Training generalist agents capable of adapting to diverse scenarios requires interactive environments for self-exploration. However, interactive environments remain critically scarce, and existing synthesis methods suffer from significant limitations regarding environmental diversity and scalability. To address these challenges, we introduce ScaleEnv, a framework that constructs fully interactive environments and verifiable tasks entirely from scratch. Specifically, ScaleEnv ensures environment reliability through procedural testing, and guarantees task completeness and solvability via tool dependency graph expansion and executable action verification. By enabling agents to learn through exploration within ScaleEnv, we demonstrate significant performance improvements on unseen, multi-turn tool-use benchmarks such as $τ^2$-Bench and VitaBench, highlighting strong generalization capabilities. Furthermore, we investigate the relationship between increasing number of domains and model generalization performance, providing empirical evidence that scaling environmental diversity is critical for robust agent learning.

Human concept learning is typically active: learners choose which instances to query or test in order to reduce uncertainty about an underlying rule or category. Active concept learning must balance informativeness of queries against the stability of the learner that generates and scores hypotheses. We study this trade-off in a neuro-symbolic Bayesian learner whose hypotheses are executable programs proposed by a large language model (LLM) and reweighted by Bayesian updating. We compare a Rational Active Learner that selects queries to maximize approximate expected information gain (EIG) and the human-like Positive Test Strategy (PTS) that queries instances predicted to be positive under the current best hypothesis. Across concept-learning tasks in the classic Number Game, EIG is effective when falsification is necessary (e.g., compound or exception-laden rules), but underperforms on simple concepts. We trace this failure to a support mismatch between the EIG policy and the LLM proposal distribution: highly diagnostic boundary queries drive the posterior toward regions where the generator produces invalid or overly specific programs, yielding a support-mismatch trap in the particle approximation. PTS is information-suboptimal but tends to maintain proposal validity by selecting "safe" queries, leading to faster convergence on simple rules. Our results suggest that "confirmation bias" may not be a cognitive error, but rather a rational adaptation for maintaining tractable inference in the sparse, open-ended hypothesis spaces characteristic of human thought.

Tabular anomaly detection (TAD) remains challenging due to the heterogeneity of tabular data: features lack natural relationships, vary widely in distribution and scale, and exhibit diverse types. Consequently, each TAD method makes implicit assumptions about anomaly patterns that work well on some datasets but fail on others, and no method consistently outperforms across diverse scenarios. We present CTAD (Calibrating Tabular Anomaly Detection), a model-agnostic post-processing framework that enhances any existing TAD detector through sample-specific calibration. Our approach characterizes normal data via two complementary distributions, i.e., an empirical distribution from random sampling and a structural distribution from K-means centroids, and measures how adding a test sample disrupts their compatibility using Optimal Transport (OT) distance. Normal samples maintain low disruption while anomalies cause high disruption, providing a calibration signal to amplify detection. We prove that OT distance has a lower bound proportional to the test sample's distance from centroids, and establish that anomalies systematically receive higher calibration scores than normals in expectation, explaining why the method generalizes across datasets. Extensive experiments on 34 diverse tabular datasets with 7 representative detectors spanning all major TAD categories (density estimation, classification, reconstruction, and isolation-based methods) demonstrate that CTAD consistently improves performance with statistical significance. Remarkably, CTAD enhances even state-of-the-art deep learning methods and shows robust performance across diverse hyperparameter settings, requiring no additional tuning for practical deployment.

In this technical note, we derive a closed-form expression for the affine transformation mapping local image patches between two calibrated views. We show that the transformation is a function of the relative camera pose, the image coordinates, and the local surface normal.

Data assimilation (DA) is a fundamental component of modern weather prediction, yet it remains a major computational bottleneck in machine learning (ML)-based forecasting pipelines due to reliance on traditional variational methods. Recent generative ML-based DA methods offer a promising alternative but typically require many sampling steps and suffer from error accumulation under long-horizon auto-regressive rollouts with cycling assimilation. We propose FlowDA, a low-latency weather-scale generative DA framework based on flow matching. FlowDA conditions on observations through a SetConv-based embedding and fine-tunes the Aurora foundation model to deliver accurate, efficient, and robust analyses. Experiments across observation rates decreasing from $3.9\%$ to $0.1\%$ demonstrate superior performance of FlowDA over strong baselines with similar tunable-parameter size. FlowDA further shows robustness to observational noise and stable performance in long-horizon auto-regressive cycling DA. Overall, FlowDA points to an efficient and scalable direction for data-driven DA.

