Recently, learning-based stereo matching networks have advanced significantly. However, they often lack robustness and struggle to achieve impressive cross-domain performance due to domain shifts and imbalanced disparity distributions among diverse datasets. Leveraging Vision Foundation Models (VFMs) can intuitively enhance the model's robustness, but integrating such a model into stereo matching cost-effectively to fully realize their robustness remains a key challenge. To address this, we propose SMoEStereo, a novel framework that adapts VFMs for stereo matching through a tailored, scene-specific fusion of Low-Rank Adaptation (LoRA) and Mixture-of-Experts (MoE) modules. SMoEStereo introduces MoE-LoRA with adaptive ranks and MoE-Adapter with adaptive kernel sizes. The former dynamically selects optimal experts within MoE to adapt varying scenes across domains, while the latter injects inductive bias into frozen VFMs to improve geometric feature extraction. Importantly, to mitigate computational overhead, we further propose a lightweight decision network that selectively activates MoE modules based on input complexity, balancing efficiency with accuracy. Extensive experiments demonstrate that our method exhibits state-of-the-art cross-domain and joint generalization across multiple benchmarks without dataset-specific adaptation. The code is available at \textcolor{red}{https://github.com/cocowy1/SMoE-Stereo}.
Brain-computer interface (BCI) technology utilizing electroencephalography (EEG) marks a transformative innovation, empowering motor-impaired individuals to engage with their environment on equal footing. Despite its promising potential, developing subject-invariant and session-invariant BCI systems remains a significant challenge due to the inherent complexity and variability of neural activity across individuals and over time, compounded by EEG hardware constraints. While prior studies have sought to develop robust BCI systems, existing approaches remain ineffective in capturing the intricate spatiotemporal dependencies within multichannel EEG signals. This study addresses this gap by introducing the attentive graph-temporal convolutional network (AGTCNet), a novel graph-temporal model for motor imagery EEG (MI-EEG) classification. Specifically, AGTCNet leverages the topographic configuration of EEG electrodes as an inductive bias and integrates graph convolutional attention network (GCAT) to jointly learn expressive spatiotemporal EEG representations. The proposed model significantly outperformed existing MI-EEG classifiers, achieving state-of-the-art performance while utilizing a compact architecture, underscoring its effectiveness and practicality for BCI deployment. With a 49.87% reduction in model size, 64.65% faster inference time, and shorter input EEG signal, AGTCNet achieved a moving average accuracy of 66.82% for subject-independent classification on the BCI Competition IV Dataset 2a, which further improved to 82.88% when fine-tuned for subject-specific classification. On the EEG Motor Movement/Imagery Dataset, AGTCNet achieved moving average accuracies of 64.14% and 85.22% for 4-class and 2-class subject-independent classifications, respectively, with further improvements to 72.13% and 90.54% for subject-specific classifications.
This paper presents Segment This Thing (STT), a new efficient image segmentation model designed to produce a single segment given a single point prompt. Instead of following prior work and increasing efficiency by decreasing model size, we gain efficiency by foveating input images. Given an image and a point prompt, we extract a crop centered on the prompt and apply a novel variable-resolution patch tokenization in which patches are downsampled at a rate that increases with increased distance from the prompt. This approach yields far fewer image tokens than uniform patch tokenization. As a result we can drastically reduce the computational cost of segmentation without reducing model size. Furthermore, the foveation focuses the model on the region of interest, a potentially useful inductive bias. We show that our Segment This Thing model is more efficient than prior work while remaining competitive on segmentation benchmarks. It can easily run at interactive frame rates on consumer hardware and is thus a promising tool for augmented reality or robotics applications.
Deep neural networks trained to predict neural activity from visual input and behaviour have shown great potential to serve as digital twins of the visual cortex. Per-neuron embeddings derived from these models could potentially be used to map the functional landscape or identify cell types. However, state-of-the-art predictive models of mouse V1 do not generate functional embeddings that exhibit clear clustering patterns which would correspond to cell types. This raises the question whether the lack of clustered structure is due to limitations of current models or a true feature of the functional organization of mouse V1. In this work, we introduce DECEMber -- Deep Embedding Clustering via Expectation Maximization-based refinement -- an explicit inductive bias into predictive models that enhances clustering by adding an auxiliary $t$-distribution-inspired loss function that enforces structured organization among per-neuron embeddings. We jointly optimize both neuronal feature embeddings and clustering parameters, updating cluster centers and scale matrices using the EM-algorithm. We demonstrate that these modifications improve cluster consistency while preserving high predictive performance and surpassing standard clustering methods in terms of stability. Moreover, DECEMber generalizes well across species (mice, primates) and visual areas (retina, V1, V4). The code is available at https://github.com/Nisone2000/sensorium/tree/neuroips_version.
