#01Nov 2, 2026
cs.LG
Variational Functional Neural Networks (vfNN)
Chinmay Katke, C. Nadir Kaplan
We present a variational functional neural network (vfNN) algorithm that optimizes physically motivated continuum functionals in integral form (e.g., Lagrangian, Hamiltonian, or free energy) to find the states of a system. That way, vfNN bypasses solving the equations of motion (a.k.a. the Euler-Lagrange equations), which are in the form of differential equations. To this end, our approach is fundamentally different from conventional physics-informed neural networks (PINN) that solve differential equations by minimizing a phenomenological loss function involving higher order derivatives and ad hoc weight factors. In contrast, vfNN merely evaluates lower order derivatives of the generating functional and replaces the weight factors with rigorous physical scales. This also fundamentally changes the loss landscape, and the desired solutions may become unstable. For this emergent nonconvex optimization problem, we develop a quasi-Newton optimization algorithm with simulated annealing that converges to the solutions of the corresponding Euler-Lagrange equations of the functional regardless of their stability properties. Our simulations using vfNN give accurate results for benchmark systems governed by linear or nonlinear ordinary differential equations.
#02Nov 2, 2026
cs.CV
Structured Visual Landscape: Generating Preferred Representations in Biological and Artificial Neural Networks
Yusong Zhao, Edgar Y. Walker, Hao Wang and 1 more
Understanding how neurons respond to visual stimulus is an important question in both deep learning and neuroscience. It has significant implications for enhancing the interpretability of black-box artificial neural networks and for understanding the visual representation in the human brain. We propose a structured visual representations landscape and design an activation-based prior that allows us to effectively regularize the landscape with activations from brain regions or neural network units. Our model Vis-Lens integrates a variational autoencoder and a diffusion model into an image generation framework. It enables the generation of natural, realistic preferred images by directly modifying the activation-regularized latent codes without per-image iterative optimization. We demonstrate the effectiveness of our framework on both artificial neural networks and human visual cortex using functional magnetic resonance imaging (fMRI) data. Our framework improves activation modulation and image realism compared with a recent state-of-the-art method for generating preferred visual representations of these neural targets.
#03Nov 2, 2026
cs.LG
Library of Layers (LoL): Adaptively Ordering Transformer Layers at Runtime
Abdellah Rahmani, Sean McLeish, Ang Li and 3 more
Computer programmers chain together the same reusable computational primitives, for example, conditional statements or loops, but in different orders to implement different algorithms. In contrast, existing language model architectures always execute their layers in the same order. We introduce Library of Layers (LoL), an architecture that dynamically orders its layers during inference to solve the problem at hand. LoL has a single hyperparameter, the size of its global library of transformer blocks, that allows it to transition seamlessly between parameter reuse and sparsity, generalizing the parameter-efficiency and FLOPs-efficiency tradeoffs of dense, depth-recurrent, and mixture of experts architectures in one unified family. We show that LoL achieves competitive performance with all three above baselines when pretrained on text data. On synthetic sudoku and maze data, we observe that the model employs distinct layer orderings to implement different solution strategies, and we can intervene on routing to force a model to apply a specific solution strategy to a problem instance. In a multilingual natural language setting, we find that LoL chooses different layer order patterns based on language and script. Similarly, we train LoL on safety data and fit probes to its router outputs, finding that these probes distinguish safe from unsafe text with high AUROC. LoL provides a path toward a future in which models dynamically compose their own computational graph, enabling more efficient and controllable reasoning.
#04Nov 2, 2026
cs.LG
Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches
Rileigh Bandy, Teresa Portone, Mohammad Khalil and 2 more
Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require rapid evaluations for fast design iterations. Closure models address this challenge by approximating unresolved effects in reduced or incomplete dynamical systems. Data-driven closures offer a flexible mechanism for improving model accuracy and applicability, but approaches that embed the closure within a computational model for construction and training phases can be computationally expensive and cause numerical instabilities in the computational model during training. To avoid the challenges posed by embedded approaches, staged approaches to closure-model learning have been developed. The first stage uses data assimilation to infer state and closure trajectories from observations. The second stage trains a machine learning closure model offline using the assimilated data, thereby avoiding repeated simulator calls during training. In this work, we investigate the cost and accuracy tradeoffs between embedded and staged data-driven closure modeling approaches for a synthetic epidemiological SIQR model with a nonlinear state-dependent quarantine closure. The results illustrate a practical accuracy-efficiency trade-off: for this exemplar, embedded training provides the strongest average accuracy, while the staged approach yields comparable qualitative behavior with a moderate increase in error, substantially fewer model evaluations, and improved optimization robustness.
#05Nov 2, 2026
cs.RO
PanoTac: A Dense Three-Axis Tactile Sensor for Robust Touch-Centric Manipulation
Binglin, Wang, Xiaole and 7 more
Contact-rich manipulation benefits from tactile feedback that captures both detailed contact geometry and interaction forces. When scooping grains, contact patterns help infer spoon orientation, while resistance transmitted through the grasp guides motion. To provide these complementary sensing capabilities, we present PanoTac, a low-cost, compliant tactile fingertip designed for dense three-axis tactile sensing. Each fingertip provides a $12 \times 32 \times 3$ tactile representation, with one normal ($z$) and two shear ($x$, $y$) response components at each taxel. The sensor operates at 60 Hz and costs less than $50 per fingertip. Sensor characterization quantifies response repeatability and consistency across sensor instances and contact locations. We integrate PanoTac into a robotic system with a visuo-tactile pipeline. Across test-tube preparation, grain scooping, and salt pouring, the resulting policies outperform vision-only baselines by an average of 46.7 percentage points. Ablations show that removing either spatial contact information or shear feedback reduces overall performance across the task suite. Our project page is available at https://panotac.github.io.