Recent disentangled representation learning (DRL) methods heavily rely on factorspecific strategies--either learning objectives for attributes or model architectures for objects--to embed inductive biases. Such divergent approaches result in significant overhead when novel factors of variation do not align with prior assumptions, such as statistical independence or spatial exclusivity, or when multiple factors coexist, as practitioners must redesign architectures or objectives. To address this, we propose a compositional bias, a modular inductive bias decoupled from both objectives and architectures. Our key insight is that different factors obey distinct "recombination rules" in the data distribution: global attributes are mutually exclusive, e.g., a face has one nose, while objects share a common support (any subset of objects can co-exist). We therefore randomly remix latents according to factor-specific rules, i.e., a mixing strategy, and force the encoder to discover whichever factor structure the mixing strategy reflects through two complementary objectives: (i) a prior loss that ensures every remix decodes into a realistic image, and (ii) the compositional consistency loss introduced by Wiedemer et al. [50], which aligns each composite image with its corresponding composite latent. Under this general framework, simply adjusting the mixing strategy enables disentanglement of attributes, objects, and even both, without modifying the objectives or architectures. Extensive experiments demonstrate that our method shows competitive performance in both attribute and object disentanglement, and uniquely achieves joint disentanglement of global style and objects.

In this paper, we propose integrating this inductive bias into ViTs, not through an architectural intervention but solely through initialization. The motivation here is to have a ViT that can enjoy strong CNN-like performance when data assets are small, but can still scale to ViTlike performance as the data expands. Our approach is motivated by our empirical results that random impulse filters can achieve commensurate performance to learned filters within a CNN. We improve upon current ViT initialization strategies, which typically rely on empirical heuristics such as using attention weights from pretrained models or focusing on the distribution of attention weights without enforcing structures. Empirical results demonstrate that our method significantly outperforms standard ViT initialization across numerous small and medium-scale benchmarks, including Food-101, CIFAR-10, CIFAR-100, STL-10, Flowers, and Pets, while maintaining comparative performance on large-scale datasets such as ImageNet-1K. Moreover, our initialization strategy can be easily integrated into various transformer-based architectures such as Swin Transformer and MLP-Mixer with consistent improvements in performance.

Mamba extends earlier state space models (SSMs) by introducing input-dependent dynamics, and has demonstrated strong empirical performance across a range of domains, including language modeling, computer vision, and foundation models. However, a surprising weakness remains: despite being built on architectures designed for long-range dependencies, Mamba performs poorly on long-range sequential tasks. Understanding and addressing this gap is important for improving Mamba's universality and versatility. In this work, we analyze Mamba's limitations through three perspectives: expressiveness, inductive bias, and training stability. Our theoretical results show how Mamba falls short in each of these aspects compared to earlier SSMs such as S4D. To address these issues, we propose B2S6, a simple extension of Mamba's S6 unit that combines block-wise selective dynamics with a channel-specific bias. We prove that these changes equip the model with a better-suited inductive bias and improve its expressiveness and stability. Empirically, B2S6 outperforms S4 and S4D on Long-Range Arena (LRA) tasks while maintaining Mamba's performance on language modeling benchmarks.

We demonstrate that architectures which traditionally are considered to be ill-suited for a task can be trained using inductive biases from another architecture. We call a network untrainable when it overfits, underfits, or converges to poor results even when tuning their hyperparameters. For example, fully connected networks overfit on object recognition while deep convolutional networks without residual connections underfit. The traditional answer is to change the architecture to impose some inductive bias, although the nature of that bias is unknown. We introduce guidance, where a guide network steers a target network using a neural distance function.

Deep neural networks often underperform on tabular data due to sensitivity to irrelevant features and a spectral bias toward smooth, low-frequency functions, limiting their ability to capture sharp, high-frequency signals in low-label regimes. While self-supervised learning (SSL) holds promise in such settings, it remains challenging in tabular domains due to the limited availability of effective data augmentations. We introduce TANDEM (Tree-And-Neural Dual Encoder Model), a hybrid autoencoder that trains a neural encoder alongside an oblivious soft decision tree (OSDT) encoder, both guided by dedicated stochastic gating networks for sample-specific feature selection. The encoders share a decoder and are coupled via alignment losses, encouraging complementary yet consistent representations. The training-only use of the tree operates as model-based augmentation, nudging representations toward tabular-relevant features while preserving a lean inference path (only the neural encoder is deployed). Spectral analysis highlights distinct yet complementary inductive biases across encoders, and experiments on classification and regression benchmarks in low-label settings show consistent gains over strong deep, tree-based, and SSL baselines.

Deep learning has managed to evade numerous intuitions from classical statistics to achieve unprecedented performance on a number of real-world tasks. In this article, we investigate the key features and surprises of deep learning from a physics-informed perspective, taking care to point out and justify where possible the many choices inherent in constructing a deep learning model. In particular, we review the phenomenon of neural scaling laws and discuss their interplay with the constraints and inductive biases which may be present when applying machine learning to problems in physics.

Recent work studying the generalization of diffusion models with locally linear UNet-based denoisers reveals inductive biases that can be expressed via geometryadaptive harmonic bases. For such locally linear UNets, these geometry-adaptive harmonic bases can be conveniently visualized through the eigen-decomposition of a UNet's Jacobian matrix. In practice, however, more recent denoising networks are often transformer-based, e.g., the diffusion transformer (DiT). Due to the presence of nonlinear operations, similar eigen-decomposition analyses cannot be used to reveal the inductive biases of transformer-based denoisers. This motivates our search for alternative ways to explain the strong generalization ability observed in DiT models.

Missing values, frequently encountered in time series data, can significantly impair the effectiveness of analytical methods. While deep imputation models have emerged as the predominant approach due to their superior performance, explicitly incorporating inductive biases aligned with time-series characteristics offers substantial improvement potential. Taking advantage of non-stationarity and periodicity in time series, two domain-specific inductive biases are designed: (1) Non-Stationary Guidance, which operationalizes the proximity principle to address highly non-stationary series by emphasizing temporal neighbors, and (2) Periodic Guidance, which exploits periodicity patterns through learnable weight allocation across historical periods. Building upon these complementary mechanisms, the overall module, named Meta Guidance, dynamically fuses both guidances through data-adaptive weights learned from the specific input sample. Experiments on nine benchmark datasets demonstrate that integrating Meta Guidance into existing deep imputation architectures achieves an average 27.39% reduction in imputation error compared to state-of-the-art baselines.

In this paper, we propose integrating this inductive bias into ViTs, not through an architectural intervention but solely through initialization. The motivation here is to have a ViT that can enjoy strong CNN-like performance when data assets are small, but can still scale to ViT-like performance as the data expands. Our approach is motivated by our empirical results that random impulse filters can achieve commensurate performance to learned filters within a CNN. We improve upon current ViT initialization strategies, which typically rely on empirical heuristics such as using attention weights from pretrained models or focusing on the distribution of attention weights without enforcing structures. Empirical results demonstrate that our method significantly outperforms standard ViT initialization across numerous small and medium-scale benchmarks, including Food-101, CIFAR-10, CIFAR-100, STL-10, Flowers, and Pets, while maintaining comparative performance on large-scale datasets such as ImageNet-1K. Moreover, our initialization strategy can be easily integrated into various transformer-based architectures such as Swin Transformer and MLP-Mixer with consistent improvements in performance.

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.