The empirical success of deep learning is often attributed to scaling laws that predict consistent gains as model, data, and compute grow; however, large models can exhibit training instability and diminishing returns, suggesting that scaling laws describe what success looks like but not when and why scaling succeeds or fails. A central obstacle is the lack of a rigorous understanding of feature learning at large depth. While muP characterizes feature-learning dynamics in the infinite-width limit and enables hyperparameter transfer across width, its depth extension (depth-muP) breaks down for residual blocks with more than one internal layer. We derive Neural Feature Dynamics (NFD) for ResNets with single-layer residual blocks, characterizing feature learning via a coupled forward-backward stochastic system in the joint infinite-width and infinite-depth limit. In this regime, NFD identifies when scaling-law trends persist and explains diminishing returns. It also reveals a vanishing mechanism induced by the 1/sqrt(depth) residual scaling under which the gradient-independence assumption (GIA), known to fail during training at finite depth, becomes provably valid again at infinite depth, yielding an analytically tractable regime for end-to-end feature learning. Motivated by this insight, we study two-layer residual blocks and show that the same mechanism causes feature-learning collapse in the first internal layer at large depth, providing a structural explanation for the empirical failure of depth-muP. Based on this diagnosis, we propose a depth-aware learning-rate correction that counteracts the collapse and empirically restores depth-wise hyperparameter transfer, yielding stronger performance in deeper ResNets.

We study the problem of subgroup discovery for survival analysis, where the goal is to find an interpretable subset of the data on which a Cox model is highly accurate. Our work is the first to study this particular subgroup problem, for which we make several contributions. Subgroup discovery methods generally require a "quality function" in order to sift through and select the most advantageous subgroups. We first examine why existing natural choices for quality functions are insufficient to solve the subgroup discovery problem for the Cox model. To address the shortcomings of existing metrics, we introduce two technical innovations: the *expected prediction entropy (EPE)*, a novel metric for evaluating survival models which predict a hazard function; and the *conditional rank statistics (CRS)*, a statistical object which quantifies the deviation of an individual point to the distribution of survival times in an existing subgroup. We study the EPE and CRS theoretically and show that they can solve many of the problems with existing metrics. We introduce a total of eight algorithms for the Cox subgroup discovery problem. The main algorithm is able to take advantage of both the EPE and the CRS, allowing us to give theoretical correctness results for this algorithm in a well-specified setting. We evaluate all of the proposed methods empirically on both synthetic and real data. The experiments confirm our theory, showing that our contributions allow for the recovery of a ground-truth subgroup in well-specified cases, as well as leading to better model fit compared to naively fitting the Cox model to the whole dataset in practical settings. Lastly, we conduct a case study on jet engine simulation data from NASA. The discovered subgroups uncover known nonlinearities/homogeneity in the data, and which suggest design choices which have been mirrored in practice.

In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional gradient descent over a parametrization of the functions, such as neural networks, an interesting alternative is to instead perform gradient descent directly in the function space by leveraging its Hilbert space structure, thus enabling provable guarantees and fast convergence. However, infinite-dimensional gradients are often hard to compute in practice, hindering the applicability of such methods. To overcome this limitation, our framework requires only the computation of directional derivatives and a pre-basis for the Hilbert space domain, i.e., a linearly-independent set whose span is dense in the Hilbert space. This fully resolves the tractability issue, as pre-bases are much more easily obtained than full orthonormal bases or reproducing kernels -- which may not even exist -- and individual directional derivatives can be easily computed using forward-mode scalar automatic differentiation. We showcase the use of our method to solve partial differential equations à la physics informed neural networks (PINNs), where it effectively enables provable convergence.

We present a comprehensive study on fully automated pollen recognition across both conventional optical and digital in-line holographic microscopy (DIHM) images of sample slides. Visually recognizing pollen in unreconstructed holographic images remains challenging due to speckle noise, twin-image artifacts and substantial divergence from bright-field appearances. We establish the performance baseline by training YOLOv8s for object detection and MobileNetV3L for classification on a dual-modality dataset of automatically annotated optical and affinely aligned DIHM images. On optical data, detection mAP50 reaches 91.3% and classification accuracy reaches 97%, whereas on DIHM data, we achieve only 8.15% for detection mAP50 and 50% for classification accuracy. Expanding the bounding boxes of pollens in DIHM images over those acquired in aligned optical images achieves 13.3% for detection mAP50 and 54% for classification accuracy. To improve object detection in DIHM images, we employ a Wasserstein GAN with spectral normalization (WGAN-SN) to create synthetic DIHM images, yielding an FID score of 58.246. Mixing real-world and synthetic data at the 1.0 : 1.5 ratio for DIHM images improves object detection up to 15.4%. These results demonstrate that GAN-based augmentation can reduce the performance divide, bringing fully automated DIHM workflows for veterinary imaging a small but important step closer to practice.

