Classical statistical inference and learning theory often fail to explain the success of modern neural networks. A key reason is that these models are non-identifiable (singular), violating core assumptions behind PAC bounds and asymptotic normality. Singular learning theory (SLT), a physics-inspired framework grounded in algebraic geometry, has gained popularity for its ability to close this theory-practice gap. In this paper, we empirically study SLT in toy settings relevant to interpretability and phase transitions. First, we understand the SLT free energy $\mathcal{F}_n$ by testing an Arrhenius-style rate hypothesis using both a grokking modulo-arithmetic model and Anthropic's Toy Models of Superposition. Second, we understand the local learning coefficient $λ_α$ by measuring how it scales with problem difficulty across several controlled network families (polynomial regressors, low-rank linear networks, and low-rank autoencoders). Our experiments recover known scaling laws while others yield meaningful deviations from theoretical expectations. Overall, our paper illustrates the many merits of SLT for understanding neural network phase transitions, and poses open research questions for the field.

Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood, as many works have focused on their theoretical analysis. In contrast, results for diffusion models on discrete state spaces remain limited and pose significant challenges, particularly due to their combinatorial structure and their more recent introduction in generative modelling. In this work, we establish new and sharp convergence guarantees for three popular discrete diffusion models (DDMs). Two of these models are designed for finite state spaces and are based respectively on the random walk and the masking process. The third DDM we consider is defined on the countably infinite space $\mathbb{N}^d$ and uses a drifted random walk as its forward process. For each of these models, the backward process can be characterized by a discrete score function that can, in principle, be estimated. However, even with perfect access to these scores, simulating the exact backward process is infeasible, and one must rely on approximations. In this work, we study Euler-type approximations and establish convergence bounds in both Kullback-Leibler divergence and total variation distance for the resulting models, under minimal assumptions on the data distribution. In particular, we show that the computational complexity of each method scales linearly in the dimension, up to logarithmic factors. Furthermore, to the best of our knowledge, this study provides the first non-asymptotic convergence guarantees for these noising processes that do not rely on boundedness assumptions on the estimated score.

This work shows how human physical reasoning can guide machine-driven symbolic regression toward discovering empirical laws from observations. As an example, we derive a simple equation that classifies fast radio bursts (FRBs) into two distinct Gaussian distributions, indicating the existence of two physical classes. This human-AI workflow integrates feature selection, dimensional analysis, and symbolic regression: deep learning first analyzes CHIME Catalog 1 and identifies six independent parameters that collectively provide a complete description of FRBs; guided by Buckingham-$π$ analysis and correlation analysis, humans then construct dimensionless groups; finally, symbolic regression performed by the machine discovers the governing equation. When applied to the newer CHIME Catalog, the equation produces consistent results, demonstrating that it captures the underlying physics. This framework is applicable to a broad range of scientific domains.

A standard assumption in deep learning is that the inductive bias introduced by a neural network architecture must persist from training through inference. The architecture you train with is the architecture you deploy. This assumption constrains the community from selecting architectures that may have desirable efficiency or design properties due to difficulties with optimization. We challenge this assumption with Network of Theseus (NoT), a method for progressively converting a trained, or even untrained, guide network architecture part-by-part into an entirely different target network architecture while preserving the performance of the guide network. At each stage, components in the guide network architecture are incrementally replaced with target architecture modules and aligned via representational similarity metrics. This procedure largely preserves the functionality of the guide network even under substantial architectural changes-for example, converting a convolutional network into a multilayer perceptron, or GPT-2 into a recurrent neural network. By decoupling optimization from deployment, NoT expands the space of viable inference-time architectures, opening opportunities for better accuracy-efficiency tradeoffs and enabling more directed exploration of the architectural design space.

Earth observation (EO) models are frequently trained under implicit sampling policies that optimize global accuracy but provide no explicit guarantees on who (which regions, classes, or mission-critical strata) is being served throughout training. This paper introduces a contract-governed training paradigm for EO in which training samples are grouped into service contracts -- semantically meaningful units such as (dataset, region, rare-crop indicator) -- and each contract is assigned a target service share. We instantiate this paradigm as an Observed Service Agreement Graph (OSAG), a lightweight governance layer that (i) monitors contract-level exposure (coverage) during optimization, (ii) drives empirical coverage toward target shares via contract-normalized sampling weights, and (iii) exposes explicit accuracy-governance trade-offs through two knobs: a sampling mixture coefficient alpha and a contract-regularization weight lambda_C. We provide a compact theory in a toy setting: OSAG sampling concentrates empirical coverage to targets; coverage deviations upper-bound service-risk deviations; and contract design (coarse vs. fine) modulates governance cost. Experiments on AVIRIS hyperspectral scenes (Indian Pines plus Salinas) and multispectral Sentinel-2 EuroSAT demonstrate that OSAG can substantially reduce priority coverage error while maintaining global accuracy and improving high-priority accuracy. A EuroSAT coarse-vs-fine contract ablation further evidences how semantically refined contracts can reduce the accuracy cost per unit of governance improvement.

