Accurate canal network mapping is essential for water management, including irrigation planning and infrastructure maintenance. State-of-the-art semantic segmentation models for infrastructure mapping, such as roads, rely on large, well-annotated remote sensing datasets. However, incomplete or inadequate ground truth can hinder these learning approaches. Many infrastructure networks have graph-level properties such as reachability to a source (like canals) or connectivity (roads) that can be leveraged to improve these existing ground truth. This paper develops a novel iterative framework IGraSS, combining a semantic segmentation module-incorporating RGB and additional modalities (NDWI, DEM)-with a graph-based ground-truth refinement module. The segmentation module processes satellite imagery patches, while the refinement module operates on the entire data viewing the infrastructure network as a graph. Experiments show that IGraSS reduces unreachable canal segments from around 18% to 3%, and training with refined ground truth significantly improves canal identification. IGraSS serves as a robust framework for both refining noisy ground truth and mapping canal networks from remote sensing imagery. We also demonstrate the effectiveness and generalizability of IGraSS using road networks as an example, applying a different graph-theoretic constraint to complete road networks.

We introduce Princeton365, a large-scale diverse dataset of 365 videos with accurate camera pose. Our dataset bridges the gap between accuracy and data diversity in current SLAM benchmarks by introducing a novel ground truth collection framework that leverages calibration boards and a 360-camera. We collect indoor, outdoor, and object scanning videos with synchronized monocular and stereo RGB video outputs as well as IMU. We further propose a new scene scale-aware evaluation metric for SLAM based on the optical flow induced by the camera pose estimation error. In contrast to the current metrics, our new metric allows for comparison between the performance of SLAM methods across scenes as opposed to existing metrics such as Average Trajectory Error (ATE), allowing researchers to analyze the failure modes of their methods. We also propose a challenging Novel View Synthesis benchmark that covers cases not covered by current NVS benchmarks, such as fully non-Lambertian scenes with 360-degree camera trajectories. Please visit https://princeton365.cs.princeton.edu for the dataset, code, videos, and submission.

The Linux kernel is a critical system, serving as the foundation for numerous systems. Bugs in the Linux kernel can cause serious consequences, affecting billions of users. Fault localization (FL), which aims at identifying the buggy code elements in software, plays an essential role in software quality assurance. While recent LLM agents have achieved promising accuracy in FL on recent benchmarks like SWE-bench, it remains unclear how well these methods perform in the Linux kernel, where FL is much more challenging due to the large-scale code base, limited observability, and diverse impact factors. In this paper, we introduce LinuxFLBench, a FL benchmark constructed from real-world Linux kernel bugs. We conduct an empirical study to assess the performance of state-of-the-art LLM agents on the Linux kernel. Our initial results reveal that existing agents struggle with this task, achieving a best top-1 accuracy of only 41.6% at file level. To address this challenge, we propose LinuxFL$^+$, an enhancement framework designed to improve FL effectiveness of LLM agents for the Linux kernel. LinuxFL$^+$ substantially improves the FL accuracy of all studied agents (e.g., 7.2% - 11.2% accuracy increase) with minimal costs.

Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem. To tackle this challenge, the straight-through estimator (STE) has become the most widely adopted heuristic, allowing backpropagation through discrete operations by introducing biased yet valid surrogate gradients. However, its theoretical properties remain largely unexplored, with few existing analyses focus on the generalization error by assuming an infinite amount of training data. In contrast, this work presents the first sample complexity analysis of STE in the context of neural network quantization. Our theoretical results highlight the critical role of sample size in the success of STE, a key insight absent from existing studies. Specifically, by analyzing the quantization-aware training of a two-layer neural network with binary weights and activations, we derive the sample complexity bounds in terms of the data dimensionality that guarantee the convergence of STE-based optimization to the global minimum for both ergodic and non-ergodic analyses. Moreover, in the presence of label noises, we prove an intriguing recurrence property of STE-gradient method, where the iterate repeatedly escape from and return to the optimal binary weights. Finally, we empirically demonstrate that STE fails for general non-Gaussian data but its effectiveness can be restored through normalization, underscoring its practical importance in effective quantization.