The local inductive bias of message-passing graph neural networks (GNNs) hampers their ability to exploit key structural information (e.g., connectivity and cycles). Positional encoding (PE) and Persistent Homology (PH) have emerged as two promising approaches to mitigate this issue. PE schemes endow GNNs with location-aware features, while PH methods enhance GNNs with multiresolution topological features. However, a rigorous theoretical characterization of the relative merits and shortcomings of PE and PH has remained elusive. We bridge this gap by establishing that neither paradigm is more expressive than the other, providing novel constructions where one approach fails but the other succeeds. Our insights inform the design of a novel learnable method, PiPE (Persistence-informed Positional Encoding), which is provably more expressive than both PH and PE. PiPE demonstrates strong performance across a variety of tasks (e.g., molecule property prediction, graph classification, and out-of-distribution generalization), thereby advancing the frontiers of graph representation learning. Code is available at https://github.com/Aalto-QuML/PIPE.
Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance on a wide variety of tasks. However, existing equivariant methods can be computationally intensive, with high parameter counts, and are often tied to a specific architecture. We propose a simple zero-parameter approach that imposes approximate equivariance for a finite group in the latent representation, as an additional term in the loss function. We conduct experiments which allow the network to learn a group representation on the latent space, and show in every case it prefers to learn the regular representation. Fixing this action on the latent space, this yields a simple method to impose approximate equivariance as an additional loss penalty. We benchmark our approach on three datasets and compare it against several existing equivariant methods, showing that in many cases it achieves similar or better performance for a fraction of the parameters.
Inductive biases are inherent in every machine learning system, shaping how models generalize from finite data. In the case of neural language models (LMs), debates persist as to whether these biases align with or diverge from human processing constraints. To address this issue, we propose a quantitative framework that allows for controlled investigations into the nature of these biases. Within our framework, we introduce $m$-local entropy$\unicode{x2013}$an information-theoretic measure derived from average lossy-context surprisal$\unicode{x2013}$that captures the local uncertainty of a language by quantifying how effectively the $m-1$ preceding symbols disambiguate the next symbol. In experiments on both perturbed natural language corpora and languages defined by probabilistic finite-state automata (PFSAs), we show that languages with higher $m$-local entropy are more difficult for Transformer and LSTM LMs to learn. These results suggest that neural LMs, much like humans, are highly sensitive to the local statistical structure of a language.
Time series forecasting plays a critical role in domains such as energy, finance, and healthcare, where accurate predictions inform decision-making under uncertainty. Although Transformer-based models have demonstrated success in sequential modeling, their adoption for time series remains limited by challenges such as noise sensitivity, long-range dependencies, and a lack of inductive bias for temporal structure. In this work, we present a unified and principled framework for benchmarking three prominent Transformer forecasting architectures-Autoformer, Informer, and Patchtst-each evaluated through three architectural variants: Minimal, Standard, and Full, representing increasing levels of complexity and modeling capacity. We conduct over 1500 controlled experiments on a suite of ten synthetic signals, spanning five patch lengths and five forecast horizons under both clean and noisy conditions. Our analysis reveals consistent patterns across model families. To advance this landscape further, we introduce the Koopman-enhanced Transformer framework, Deep Koopformer, which integrates operator-theoretic latent state modeling to improve stability and interpretability. We demonstrate its efficacy on nonlinear and chaotic dynamical systems. Our results highlight Koopman based Transformer as a promising hybrid approach for robust, interpretable, and theoretically grounded time series forecasting in noisy and complex real-world conditions.
Determining the 3D pose of a patient from a limited set of 2D X-ray images is a critical task in interventional settings. While preoperative volumetric imaging (e.g., CT and MRI) provides precise 3D localization and visualization of anatomical targets, these modalities cannot be acquired during procedures, where fast 2D imaging (X-ray) is used instead. To integrate volumetric guidance into intraoperative procedures, we present PolyPose, a simple and robust method for deformable 2D/3D registration. PolyPose parameterizes complex 3D deformation fields as a composition of rigid transforms, leveraging the biological constraint that individual bones do not bend in typical motion. Unlike existing methods that either assume no inter-joint movement or fail outright in this under-determined setting, our polyrigid formulation enforces anatomically plausible priors that respect the piecewise rigid nature of human movement. This approach eliminates the need for expensive deformation regularizers that require patient- and procedure-specific hyperparameter optimization. Across extensive experiments on diverse datasets from orthopedic surgery and radiotherapy, we show that this strong inductive bias enables PolyPose to successfully align the patient's preoperative volume to as few as two X-ray images, thereby providing crucial 3D guidance in challenging sparse-view and limited-angle settings where current registration methods fail.
