This paper sets out the most general computational and econometric implications of the rigorous stochastic equilibrium theory from SELCKE (Staines (2024a)) arXiv:2312.16214. The analytical backbone is the discovery that the system converges geometrically to long-run equilibrium, at a rate given by the greater of the eigenvalue or inverse eigenvalue (from outside) closest to the unit circle and the maximum shock persistence. High-order shocks converge faster. I develop a simulation procedure to test, with asymptotic power, whether stochastic equilibrium exists for a particular model. The fundamental approximation result asserts that, whatever the order of expansion or loss function, the stochastic steady state delivers the most accurate perturbation solution. I also show that super-consistent parameter estimators $O(1/T)$ arise whenever second-order terms vanish. Besides Calvo, I study stochastic equilibrium in two alternative pricing models. Dynamics simplify considerably. I bound the time the impulse response peaks, by the maximum lag in the errors. This lends empirical support to Taylor contracts, although there are issues surrounding unit roots and the strong cost-channel. For menu costs, I demonstrate that the initial price distribution decays away super-exponentially, producing a system equivalent to Calvo with an endogenous reset probability. The impact of idiosyncratic disturbances appears as an additional wedge between actual and efficient output. Blow-up of the objective function at the boundary is proven, with the help of new distributional arguments, so the model meets existing eigenvalue existence conditions for the recursive equilibrium. Along the way, new light is shone on existing theoretical models and statistical procedures.

Pre-layout design space exploration (DSE) for high-speed signal integrity (SI) analysis is often limited by the computational cost of simulations and iterative optimization algorithms within modern electronic design automation (EDA) workflows. While machine learning surrogate models accelerate the simulation step, optimizing designs still requires utilizing iterative black-box search methods. This iterative nature scales poorly, making multi-corner sweeps computationally expensive. As a solution, this paper proposes amortized neural optimization (ANO) for pre-layout SI design. ANO entirely eliminates iterative black-box inference by utilizing fully differentiable neural network surrogate models. ANO extracts analytical gradients from the surrogate to train a global optimization policy. Instead of solving the optimization problem repeatedly at inference, the optimization process is learned offline and therefore amortized. Once the ANO policy is trained, it maps different channel contexts directly to near-optimal design parameters in a single deterministic forward pass. The efficiency and accuracy of the ANO framework are demonstrated based on three complex SI design scenarios, including DDR5 decision feedback equalization (DFE), 9-dimensional SerDes Tx/Rx co-equalization, and DDR3 DQS differential pair routing to optimize eye diagram metrics under intra-pair skew constraints. By trading roughly 10% in optimality compared to instance-specific black-box algorithms, it realizes speedups of three to four orders of magnitude. For a large-scale 320,000-instance multi-corner SerDes sweep optimization, ANO collapses what would have taken days of computation using iterative search algorithms into a single batched forward pass that completes in milliseconds. This transforms computationally expensive SI optimization into real-time and interactive pre-layout DSE.

Background and Purpose: Automated detection of focal cortical dysplasia (FCD) requires large volumes of voxelwise lesion-delineated MRI data, which are difficult to acquire. This study aims to generate synthetic MRI data exhibiting FCD, assess their realism, and evaluate their impact on automated FCD detection, particularly in reducing the need for manual annotations. Methods: T1-weighted (T1w) and T2-weighted Fluid-Attenuated Inversion Recovery (FLAIR) MRI scans from 131 FCD patients and 90 healthy controls from multiple (3) sites were retrospectively studied. Synthetic MRIs were generated by conditioning a generative network on binary FCD masks. Two neuroradiologists identified real images from a random set of 14 real and 14 synthetic scans. Three nnU-Net models were trained to detect FCD using: (i) real-only (35 FCD / 35 controls), (ii) real (35 FCD / 35 controls) plus synthetic augmentation, and (iii) expanded real data (70 FCD / 70 controls). Results: Experts showed limited ability to distinguish real from synthetic images, with classification accuracy of 60% for T1w and 70% for FLAIR (inter-rater agreement kappa = 0.86). Augmenting automated FCD detection with synthetic data increased sensitivity by 8.14% (p = 0.12) and improved model confidence at true lesion sites (0.83 +/- 0.11 to 0.89 +/- 0.12; p = 0.02). The expanded real-data model further improved sensitivity to 73.8% (p < 0.001) and confidence to 0.90 +/- 0.14 (p = 0.01). Conclusion: Conditional generative networks can generate realistic synthetic FCD-MRIs, reducing labeled data needs by approximately 20% while maintaining equivalent sensitivity. Equivalent amounts of real data, when available, remain more effective than synthetic augmentation.