While methods exist for aligning flow matching models--a popular and effective class of generative models--with human preferences, existing approaches fail to achieve both adaptation efficiency and probabilistically sound prior preservation. In this work, we leverage the theory of optimal control and propose VGG-Flow, a gradient-matching-based method for finetuning pretrained flow matching models. The key idea behind this algorithm is that the optimal difference between the finetuned velocity field and the pretrained one should be matched with the gradient field of a value function. This method not only incorporates first-order information from the reward model but also benefits from heuristic initialization of the value function to enable fast adaptation. Empirically, we show on a popular text-to-image flow matching model, Stable Diffusion 3, that our method can finetune flow matching models under limited computational budgets while achieving effective and prior-preserving alignment.

However, in infants and young children, accurate segmentation is challenging due to development and imaging constraints. Pediatric brain MRI is notoriously difficult to acquire, with inconsistent availability of imaging modalities, substantial non-head anatomy in the field of view, and frequent motion artifacts. This has led to specialized segmentation models that are often limited to specific image types or narrow age groups, or that are fragile for more variable images such as those acquired clinically. We address this method fragmentation with BabySeg, a deep learning brain segmentation framework for infants and young children that supports diverse MRI protocols, including repeat scans and image types unavailable during training. Our approach builds on recent domain randomization techniques, which synthesize training images far beyond realistic bounds to promote dataset shift invariance. We also describe a mechanism that enables models to flexibly pool and interact features from any number of input scans. We demonstrate state-of-the-art performance that matches or exceeds the accuracy of several existing methods for various age cohorts and input configurations using a single model, in a fraction of the runtime required by many existing tools.

Recent works on structured text translation remain limited to the sentence level, as they struggle to effectively handle the complex document-level XML or HTML structures. To address this, we propose \textbf{Format Reinforcement Learning (FormatRL)}, which employs Group Relative Policy Optimization on top of a supervised fine-tuning model to directly optimize novel structure-aware rewards: 1) TreeSim, which measures structural similarity between predicted and reference XML trees and 2) Node-chrF, which measures translation quality at the level of XML nodes. Additionally, we apply StrucAUC, a fine-grained metric distinguishing between minor errors and major structural failures. Experiments on the SAP software-documentation benchmark demonstrate improvements across six metrics and an analysis further shows how different reward functions contribute to improvements in both structural and translation quality.

Abstract-- Object geometry is key information for robot manipulation. Y et, object reconstruction is a challenging task because cameras only capture partial observations of objects, especially when occlusion occurs. In this paper, we leverage two extra sources of information to reduce the ambiguity of vision signals. First, generative models learn priors of the shapes of commonly seen objects, allowing us to make reasonable guesses of the unseen part of geometry. Second, contact information, which can be obtained from videos and physical interactions, provides sparse constraints on the boundary of the geometry. We combine the two sources of information through contact-guided 3D generation. The guidance formulation is inspired by drag-based editing in generative models. Experiments on synthetic and real-world data show that our approach improves the reconstruction compared to pure 3D generation and contact-based optimization.

Unsupervised anomaly-based intrusion detection requires models that can generalize to attack patterns not observed during training. This work presents the first large-scale evaluation of hybrid quantum-classical (HQC) autoencoders for this task. We construct a unified experimental framework that iterates over key quantum design choices, including quantum-layer placement, measurement approach, variational and non-variational formulations, and latent-space regularization. Experiments across three benchmark NIDS datasets show that HQC autoencoders can match or exceed classical performance in their best configurations, although they exhibit higher sensitivity to architectural decisions. Under zero-day evaluation, well-configured HQC models provide stronger and more stable generalization than classical and supervised baselines. Simulated gate-noise experiments reveal early performance degradation, indicating the need for noise-aware HQC designs. These results provide the first data-driven characterization of HQC autoencoder behavior for network intrusion detection and outline key factors that govern their practical viability. All experiment code and configurations are available at https://github.com/arasyi/hqcae-network-intrusion-detection.