Simplicity is a powerful inductive bias. In reinforcement learning, regularization is used for simpler policies, data augmentation for simpler representations, and sparse reward functions for simpler objectives, all that, with the underlying motivation to increase generalizability and robustness by focusing on the essentials. Supplementary to these techniques, we investigate how to promote simple behavior throughout the episode. To that end, we introduce a modification of the reinforcement learning problem that additionally maximizes the total correlation within the induced trajectories. We propose a practical algorithm that optimizes all models, including policy and state representation, based on a lower-bound approximation. In simulated robot environments, our method naturally generates policies that induce periodic and compressible trajectories, and that exhibit superior robustness to noise and changes in dynamics compared to baseline methods, while also improving performance in the original tasks.
Recent efforts at scaling computer vision models have established Vision Transformers (ViTs) as the leading architecture. ViTs incorporate weight sharing over image patches as an important inductive bias. In this work, we show that ViTs benefit from incorporating equivariance under the octic group, i.e., reflections and 90-degree rotations, as a further inductive bias. We develop new architectures, octic ViTs, that use octic-equivariant layers and put them to the test on both supervised and self-supervised learning. Through extensive experiments on DeiT-III and DINOv2 training on ImageNet-1K, we show that octic ViTs yield more computationally efficient networks while also improving performance. In particular, we achieve approximately 40% reduction in FLOPs for ViT-H while simultaneously improving both classification and segmentation results.
State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the choice of regularization method plays a crucial role: when trained on formal languages with standard regularization ($L_1$, $L_2$, or none), expressive architectures not only fail to converge to correct solutions but are actively pushed away from perfect initializations. In contrast, applying the Minimum Description Length (MDL) principle to balance model complexity with data fit provides a theoretically grounded regularization method. Using MDL, perfect solutions are selected over approximations, independently of the optimization algorithm. We propose that unlike existing regularization techniques, MDL introduces the appropriate inductive bias to effectively counteract overfitting and promote generalization.
We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.
Graph Transformers (GTs) have shown advantages in numerous graph structure tasks but their self-attention mechanism ignores the generalization bias of graphs, with existing methods mainly compensating for this bias from aspects like position encoding, attention bias and relative distance yet still having sub-optimal performance and being insufficient by only considering the structural perspective of generalization bias. To address this, this paper proposes Grafourierformer, which innovatively combines GT with inductive bias containing Frequency-Structure information by applying Graph Fourier Transform to the Attention Matrix: specifically, eigenvalues from the Graph Laplacian matrix are used to construct an Eigenvalue matrix mask (reflecting node positions and structural relationships with neighboring nodes to enable consideration of node range structural characteristics and focus on local graph details), and inverse Fourier transform is employed to extract node high-frequency and low-frequency features, calculate low-frequency and high-frequency energy, and construct a node frequency-energy matrix to filter the eigenvalue matrix mask, allowing attention heads to incorporate both graph structural information and node frequency information optimization, adaptively distinguish global trends from local details, and effectively suppress redundant information interference. Extensive experiments on various benchmarks show Grafourierformer consistently outperforms GNN and GT-based models in graph classification and node classification tasks, with ablation experiments further validating the effectiveness and necessity of the method. Codes are available at https://github.com/Arichibald/Grafourierformer.git
How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usually used to train diffusion models is the score function of the training distribution; and the networks usually used to learn the score function are expressive enough to learn this score to high accuracy. We claim that a certain feature of the DSM objective -- the fact that its target is not the training distribution's score, but a noisy quantity only equal to it in expectation -- strongly impacts whether and to what extent diffusion models generalize. In this paper, we develop a mathematical theory that partly explains this 'generalization through variance' phenomenon. Our theoretical analysis exploits a physics-inspired path integral approach to compute the distributions typically learned by a few paradigmatic under- and overparameterized diffusion models. We find that the distributions diffusion models effectively learn to sample from resemble their training distributions, but with 'gaps' filled in, and that this inductive bias is due to the covariance structure of the noisy target used during training. We also characterize how this inductive bias interacts with feature-related inductive biases.