Ambiguity poses persistent challenges in natural language understanding for large language models (LLMs). To better understand how lexical ambiguity can be resolved through the visual domain, we develop an interpretable Visual Word Sense Disambiguation (VWSD) framework. The model leverages CLIP to project ambiguous language and candidate images into a shared multimodal space. We enrich textual embeddings using a dual-channel ensemble of semantic and photo-based prompts with WordNet synonyms, while image embeddings are refined through robust test-time augmentations. We then use cosine similarity to determine the image that best aligns with the ambiguous text. When evaluated on the SemEval-2023 VWSD dataset, enriching the embeddings raises the MRR from 0.7227 to 0.7590 and the Hit Rate from 0.5810 to 0.6220. Ablation studies reveal that dual-channel prompting provides strong, low-latency performance, whereas aggressive image augmentation yields only marginal gains. Additional experiments with WordNet definitions and multilingual prompt ensembles further suggest that noisy external signals tend to dilute semantic specificity, reinforcing the effectiveness of precise, CLIP-aligned prompts for visual word sense disambiguation.

An impediment to using Large Language Models (LLMs) for reasoning output verification is that LLMs struggle to reliably identify errors in thinking traces, particularly in long outputs, domains requiring expert knowledge, and problems without verifiable rewards. We propose a data-driven approach to automatically construct highly granular reasoning error taxonomies to enhance LLM-driven error detection on unseen reasoning traces. Our findings indicate that classification approaches that leverage these error taxonomies, or "rubrics", demonstrate strong error identification compared to baseline methods in technical domains like coding, math, and chemical engineering. These rubrics can be used to build stronger LLM-as-judge reward functions for reasoning model training via reinforcement learning. Experimental results show that these rewards have the potential to improve models' task accuracy on difficult domains over models trained by general LLMs-as-judges by +45%, and approach performance of models trained by verifiable rewards while using as little as 20% as many gold labels. Through our approach, we extend the usage of reward rubrics from assessing qualitative model behavior to assessing quantitative model correctness on tasks typically learned via RLVR rewards. This extension opens the door for teaching models to solve complex technical problems without a full dataset of gold labels, which are often highly costly to procure.

DPO and related algorithms align language models by directly optimizing the RLHF objective: find a policy that maximizes the Bradley-Terry reward while staying close to a reference policy through a KL divergence penalty. Previous work showed that this approach could be further generalized: the original problem remains tractable even if the KL divergence is replaced by a family of $f$-divergence with a convex generating function $f$. Our first contribution is to show that convexity of $f$ is not essential. Instead, we identify a more general condition, referred to as DPO-inducing, that precisely characterizes when the RLHF problem remains tractable. Our next contribution is to establish a second condition on $f$ that is necessary to prevent probability displacement, a known empirical phenomenon in which the probabilities of the winner and the loser responses approach zero. We refer to any $f$ that satisfies this condition as displacement-resistant. We finally focus on a specific DPO-inducing and displacement-resistant $f$, leading to our novel SquaredPO loss. Compared to DPO, this new loss offers stronger theoretical guarantees while performing competitively in practice.

While lifting map has significantly enhanced the expressivity of graph neural networks, extending this paradigm to hypergraphs remains fragmented. To address this, we introduce the categorical Weisfeiler-Lehman framework, which formalizes lifting as a functorial mapping from an arbitrary data category to the unifying category of graded posets. When applied to hypergraphs, this perspective allows us to systematically derive Hypergraph Isomorphism Networks, a family of neural architectures where the message passing topology is strictly determined by the choice of functor. We introduce two distinct functors from the category of hypergraphs: an incidence functor and a symmetric simplicial complex functor. While the incidence architecture structurally mirrors standard bipartite schemes, our functorial derivation enforces a richer information flow over the resulting poset, capturing complex intersection geometries often missed by existing methods. We theoretically characterize the expressivity of these models, proving that both the incidence-based and symmetric simplicial approaches subsume the expressive power of the standard Hypergraph Weisfeiler-Lehman test. Extensive experiments on real-world benchmarks validate these theoretical findings.