The expansion of ride-sourcing services such as Uber and Lyft has reshaped urban transportation by offering flexible, on-demand mobility via mobile applications. Despite convenience, these platforms confront significant operational challenges, particularly vehicle rebalancing-strategic repositioning of a fleet of vehicles to address spatiotemporal mismatches in supply and demand. Inadequate rebalancing results in prolonged rider waiting times and inefficient vehicle utilization, but also leads to fairness issues, such as the inequitable distribution of service and disparities in driver income. To tackle these, we introduce continuous-state mean-field control (MFC) and mean-field reinforcement learning (MFRL) models with continuous repositioning actions. MFC and MFRL offer scalable solutions by modeling each vehicle's behavior through interaction with the vehicle distribution, rather than with individual vehicles. This mitigates the curse of dimensionality with respect to the number of agents, enabling coordination across large fleets with significantly reduced computational complexity and eliminating the need to retrain the model when fleet size changes. To ensure equitable service access across geographic regions, we integrate an accessibility constraint into models and derive rebalancing policies that strike a balance between high fulfillment of rider demand and fair coverage of vehicle supply. Extensive evaluation using data-driven simulation of Shenzhen demonstrates the efficiency and robustness of our approach. Remarkably, it scales to tens of thousands of vehicles, with training times comparable to linear programming rebalancing. Besides, our policies effectively explore the efficiency-equity Pareto front, outperforming conventional benchmarks across key metrics like fleet utilization, fulfilled requests, and pickup distance, while ensuring equitable service access.

Large text-to-image diffusion models rarely expose reliable signals of when a prompt is likely to produce a poorly aligned generation, especially when training data is undisclosed. We study whether expert disagreement inside pre-trained mixture-of-experts (MoE) diffusion models can serve as a reliable estimate for epistemic uncertainty. We introduce EMoE, a training-free method that separates expert-specific computation paths at an early MoE layer, uses the same initial noise across paths, and measures variance among their latent representations after the first denoising step. This provides an uncertainty-aware prompt signal before full image generation, without auxiliary networks or training diffusion ensembles. On COCO and CC3M, EMoE ranks prompts by text-image alignment quality metrics more consistently than diffusion-specific and router-based baselines. We further apply EMoE to multilingual prompts and find systematic language-dependent differences in disagreement and generation quality, including shared-vocabulary effects. These results position EMoE as a practical diagnostic tool for prompt risk, model coverage, and bias analysis in MoE text-to-image diffusion models.

Constructive neural combinatorial optimization (NCO) offers a promising paradigm for solving vehicle routing problems (VRPs) by directly learning to construct approximate optimal solutions, thereby reducing reliance on expert knowledge for algorithm design. However, scaling these methods to handle large-scale instances remains challenging due to high computational complexity. While recent dynamic search space reduction (SSR) methods can improve inference efficiency through geometric distance-based pruning, they often struggle on complex instances with non-uniform distributions or when optimal solutions rely heavily on non-spatial constraints. To address this critical issue, we propose Learning to Reduce (L2R), which is the first learning-based dynamic SSR framework. L2R learns to adaptively prioritize nodes by extracting patterns from problem-specific features to prune the search space at each step, enabling efficient and scalable solution construction. Extensive experiments show that our L2R framework generalizes robustly to different problem scales and data distributions on various VRP variants. To the best of our knowledge, L2R is the first neural solver to effectively scale to VRP instances with $10$ million nodes while maintaining high solution quality, which significantly pushes the frontier of NCO in terms of generalization and scalability. Our code is available at https://github.com/CIAM-Group/L2R.

Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample. We analyze a compressed variant of Oja's algorithm for estimating the principal eigenvector of the data covariance matrix using only two adaptive measurements per sample. At each iteration, we observe one measurement along the current estimate and one in a random orthogonal direction. We prove that after $t$ iterations, the expected sine-squared error to the true eigenvector is $\mathcal{O}(λ_1λ_2 d^2 / (Δ^2 t))$, where $d$ is the ambient dimension, $λ_1, λ_2$ are the leading eigenvalues, and $Δ= λ_1 - λ_2$ is the eigengap. We complement this with a matching information-theoretic lower bound of $Ω(λ_1λ_2 d^2 / (Δ^2 t))$ -- the first for compressed eigenvector estimation -- proving that the $d^2$ factor, an additional factor of $d$ compared to the fully-observed minimax rate $Θ(λ_1λ_2 d / (Δ^2 t))$, is the fundamental cost of compression and cannot be improved. In contrast, any non-adaptive scheme with two measurements per iteration suffers $Ω(λ_2^2 d^3 / (Δ^2 t))$, an additional power of $d$. This separates fully-observed, adaptive-compressed, and non-adaptive-compressed PCA across three powers of $d$. Our analysis handles the noisy setting where the covariance has nonzero trailing eigenvalues, providing the first convergence guarantee for adaptive compressed subspace tracking beyond the noiseless case.

Growing evidence suggests that layer attention mechanisms, which enhance interaction among layers in deep neural networks, have significantly advanced network architectures. However, existing layer attention methods suffer from redundancy, as attention weights learned by adjacent layers often become highly similar. This redundancy causes multiple layers to extract nearly identical features, reducing the model's representational capacity and increasing training time. To address this issue, we propose a novel approach to quantify redundancy by leveraging the Kullback-Leibler (KL) divergence between adjacent layers. Additionally, we introduce an Enhanced Beta Quantile Mapping (EBQM) method that accurately identifies and skips redundant layers, thereby maintaining model stability. Our proposed Efficient Layer Attention (ELA) architecture, improves both training efficiency and overall performance, achieving a 30% reduction in training time while enhancing performance in tasks such as image classification and object detection.

Accurate classification of EEG signals is crucial for brain-computer interfaces (BCIs) and neuroprosthetic applications, yet many existing methods fail to account for the non-Euclidean, manifold structure of EEG data, resulting in suboptimal performance. Preserving this manifold information is essential to capture the true geometry of EEG signals, but traditional classification techniques largely overlook this need. To this end, we propose MPEC (Manifold-Preserved EEG Classification via an Ensemble of Clustering-Based Classifiers), that introduces two key innovations: (1) a feature engineering phase that combines covariance matrices and Radial Basis Function (RBF) kernels to capture both linear and non-linear relationships among EEG channels, and (2) a clustering phase that employs a modified K-means algorithm tailored for the Riemannian manifold space, ensuring local geometric sensitivity. Ensembling multiple clustering-based classifiers, MPEC achieves superior results, validated by significant improvements on the BCI Competition IV dataset 2a.

Gossip Learning (GL) is a decentralized learning paradigm where users iteratively exchange and aggregate models with a small set of neighboring peers. Recent approaches rely on dynamic communication graphs built using Random Peer Sampling (RPS) protocols which have been proven to accelerate convergence. However, we show that these approaches are vulnerable to a dual attack: Byzantine nodes can poison models and manipulate peer sampling to amplify their influence. We address this combination of threats with GRANITE, a framework for robust learning over sparse, dynamic graphs in the presence of Byzantine nodes. GRANITE accumulates knowledge about encountered node identifiers over time and dynamically adjusts local aggregation thresholds based on estimated Byzantine density in the neighbourhood of each node. We demonstrate that under GRANITE, the Byzantine presence in local neighborhoods exhibits an exponential decay. We further derive the robustness conditions of the graphs generated by GRANITE. Empirically, our results indicate that GRANITE converges within 5% of non-Byzantine accuracy under 30% Byzantines nodes, offers faster convergence and operates on graphs with up to 9x lower communication cost.