Visual environments are structured, consisting of distinct objects or entities. These entities have properties---visible or latent---that determine the manner in which they interact with one another. To partition images into entities, deep-learning researchers have proposed structural inductive biases such as slot-based architectures. To model interactions among entities, equivariant graph neural nets (GNNs) are used, but these are not particularly well suited to the task for two reasons. First, GNNs do not predispose interactions to be sparse, as relationships among independent entities are likely to be.

Recent work has shown that a simple, fast method called Simple Graph Convolution (SGC) (Wu et al., 2019), which eschews deep learning, is competitive with deep methods like graph convolutional networks (GCNs) (Kipf & Welling, 2017) in common graph machine learning benchmarks. The use of graph data in SGC implicitly assumes the common but not universal graph characteristic of homophily, wherein nodes link to nodes which are similar. Here we confirm that SGC is indeed ineffective for heterophilous (i.e., non-homophilous) graphs via experiments on synthetic and real-world datasets. We propose Adaptive Simple Graph Convolution (ASGC), which we show can adapt to both homophilous and heterophilous graph structure. Like SGC, ASGC is not a deep model, and hence is fast, scalable, and interpretable; further, we can prove performance guarantees on natural synthetic data models. Empirically, ASGC is often competitive with recent deep models at node classification on a benchmark of real-world datasets. The SGC paper questioned whether the complexity of graph neural networks is warranted for common graph problems involving homophilous networks; our results similarly suggest that, while deep learning often achieves the highest performance, heterophilous structure alone does not necessitate these more involved methods.

How to efficiently serve ever-larger trained natural language models in practice has become exceptionally challenging even for powerful cloud servers due to their prohibitive memory/computation requirements.In this work, we present an efficient and affordable post-training quantization approach to compress large Transformer-based models, termed as \OURS.

Geometric deep learning has broad applications in biology, a domain where relational structure in data is often intrinsic to modelling the underlying phenomena. Currently, efforts in both geometric deep learning and, more broadly, deep learning applied to biomolecular tasks have been hampered by a scarcity of appropriate datasets accessible to domain specialists and machine learning researchers alike. To address this, we introduce Graphein as a turn-key tool for transforming raw data from widely-used bioinformatics databases into machine learning-ready datasets in a high-throughput and flexible manner. Graphein is a Python library for constructing graph and surface-mesh representations of biomolecular structures, such as proteins, nucleic acids and small molecules, and biological interaction networks for computational analysis and machine learning. Graphein provides utilities for data retrieval from widely-used bioinformatics databases for structural data, including the Protein Data Bank, the AlphaFold Structure Database, chemical data from ZINC and ChEMBL, and for biomolecular interaction networks from STRINGdb, BioGrid, TRRUST and RegNetwork. The library interfaces with popular geometric deep learning libraries: DGL, Jraph, PyTorch Geometric and PyTorch3D though remains framework agnostic as it is built on top of the PyData ecosystem to enable inter-operability with scientific computing tools and libraries. Graphein is designed to be highly flexible, allowing the user to specify each step of the data preparation, scalable to facilitate working with large protein complexes and interaction graphs, and contains useful pre-processing tools for preparing experimental files.

In this paper we developed a computational hierarchical network model to understand the spatiotemporal sequence learning effects observed in the primate visual cortex. The model is a hierarchical recurrent neural model that learns to predict video sequences using the incoming video signals as teaching signals. The model performs fast feedforward analysis using a deep convolutional neural network with sparse convolution and feedback synthesis using a stack of LSTM modules. The network learns a representational hierarchy by minimizing its prediction errors of the incoming signals at each level of the hierarchy. We found that recurrent feedback in this network lead to the development of semantic cluster of global movement patterns in the population codes of the units at the lower levels of the hierarchy. These representations facilitate the learning of relationship among movement patterns, yielding state-of-the-art performance in long range video sequence predictions on benchmark datasets. Without further tuning, this model automatically exhibits the neurophysiological correlates of visual sequence memories that we observed in the early visual cortex of awake monkeys, suggesting the principle of self-supervised prediction learning might be relevant to understanding the cortical mechanisms of representational learning.

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired by the rich literature on meshless interpolation and its extension to spectral collocation methods in scientific computing, we develop a series of approaches for enforcing hard constraints on neural fields, which we refer to as Constrained Neural Fields (CNF). The constraints can be specified as a linear operator applied to the neural field and its derivatives. We also design specific model representations and training strategies for problems where standard models may encounter difficulties, such as conditioning of the system, memory consumption, and capacity of the network when being constrained. Our approaches are demonstrated in a wide range of real-world applications. Additionally, we develop a framework that enables highly efficient model and constraint specification, which can be readily applied to any downstream task where hard constraints need to be explicitly satisfied during optimization.