Sweetpotato weevils (Cylas spp.) are considered among the most destructive pests impacting sweetpotato production, particularly in sub-Saharan Africa. Traditional methods for assessing weevil damage, predominantly relying on manual scoring, are labour-intensive, subjective, and often yield inconsistent results. These challenges significantly hinder breeding programs aimed at developing resilient sweetpotato varieties. This study introduces a computer vision-based approach for the automated evaluation of weevil damage in both field and laboratory contexts. In the field settings, we collected data to train classification models to predict root-damage severity levels, achieving a test accuracy of 71.43%. Additionally, we established a laboratory dataset and designed an object detection pipeline employing YOLO12, a leading real-time detection model. This methodology incorporated a two-stage laboratory pipeline that combined root segmentation with a tiling strategy to improve the detectability of small objects. The resulting model demonstrated a mean average precision of 77.7% in identifying minute weevil feeding holes. Our findings indicate that computer vision technologies can provide efficient, objective, and scalable assessment tools that align seamlessly with contemporary breeding workflows. These advancements represent a significant improvement in enhancing phenotyping efficiency within sweetpotato breeding programs and play a crucial role in mitigating the detrimental effects of weevils on food security.

Facial emotion recognition has been typically cast as a single-label classification problem of one out of six prototypical emotions. However, that is an oversimplification that is unsuitable for representing the multifaceted spectrum of spontaneous emotional states, which are most often the result of a combination of multiple emotions contributing at different intensities. Building on this, a promising direction that was explored recently is to cast emotion recognition as a distribution learning problem. Still, such approaches are limited in that research datasets are typically annotated with a single emotion class. In this paper, we contribute a novel approach to describe complex emotional states as probability distributions over a set of emotion classes. To do so, we propose a solution to automatically re-label existing datasets by exploiting the result of a study in which a large set of both basic and compound emotions is mapped to probability distributions in the Valence-Arousal-Dominance (VAD) space. In this way, given a face image annotated with VAD values, we can estimate the likelihood of it belonging to each of the distributions, so that emotional states can be described as a mixture of emotions, enriching their description, while also accounting for the ambiguous nature of their perception. In a preliminary set of experiments, we illustrate the advantages of this solution and a new possible direction of investigation. Data annotations are available at https://github.com/jbcnrlz/affectnet-b-annotation.

Data augmentation can mitigate limited training data in machine-learning automated scoring engines for constructed response items. This study seeks to determine how well three approaches to large language model prompting produce essays that preserve the writing quality of the original essays and produce realistic text for augmenting ASE training datasets. We created simulated versions of student essays, and human raters assigned scores to them and rated the realism of the generated text. The results of the study indicate that the predict next prompting strategy produces the highest level of agreement between human raters regarding simulated essay scores, predict next and sentence strategies best preserve the rated quality of the original essay in the simulated essays, and predict next and 25 examples strategies produce the most realistic text as judged by human raters.

Recent advancements in zero-shot reinforcement learning (RL) have facilitated the extraction of diverse behaviors from unlabeled, offline data sources. In particular, forward-backward algorithms (FB) can retrieve a family of policies that can approximately solve any standard RL problem (with additive rewards, linear in the occupancy measure), given sufficient capacity. While retaining zero-shot properties, we tackle the greater problem class of RL with general utilities, in which the objective is an arbitrary differentiable function of the occupancy measure. This setting is strictly more expressive, capturing tasks such as distribution matching or pure exploration, which may not be reduced to additive rewards. We show that this additional complexity can be captured by a novel, maximum entropy (soft) variant of the forward-backward algorithm, which recovers a family of stochastic policies from offline data. When coupled with zero-order search over compact policy embeddings, this algorithm can sidestep iterative optimization schemes, and optimizes general utilities directly at test-time. Across both didactic and high-dimensional experiments, we demonstrate that our method retains favorable properties of FB algorithms, while also extending their range to more general RL problems.