Dual-arm robots promise greater efficiency but require planning for complex tasks with nonlinear sub-task dependencies. Current methods using Large Language Models (LLMs) suffer from a fundamental trade-off: generating linear sequences is efficient but fails to model parallelism and adapt to changes, while iterative querying is adaptive but too slow and costly. To bridge this gap, we introduce DAG-Plan, a novel task planning framework that for the first time employs a Directed Acyclic Graph (DAG) as the central representation for dual-arm coordination. The key insight is that a DAG natively captures complex sub-task dependencies and explicitly reveals opportunities for parallel execution. Within this framework, an LLM is used only once as a powerful semantic parser to translate a natural language instruction into a structured DAG. During execution, our system dynamically assigns candidate nodes to the suitable arm based on real-time environmental observations, enabling truly adaptive and parallel operation. Extensive evaluation on a dual-arm kitchen benchmark shows that DAG-Plan's structured approach fundamentally outperforms existing paradigms. It achieves a 48% higher success rate than single-query linear sequence methods with dual arm by robustly managing dependencies, and an 84.1% higher execution efficiency than iterative querying methods by eliminating the latency of repeated LLM calls. Our work demonstrates that a principled, graph-based representation is the key to unlocking efficient and reliable LLM-based planning for complex robotic systems. More demos and code are available on https://sites.google.com/view/dag-plan.

Recent studies have demonstrated that test-time compute scaling effectively improves the performance of small language models (sLMs). However, prior research has mainly examined test-time compute scaling with an additional larger model as a verifier, leaving verification by sLMs underexplored. In this work, we investigate whether sLMs can reliably verify the output candidates under test-time scaling. We find that even with knowledge distillation from larger verifiers, sLMs struggle with verification tasks requiring memorization, such as numerical calculations and fact-checking. To address this limitation, we propose Tool-integrated verification (T1), a two-stage framework that first filters candidates with external tools and then uses an sLM for final verification, offloading memorization-heavy steps to tools such as a code interpreter. Within T1, we prove that offloading to external tools reduces the memorization burden on sLMs and improves test-time scaling performance. Experiments on the MATH benchmark demonstrate that, with T1, a Llama-3.2 1B model under test-time scaling outperforms the significantly larger Llama-3.1 8B model. Moreover, T1 improves the verification accuracy of both process reward models (PRMs) and critic models. Our findings highlight the potential of tool integration to substantially improve the verification abilities of sLMs.

General-purpose multilingual vector representations, used in retrieval, regression and classification, are traditionally obtained from bidirectional encoder models. Despite their wide applicability, encoders have been recently overshadowed by advances in generative decoder-only models. However, many innovations driving this progress are not inherently tied to decoders. In this paper, we revisit the development of multilingual encoders through the lens of these advances, and introduce EuroBERT, a family of multilingual encoders covering European and widely spoken global languages. Our models outperform existing alternatives across a diverse range of tasks, spanning multilingual capabilities, mathematics, and coding, and natively supporting sequences of up to 8,192 tokens. We also examine the design decisions behind EuroBERT, offering insights into our dataset composition and training pipeline. We publicly release the EuroBERT models, including intermediate training checkpoints, together with our training framework.

Modern scene text recognition systems often depend on large end-to-end architectures that require extensive training and are prohibitively expensive for real-time scenarios. In such cases, the deployment of heavy models becomes impractical due to constraints on memory, computational resources, and latency. To address these challenges, we propose a novel, training-free plug-and-play framework that leverages the strengths of pre-trained text recognizers while minimizing redundant computations. Our approach uses context-based understanding and introduces an attention-based segmentation stage, which refines candidate text regions at the pixel level, improving downstream recognition. Instead of performing traditional text detection that follows a block-level comparison between feature map and source image and harnesses contextual information using pretrained captioners, allowing the framework to generate word predictions directly from scene context.Candidate texts are semantically and lexically evaluated to get a final score. Predictions that meet or exceed a pre-defined confidence threshold bypass the heavier process of end-to-end text STR profiling, ensuring faster inference and cutting down on unnecessary computations. Experiments on public benchmarks demonstrate that our paradigm achieves performance on par with state-of-the-art systems, yet requires substantially fewer resources.Our code can be found here: https://ritabrata04.github.io/Context-driven-STR/.

Robotic manipulation of unfamiliar objects in new environments is challenging due to limited generalisation capabilities. We propose a new skill transfer framework, GIFT (Geometry-Induced Functional Transfer), which enables a robot to transfer complex object manipulation skills and constraints from a single human demonstration. Our approach addresses the challenge of skill acquisition and task execution by deriving geometric representations from demonstrations focusing on object-centric interactions. By leveraging the Functional Maps (FMC) framework, we efficiently map interaction functions between objects and their environments, allowing the robot to replicate task operations across objects of similar topologies or categories, even when they have significantly different shapes. Additionally, our method incorporates screw interpolation (ScLERP) for generating smooth, geometrically-aware robot paths to ensure the transferred skills adhere to the demonstrated task constraints. We validate the effectiveness and adaptability of our approach through extensive experiments, demonstrating successful skill transfer and task execution in diverse real-world environments without requiring additional training.