Deep reinforcement learning agents, trained on raw pixel inputs, often fail to generalize beyond their training environments, relying on spurious correlations and irrelevant background details. To address this issue, object-centric agents have recently emerged. However, they require different representations tailored to the task specifications. Contrary to deep agents, no single object-centric architecture can be applied to any environment. Inspired by principles of cognitive science and Occam's Razor, we introduce Object-Centric Attention via Masking (OCCAM), which selectively preserves task-relevant entities while filtering out irrelevant visual information. Specifically, OCCAM takes advantage of the object-centric inductive bias. Empirical evaluations on Atari benchmarks demonstrate that OCCAM significantly improves robustness to novel perturbations and reduces sample complexity while showing similar or improved performance compared to conventional pixel-based RL. These results suggest that structured abstraction can enhance generalization without requiring explicit symbolic representations or domain-specific object extraction pipelines.
Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. However, when applied to large-scale, spatiotemporally chaotic systems, purely data-driven machine learning methods often suffer from inefficiencies, as they require a large learning model size and a massive amount of training data to achieve acceptable performance. To address this challenge, we incorporate the spatial coupling structure of the target system as an inductive bias in the network design. Specifically, we introduce physics-guided clustered echo state networks, leveraging the efficiency of the echo state networks as a base model. Experimental results on benchmark chaotic systems demonstrate that our physics-informed method outperforms existing echo state network models in learning the target chaotic systems. Additionally, our models exhibit robustness to noise in training data and remain effective even when prior coupling knowledge is imperfect. This approach has the potential to enhance other machine learning methods.
Scene flow estimation aims to recover per-point motion from two adjacent LiDAR scans. However, in real-world applications such as autonomous driving, points rarely move independently of others, especially for nearby points belonging to the same object, which often share the same motion. Incorporating this locally rigid motion constraint has been a key challenge in self-supervised scene flow estimation, which is often addressed by post-processing or appending extra regularization. While these approaches are able to improve the rigidity of predicted flows, they lack an architectural inductive bias for local rigidity within the model structure, leading to suboptimal learning efficiency and inferior performance. In contrast, we enforce local rigidity with a lightweight add-on module in neural network design, enabling end-to-end learning. We design a discretized voting space that accommodates all possible translations and then identify the one shared by nearby points by differentiable voting. Additionally, to ensure computational efficiency, we operate on pillars rather than points and learn representative features for voting per pillar. We plug the Voting Module into popular model designs and evaluate its benefit on Argoverse 2 and Waymo datasets. We outperform baseline works with only marginal compute overhead. Code is available at https://github.com/tudelft-iv/VoteFlow.
Theory-of-Mind (ToM), the ability to infer others' perceptions and mental states, is fundamental to human interaction but remains a challenging task for Large Language Models (LLMs). While existing ToM reasoning methods show promise with reasoning via perceptual perspective-taking, they often rely excessively on LLMs, reducing their efficiency and limiting their applicability to high-order ToM reasoning, which requires multi-hop reasoning about characters' beliefs. To address these issues, we present EnigmaToM, a novel neuro-symbolic framework that enhances ToM reasoning by integrating a Neural Knowledge Base of entity states (Enigma) for (1) a psychology-inspired iterative masking mechanism that facilitates accurate perspective-taking and (2) knowledge injection that elicits key entity information. Enigma generates structured representations of entity states, which construct spatial scene graphs -- leveraging spatial information as an inductive bias -- for belief tracking of various ToM orders and enhancing events with fine-grained entity state details. Experimental results on multiple benchmarks, including ToMi, HiToM, and FANToM, show that EnigmaToM significantly improves ToM reasoning across LLMs of varying sizes, particularly excelling in high-order reasoning scenarios.
Link prediction is a crucial task in many downstream applications of graph machine learning. To this end, Graph Neural Network (GNN) is a widely used technique for link prediction, mainly in transductive settings, where the goal is to predict missing links between existing nodes. However, many real-life applications require an inductive setting that accommodates for new nodes, coming into an existing graph. Thus, recently inductive link prediction has attracted considerable attention, and a multi-layer perceptron (MLP) is the popular choice of most studies to learn node representations. However, these approaches have limited expressivity and do not fully capture the graph's structural signal. Therefore, in this work we propose LEAP, an inductive link prediction method based on LEArnable toPology augmentation. Unlike previous methods, LEAP models the inductive bias from both the structure and node features, and hence is more expressive. To the best of our knowledge, this is the first attempt to provide structural contexts for new nodes via learnable augmentation in inductive settings. Extensive experiments on seven real-world homogeneous and heterogeneous graphs demonstrates that LEAP significantly surpasses SOTA methods. The improvements are up to 22\% and 17\% in terms of AUC and average precision, respectively. The code and datasets are available on GitHub (https://github.com/AhmedESamy/LEAP/)