Complex activities in real-world audio unfold over extended durations and exhibit hierarchical structure, yet most prior work focuses on short clips and isolated events. To bridge this gap, we introduce MultiAct, a new dataset and benchmark for multi-level structured understanding of human activities from long-form audio. MultiAct comprises long-duration kitchen recordings annotated at three semantic levels (activities, sub-activities and events) and paired with fine-grained captions and high-level summaries. We further propose a unified hierarchical model that jointly performs classification, detection, sequence prediction and multi-resolution captioning. Experiments on MultiAct establish strong baselines and reveal key challenges in modelling hierarchical and compositional structure of long-form audio. A promising direction for future work is the exploration of methods better suited to capturing the complex, long-range relationships in long-form audio.

Reinforcement Learning from Human Feedback (RLHF) remains indispensable for aligning large language models (LLMs) in subjective domains. To enhance robustness, recent work shifts toward Generative Reward Models (GenRMs) that generate rationales before predicting preferences. Yet in GenRM training and evaluation, practice remains outcome-label-only, leaving reasoning quality unchecked. We show that reasoning fidelity-the consistency between a GenRM's preference decision and reference decision rationales-is highly predictive of downstream RLHF outcomes, beyond standard label accuracy. Specifically, we repurpose existing reward-model benchmarks to compute Spurious Correctness (S-Corr)-the fraction of label-correct decisions with rationales misaligned with golden judgments. Our empirical evaluation reveals substantial S-Corr even for competitive GenRMs, and higher S-Corr is associated with policy degeneration under optimization. To improve fidelity, we propose Rationale-Centric Alignment, R-Align, which augments training with gold judgments and explicitly supervises rationale alignment. R-Align reduces S-Corr on RM benchmarks and yields consistent gains in actor performance across STEM, coding, instruction following, and general tasks.

Many automated manufacturing processes rely on industrial robot arms to move process-specific tools along workpiece surfaces. In applications like grinding, sanding, spray painting, or inspection, they need to cover a workpiece fully while keeping their tools perpendicular to its surface. While there are approaches to generate trajectories for these applications, there are no sufficient methods for analyzing the feasibility of full surface coverage. This work proposes a sampling-based approach for continuous coverage estimation that explores reachable surface regions in the configuration space. We define an extended ambient configuration space that allows for the representation of tool position and orientation constraints. A continuation-based approach is used to explore it using two different sampling strategies. A thorough evaluation across different kinematics and environments analyzes their runtime and efficiency. This validates our ability to accurately and efficiently calculate surface coverage for complex surfaces in complicated environments.

Satellite imagery is employed for large-scale prospectivity mapping due to the high cost and typically limited availability of on-site mineral exploration data. In this work, we present a proof-of-concept framework that leverages generative representations learned from multispectral Sentinel-2 imagery to identify gold-bearing regions from space. An autoencoder foundation model, called Isometric, which is pretrained on the large-scale FalconSpace-S2 v1.0 dataset, produces information-dense spectral-spatial representations that serve as inputs to a lightweight XGBoost classifier. We compare this representation-based approach with a raw spectral input baseline using a dataset of 63 Sentinel-2 images from known gold and non-gold locations. The proposed method improves patch-level accuracy from 0.51 to 0.68 and image-level accuracy from 0.55 to 0.73, demonstrating that generative embeddings capture transferable mineralogical patterns even with limited labeled data. These results highlight the potential of foundation-model representations to make mineral exploration more efficient, scalable, and globally applicable.

We study multi-task reinforcement learning (RL), a setting in which an agent learns a single, universal policy capable of generalising to arbitrary, possibly unseen tasks. We consider tasks specified as linear temporal logic (LTL) formulae, which are commonly used in formal methods to specify properties of systems, and have recently been successfully adopted in RL. In this setting, we present a novel task embedding technique leveraging a new generation of semantic LTL-to-automata translations, originally developed for temporal synthesis. The resulting semantically labelled automata contain rich, structured information in each state that allow us to (i) compute the automaton efficiently on-the-fly, (ii) extract expressive task embeddings used to condition the policy, and (iii) naturally support full LTL. Experimental results in a variety of domains demonstrate that our approach achieves state-of-the-art performance and is able to scale to complex specifications where existing methods fail.