Generative pre-training is often framed through a false dichotomy between autoregressive models for discrete signals and diffusion models for continuous signals. We argue that the dichotomy is false because it conflates model family, data representation, training objective, and inference procedure. Autoregression is an inference procedure that expands a sequence through normalized conditional draws, while diffusion is a refinement procedure that repeatedly revises an existing state. The more useful contrast is therefore not autoregressive versus diffusion, but discrete tokens learned with cross-entropy versus continuous tokens learned with diffusion-style objectives, together with the inference algorithms used to sample from them. From this perspective, algorithmic progress should prioritize inference-time efficiency along two axes: sequence expansion and state refinement. We advocate designing the inference procedure before the training objective, because a training method cannot compensate for an inference map that omits necessary arguments or imposes an incorrect factorization. We illustrate this principle through a target-time limitation of DDIM-style samplers, a joint-distribution limitation of multi-token prediction, and recent flow-map and few-step distillation methods that directly parameterize long-range inference moves.

Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning. We introduce a new class of data-dependent generalization bounds that apply directly to trained models, without any modification. In particular, we present an exactly computable bound that is non-vacuous across all evaluated networks, including ImageNet-scale models with 600M parameters. This this is the first work showing that meaningful generalization guarantees are achievable even for large, unaltered deep networks. Our approach reveals that generalization is governed by the interaction between the trained model and the geometry of the data distribution. We decompose the generalization error into two interpretable components: a distributional complexity term, capturing how the data mass is distributed across the input space, and local model-behavior terms, capturing the network's behavior within individual regions. This joint dependence identifies where and why generalization gaps arise. Empirically, some components of our bound are highly predictive of the true test error, and the bound tightens when the partition aligns with the intrinsic data geometry, highlighting data-dependent local regularity as a key driver of generalization.

Image-based 3D generation has vast applications in robotics and gaming, where high-quality, diverse outputs and consistent 3D representations are crucial. However, existing methods have limitations: 3D diffusion models are limited by dataset scarcity and the absence of strong pre-trained priors, while 2D diffusion-based approaches struggle with geometric consistency. We propose a method that leverages 2D diffusion models' implicit 3D reasoning ability while ensuring 3D consistency via Gaussian-splatting-based geometric distillation. Specifically, the proposed Gaussian Splatting Decoder enforces 3D consistency by transforming SV3D latent outputs into an explicit 3D representation. Unlike SV3D, which only relies on implicit 2D representations for video generation, Gaussian Splatting explicitly encodes spatial and appearance attributes, enabling multi-view consistency through geometric constraints. These constraints correct view inconsistencies, ensuring robust geometric consistency. As a result, our approach simultaneously generates high-quality, multi-view-consistent images and accurate 3D models, providing a scalable solution for single-image-based 3D generation and bridging the gap between 2D Diffusion diversity and 3D structural coherence. Experimental results demonstrate state-of-the-art multi-view consistency and strong generalization across diverse datasets. The code will be made publicly available upon acceptance.

Sustainability encompasses three key facets: economic, environmental, and social. However, the nascent discourse on sustainable artificial intelligence (AI) predominantly focuses on the environmental sustainability of AI, neglecting the economic and social aspects. Achieving truly sustainable AI necessitates addressing the tension between its environmental sustainability, which emphasises mitigating AI's climate impact, and its social sustainability, hinging on equitable access to AI development resources. This push for increased accessibility, however, often overlooks the environmental costs of expanding such resource usage. This position paper argues that reconciling climate awareness and resource awareness is essential to realising truly sustainable AI, and neglecting these factors fuels a global AI arms race. Applying Karl Marx's base-superstructure framework from historical materialism, we analyse how the material conditions are shaping the current AI progress and the discourse surrounding it. Further, we introduce the Climate and Resource Aware Machine Learning (CARAML) framework with actionable recommendations spanning individual, community, industry, government, and global levels to achieve sustainable AI.

