or architectural changes. Naive block reapplication degrades performance, so the authors motivate their approach by treating pre-norm transformer blocks as forward Euler ODE steps and replacing one large update with smaller damped sub-steps. Evaluated across seven model families including dense, sparse MoE, and MLA+MoE architectures, the method yields consistent benchmark improvements (e.g., +2.64 pp on MMLU-Pro for Qwen3-4B-Instruct) at no training cost.