Adolescent Idiopathic Scoliosis (AIS) is a prevalent spinal deformity whose progression can be mitigated through early detection. Conventional screening methods are often subjective, difficult to scale, and reliant on specialized clinical expertise. Video-based gait analysis offers a promising alternative, but current datasets and methods frequently suffer from data leakage, where performance is inflated by repeated clips from the same individual, or employ oversimplified models that lack clinical interpretability. To address these limitations, we introduce ScoliGait, a new benchmark dataset comprising 1,572 gait video clips for training and 300 fully independent clips for testing. Each clip is annotated with radiographic Cobb angles and descriptive text based on clinical kinematic priors. We propose a multi-modal framework that integrates a clinical-prior-guided kinematic knowledge map for interpretable feature representation, alongside a latent attention pooling mechanism to fuse video, text, and knowledge map modalities. Our method establishes a new state-of-the-art, demonstrating a significant performance gap on a realistic, non-repeating subject benchmark. Our approach establishes a new state of the art, showing a significant performance gain on a realistic, subject-independent benchmark. This work provides a robust, interpretable, and clinically grounded foundation for scalable, non-invasive AIS assessment.

Learning interpretable representations with variational autoencoders (VAEs) is a major goal of representation learning. The main challenge lies in obtaining disentangled representations, where each latent dimension corresponds to a distinct generative factor. This difficulty is fundamentally tied to the inability to perform nonlinear independent component analysis. Here, we introduce the framework of action-induced representations (AIRs) which models representations of physical systems given experiments (or actions) that can be performed on them. We show that, in this framework, we can provably disentangle degrees of freedom w.r.t. their action dependence. We further introduce a variational AIR architecture (VAIR) that can extract AIRs and therefore achieve provable disentanglement where standard VAEs fail. Beyond state representation, VAIR also captures the action dependence of the underlying generative factors, directly linking experiments to the degrees of freedom they influence.

We present a novel approach for verifying properties of Kolmogorov-Arnold Networks (KANs), a class of neural networks characterized by nonlinear, univariate activation functions typically implemented as piecewise polynomial splines or Gaussian processes. Our method creates mathematical ``abstractions'' by replacing each KAN unit with a piecewise affine (PWA) function, providing both local and global error estimates between the original network and its approximation. These abstractions enable property verification by encoding the problem as a Mixed Integer Linear Program (MILP), determining whether outputs satisfy specified properties when inputs belong to a given set. A critical challenge lies in balancing the number of pieces in the PWA approximation: too many pieces add binary variables that make verification computationally intractable, while too few pieces create excessive error margins that yield uninformative bounds. Our key contribution is a systematic framework that exploits KAN structure to find optimal abstractions. By combining dynamic programming at the unit level with a knapsack optimization across the network, we minimize the total number of pieces while guaranteeing specified error bounds. This approach determines the optimal approximation strategy for each unit while maintaining overall accuracy requirements. Empirical evaluation across multiple KAN benchmarks demonstrates that the upfront analysis costs of our method are justified by superior verification results.

Current Information Seeking (InfoSeeking) agents struggle to maintain focus and coherence during long-horizon exploration, as tracking search states, including planning procedure and massive search results, within one plain-text context is inherently fragile. To address this, we introduce \textbf{Table-as-Search (TaS)}, a structured planning framework that reformulates the InfoSeeking task as a Table Completion task. TaS maps each query into a structured table schema maintained in an external database, where rows represent search candidates and columns denote constraints or required information. This table precisely manages the search states: filled cells strictly record the history and search results, while empty cells serve as an explicit search plan. Crucially, TaS unifies three distinct InfoSeeking tasks: Deep Search, Wide Search, and the challenging DeepWide Search. Extensive experiments demonstrate that TaS significantly outperforms numerous state-of-the-art baselines across three kinds of benchmarks, including multi-agent framework and commercial systems. Furthermore, our analysis validates the TaS's superior robustness in long-horizon InfoSeeking, alongside its efficiency, scalability and flexibility. Code and datasets are publicly released at https://github.com/AIDC-AI/Marco-Search-Agent.