We provide an empirical investigation of the potential of pre-training vision-language models on an unprecedented scale: 100 billion examples. We find that model performance tends to saturate at this scale on many common Western-centric classification and retrieval benchmarks, such as COCO Captions. Nevertheless, tasks of cultural diversity achieve more substantial gains from the 100-billion scale web data, thanks to its coverage of long-tail concepts. Furthermore, we analyze the model's multilinguality and show gains in low-resource languages as well. In addition, we observe that reducing the size of the pretraining dataset via quality filters like using CLIP, typically used to enhance performance, may inadvertently reduce the cultural diversity represented in large-scale datasets. Our results highlight that while traditional benchmarks may not benefit significantly from scaling noisy, raw web data to 100 billion examples, this data scale is vital for building truly inclusive multimodal systems.

AI advancements have been significantly driven by a combination of foundation models and curiosity-driven learning aimed at increasing capability and adaptability. Within this landscape, open-endedness, where AI agents autonomously and indefinitely generate novel behaviors, representations, or solutions, has gained increasing interest. This has become relevant in the context of self-evolving agents and long-horizon discovery. This position paper argues that the defining properties of open-ended AI systems introduce a distinct and underexplored class of safety challenges, including loss of predictability, emergent misalignment, and difficulties in maintaining effective control as systems evolve beyond their initial design assumptions, that must be addressed preemptively. These challenges differ qualitatively from those associated with task-bounded or static models and are unlikely to be addressed by existing safety frameworks alone, which is why these risks must be examined proactively, before large-scale deployment. The paper proposes a taxonomy for key challenges, discusses research opportunities, and calls for coordinated action to support the safe and responsible development of open-ended AI.

With AI systems widely applied to assist humans in decision-making processes such as talent hiring, school admission, and loan approval; there is an increasing need to ensure that the decisions made are fair. One major challenge for analyzing fairness in decisions is that the standards are highly subjective and contextual -- there is no consensus for what absolute fairness means for every scenario. That is not to say that different fairness standards often conflict with each other. To bypass this issue, this work aims to test relative fairness in decisions. That is, instead of defining what are ``absolutely'' fair decisions, we propose to test the relative fairness of one decision set against another with differential parity -- the difference between two sets of decisions should be independent of a certain sensitive attribute. This proposed notion of differential parity fairness has the following benefits: (1) it avoids the ambiguous and contradictory definition of what absolutely fair decisions are; (2) when a reference set (of ground truth or reliable fair decisions) is available, differential parity can serve as a new group fairness notion (similar to but different from separation and sufficiency); (3) even when no reference set is available, it reveals the relative preference or bias between different decision sets. One limitation for differential parity is that it requires the two sets of decisions under comparison to be made on the same data subjects. To overcome this limitation, we propose to utilize a machine learning model to bridge the gap between the two sets of decisions made on difference data and estimate the differential parity.

Weighted sampling -- sampling from a probability density function (PDF) proportional to the product of a base PDF and a weight function -- is a fundamental technique with wide-ranging applications in variance reduction, biased sampling, data augmentation, and more. Leveraging the increasing availability of pretrained score-based generative models (SGMs), we propose a training-free weighted sampling framework that approximates the backward diffusion process of the target distribution by augmenting the pretrained base score function with an auxiliary guidance term, in a principled and computationally efficient manner. Our approach builds on two key components: a lightweight approximation of the guidance that avoids costly higher-order derivatives of both the score and weight functions, and an uncertainty-aware scheduler that dynamically adjusts the guidance strength based on a temporal analysis of approximation error. Together, these components enable accurate and stable sampling without relying on particle-based resampling or Hessian evaluations commonly required by existing methods. We validate the effectiveness of our method from synthetic to large-scale settings such as Stable Diffusion XL, where our framework achieves $1.2\times$ to $4.7\times$ speedups while consistently matching or outperforming state-of-the-art baselines in task performance. These results position our method as a scalable and inference-efficient solution for task-adaptive, time-sensitive sampling in generative applications.