Knowledge Graph (KG) generation requires models to learn complex semantic dependencies between triples while maintaining domain validity constraints. Unlike link prediction, which scores triples independently, generative models must capture interdependencies across entire subgraphs to produce semantically coherent structures. We present ARK (Auto-Regressive Knowledge Graph Generation), a family of autoregressive models that generate KGs by treating graphs as sequences of (head, relation, tail) triples. ARK learns implicit semantic constraints directly from data, including type consistency, temporal validity, and relational patterns, without explicit rule supervision. On the IntelliGraphs benchmark, our models achieve 89.2% to 100.0% semantic validity across diverse datasets while generating novel graphs not seen during training. We also introduce SAIL, a variational extension of ARK that enables controlled generation through learned latent representations, supporting both unconditional sampling and conditional completion from partial graphs. Our analysis reveals that model capacity (hidden dimensionality >= 64) is more critical than architectural depth for KG generation, with recurrent architectures achieving comparable validity to transformer-based alternatives while offering substantial computational efficiency. These results demonstrate that autoregressive models provide an effective framework for KG generation, with practical applications in knowledge base completion and query answering.

Generative models for de novo protein backbone design have achieved remarkable success in creating novel protein structures. However, these diffusion-based approaches remain computationally intensive and slower than desired for large-scale structural exploration. While recent efforts like Proteina have introduced flow-matching to improve sampling efficiency, the potential of tokenization for structural compression and acceleration remains largely unexplored in the protein domain. In this work, we present SaDiT, a novel framework that accelerates protein backbone generation by integrating SaProt Tokenization with a Diffusion Transformer (DiT) architecture. SaDiT leverages a discrete latent space to represent protein geometry, significantly reducing the complexity of the generation process while maintaining theoretical SE(3) equivalence. To further enhance efficiency, we introduce an IPA Token Cache mechanism that optimizes the Invariant Point Attention (IPA) layers by reusing computed token states during iterative sampling. Experimental results demonstrate that SaDiT outperforms state-of-the-art models, including RFDiffusion and Proteina, in both computational speed and structural viability. We evaluate our model across unconditional backbone generation and fold-class conditional generation tasks, where SaDiT shows superior ability to capture complex topological features with high designability.

We investigate grokking in transformers through the lens of inductive bias: dispositions arising from architecture or optimization that let the network prefer one solution over another. We first show that architectural choices such as the position of Layer Normalization (LN) strongly modulates grokking speed. This modulation is explained by isolating how LN on specific pathways shapes shortcut-learning and attention entropy. Subsequently, we study how different optimization settings modulate grokking, inducing distinct interpretations of previously proposed controls such as readout scale. Particularly, we find that using readout scale as a control for lazy training can be confounded by learning rate and weight decay in our setting. Accordingly, we show that features evolve continuously throughout training, suggesting grokking in transformers can be more nuanced than a lazy-to-rich transition of the learning regime. Finally, we show how generalization predictably emerges with feature compressibility in grokking, across different modulators of inductive bias. Our code is released at https://tinyurl.com/y52u3cad.

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and averaging-based methods, focus on compact, finite, or low-dimensional groups with linear actions, this work explores how equivariance can be extended to infinite-dimensional groups. We propose a strategy designed to induce diffeomorphism equivariance in pre-trained neural networks via energy-based canonicalisation. Formulating equivariance as an optimisation problem allows us to access the rich toolbox of already established differentiable image registration methods. Empirical results on segmentation and classification tasks confirm that our approach achieves approximate equivariance and generalises to unseen transformations without relying on extensive data augmentation or retraining.

The groundbreaking capabilities of Large Language Models (LLMs) offer new opportunities for enhancing human-computer interaction through emotion-adaptive Artificial Intelligence (AI). However, deliberately controlling the sentiment in these systems remains challenging. The present study investigates the potential of prompt engineering for controlling sentiment in LLM-generated text, providing a resource-sensitive and accessible alternative to existing methods. Using Ekman's six basic emotions (e.g., joy, disgust), we examine various prompting techniques, including Zero-Shot and Chain-of-Thought prompting using gpt-3.5-turbo, and compare it to fine-tuning. Our results indicate that prompt engineering effectively steers emotions in AI-generated texts, offering a practical and cost-effective alternative to fine-tuning, especially in data-constrained settings. In this regard, Few-Shot prompting with human-written examples was the most effective among other techniques, likely due to the additional task-specific guidance. The findings contribute valuable insights towards developing emotion-adaptive AI systems.

Autoregressive generative PDE solvers can be accurate one step ahead yet drift over long rollouts, especially in coarse-to-fine regimes where each step must regenerate unresolved fine scales. This is the regime of diffusion and flow-matching generators: although their internal dynamics are Markovian, rollout stability is governed by per-step \emph{conditional law} errors. Using the Mori--Zwanzig projection formalism, we show that eliminating unresolved variables yields an exact resolved evolution with a Markov term, a memory term, and an orthogonal forcing, exposing a structural limitation of memoryless closures. Motivated by this, we introduce memory-conditioned diffusion/flow-matching with a compact online state injected into denoising via latent features. Via disintegration, memory induces a structured conditional tail prior for unresolved scales and reduces the transport needed to populate missing frequencies. We prove Wasserstein stability of the resulting conditional kernel. We then derive discrete Grönwall rollout bounds that separate memory approximation from conditional generation error. Experiments on compressible flows with shocks and multiscale mixing show improved accuracy and markedly more stable long-horizon rollouts, with better fine-scale spectral and statistical fidelity.

Pruning at Initialisation methods discover sparse, trainable subnetworks before training, but their theoretical mechanisms remain elusive. Existing analyses are often limited to finite-width statistics, lacking a rigorous characterisation of the global sparsity patterns that emerge as networks grow large. In this work, we connect discrete pruning heuristics to graph limit theory via graphons, establishing the graphon limit of PaI masks. We introduce a Factorised Saliency Model that encompasses popular pruning criteria and prove that, under regularity conditions, the discrete masks generated by these algorithms converge to deterministic bipartite graphons. This limit framework establishes a novel topological taxonomy for sparse networks: while unstructured methods (e.g., Random, Magnitude) converge to homogeneous graphons representing uniform connectivity, data-driven methods (e.g., SNIP, GraSP) converge to heterogeneous graphons that encode implicit feature selection. Leveraging this continuous characterisation, we derive two fundamental theoretical results: (i) a Universal Approximation Theorem for sparse networks that depends only on the intrinsic dimension of active coordinate subspaces; and (ii) a Graphon-NTK generalisation bound demonstrating how the limit graphon modulates the kernel geometry to align with informative features. Our results transform the study of sparse neural networks from combinatorial graph problems into a rigorous framework of continuous operators, offering a new mechanism for analysing expressivity and generalisation in sparse neural networks.

High-quality annotated datasets are crucial for advancing machine learning in medical image analysis. However, a critical gap exists: most datasets either offer a single, clean ground truth, which hides real-world expert disagreement, or they provide multiple annotations without a separate gold standard for objective evaluation. To bridge this gap, we introduce CytoCrowd, a new public benchmark for cytology analysis. The dataset features 446 high-resolution images, each with two key components: (1) raw, conflicting annotations from four independent pathologists, and (2) a separate, high-quality gold-standard ground truth established by a senior expert. This dual structure makes CytoCrowd a versatile resource. It serves as a benchmark for standard computer vision tasks, such as object detection and classification, using the ground truth. Simultaneously, it provides a realistic testbed for evaluating annotation aggregation algorithms that must resolve expert disagreements. We provide comprehensive baseline results for both tasks. Our experiments demonstrate the challenges presented by CytoCrowd and establish its value as a resource for developing the next generation of models for medical image analysis.