We apply augmentations to our dataset to enhance the quality of our predictions and make our final models more resilient to noisy data and domain drifts. Yet the question remains, how are these augmentations going to perform with different hyper-parameters? In this study we evaluate the sensitivity of augmentations with regards to the model's hyper parameters along with their consistency and influence by performing a Local Surrogate (LIME) interpretation on the impact of hyper-parameters when different augmentations are applied to a machine learning model. We have utilized Linear regression coefficients for weighing each augmentation. Our research has proved that there are some augmentations which are highly sensitive to hyper-parameters and others which are more resilient and reliable.

Medical imaging studies often rely on a single sample per subject, assuming it is representative of their physiological traits. However, variations in how input descriptors are defined or computed (e.g. due to a lack of consensus in the scientific field) may have a crucial impact on the analysis, and are hardly considered in practice. In this paper, we propose an original strategy based on representation learning to estimate a parametric map reflecting the impact of such definitional differences on a given physiological descriptor, previously extracted from medical images. We consider the different definitions or computations of such physiological descriptors as different high-dimensional data, potentially of heterogeneous types. We specifically focus on myocardial deformation (strain), for which there is limited agreement on its definition. We first use manifold alignment to match the latent representations associated with the different definitions of this descriptor. Then, we formulate plausible distributions in the latent space to represent definitional divergence across descriptors, from which we reconstruct a high-dimensional parametric map to visualize such definitional divergence. Due to the lack of proper ground truth for this specific clinical application, we first demonstrate this methodology on toy experiments and then expand the evaluation on right ventricular strain data from subjects obtained from 3D echocardiographic image sequences, for which different types of strain are available at each point of the right ventricle endocardial surface mesh. Beyond this illustrative application, our methodology has the potential to be generalised to many other population analyses considering heterogeneous high-dimensional descriptors.

We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the generalisation bounds scale with growing numbers of qubits. Applying our results to classes with polynomial readout functions, we find that the risk bounds converge in the number of training samples. The explicit dependence on the quantum reservoir and readout parameters in our bounds can be used to control the generalisation error to a certain extent. It should be noted that the bounds scale exponentially with the number of qubits n. The upper bounds on the Rademacher complexity can be applied to other reservoir classes that fulfill a few hypotheses on the quantum dynamics and the readout function.

The Abstraction and Reasoning Corpus (ARC) evaluates general reasoning capabilities that are difficult for both machine learning models and combinatorial search methods. We propose a neuro-symbolic approach that combines a transformer for proposal generation with combinatorial search using a domain-specific language. The transformer narrows the search space by proposing promising search directions, which allows the combinatorial search to find the actual solution in short time. We pre-train the trainsformer with synthetically generated data. During test-time we generate additional task-specific training tasks and fine-tune our model. Our results surpass comparable state of the art on the ARC evaluation set by 27% and compare favourably on the ARC train set. We make our code and dataset publicly available at https://github.com/Batorskq/NSA.

Optimization algorithms such as AdaGrad and Adam have significantly advanced the training of deep models by dynamically adjusting the learning rate during the optimization process. However, ad-hoc tuning of learning rates poses a challenge and leads to inefficiencies in practice. To address this issue, recent research has focused on developing ``parameter-free'' algorithms that operate effectively without the need for learning rate tuning. Despite these efforts, existing parameter-free variants of AdaGrad and Adam tend to be overly complex and/or lack formal convergence guarantees. In this paper, we present AdaGrad++ and Adam++, novel and simple parameter-free variants of AdaGrad and Adam with convergence guarantees. We prove that AdaGrad++ achieves comparable convergence rates to AdaGrad in convex optimization without predefined learning rate assumptions. Similarly, Adam++ matches the convergence rate of Adam without relying on any conditions on the learning rates. Experimental results across various deep learning tasks validate the competitive performance of Adam++.

Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on a broad range of tasks. This survey introduces graph neural networks through the encoder-decoder framework and provides examples of decoders for a range of graph analytic tasks. It uses theory and numerous experiments on homogeneous graphs to illustrate the behavior of graph neural networks under different training sizes and degrees of graph complexity, with an emphasis on oversmoothing and oversquashing.