In this work, we propose a deep learning framework for coherence regression directly from detected SAR images, without the need for accurate coregistration. A Residual U-Net is trained using coherence maps derived from precisely coregistered Sentinel-1 SLC data to learn the relationship between backscatter magnitudes and coherence. The model is trained on 12-day SLC pairs and evaluated across different datasets, including coregistered SLC products and open access analysis-ready data, covering diverse radiometric properties, geometries, and locations. Experimental results demonstrate that the proposed method achieves high-resolution coherence regression with improved accuracy compared to existing intensity-based approaches. The network generalizes well across diverse geographical locations and even across different temporal baselines that were never seen at training time. Additionally, the ability to operate on globally available analysis-ready data, such as ground range detected data, e.g., distributed through Google Earth Engine, enables its large-scale application in mission design, change monitoring, and diverse mapping tasks.

This paper presents a low-complexity motion detection method for outdoor Wi-Fi sensing based on a model-driven approach. The method exploits the structural characteristics of the phase components in channel state information (CSI) for low-multipath propagation environments, which are generally considered disadvantageous for Wi-Fi sensing, to mitigate the phase offset errors originating from wireless devices. In addition, phase averaging provides a processing gain that reduces the random noise components, including quantization and thermal noise. The theoretical basis of the method is described and its effectiveness is experimentally evaluated using Compressed Beamforming frames obtained from commercial IEEE 802.11ac devices. The experiments primarily focus wild crows flying in an outdoor orchard environment. The experimental results demonstrate that the method can detect birds even when they fly several meters away from the direct line-of-sight path between the transmitter and receiver antennas. Furthermore, the results indicated that fluctuations caused by vegetation movement were negligible when the wind speed was less than 3~m/s. The proposed approach is expected to be applicable not only to orchard monitoring but also to other outdoor Wi-Fi sensing applications in low-multipath environments.

Current Audio-Visual Speech Recognition (AVSR) models achieve near-perfect performance on the standard LRS3 benchmark, raising concerns of adaptive overfitting. To systematically assess true generalisability, we construct a highly controlled, unseen evaluation set subsampled from the massive MultiVSR dataset. Unlike standard out-of-distribution benchmarks, our subset strictly matches the acoustic, visual, and demographic distributions of the LRS3 test set. Evaluating five state-of-the-art architectures reveals a universal performance collapse, proving that current systems fail to generalise even under strictly aligned conditions. Through a fine-grained attribute analysis across seven factors, we isolate the specific drivers of this degradation. Furthermore, we uncover a profound lexical bias, expose distinct error patterns, and surprisingly reveal that audio-visual performance even lags behind audio-only settings. We release our matched test set for future benchmarking.

Dynamic Facial Expression Recognition (DFER) is a key enabling technology in affective computing, human-computer interaction, and intelligent multimedia systems. Despite the significant influence of cultural nuances on FER performance, most existing FER systems assume that emotional expressions are universally consistent across populations. This variation can be attributed to systematic differences in facial muscle activation patterns across cultures. A major challenge in advancing cross-cultural FER lies in the scarcity of culturally diverse benchmark datasets. To address this, a new hybrid multicultural video dataset termed Global Cross-Cultural Facial Expression Recognition (GCC-FER) is introduced. GCC-FER comprises 23,934 video samples spanning four cultural groups (African, Caucasian, East Asian, and South Asian) across seven basic expressions, combining psychologically supervised in-house data collection for underrepresented populations with rigorous ethnicity filtering of existing sources. To the best of our knowledge, GCC-FER is the first large-scale global cross-cultural DFER dataset designed to address these demographic gaps. Leveraging this dataset, behaviorally grounded cultural priors are derived for each cultural group and a global prior for practical deployment. A Culture-Aware FER (CA-FER) system is proposed to mitigate cultural bias by adaptively recalibrating latent facial representations. Extensive experiments on GCC-FER and DFEW demonstrate that the proposed system consistently improves FER performance across multicultural settings.

Computational pathology requires visual representations that transfer across diverse clinical endpoints and remain robust to variation in magnification, staining, scanner type, slide preparation, and input resolution. We present DaX, a pathology vision foundation model that adapts DINOv3-style self-supervised learning to whole-slide histopathology. DaX is initialized from natural-image DINOv3 weights and incorporates continuous magnification training, cross-scale tissue views, orientation-agnostic and acquisition-robust augmentation, multi-input-size training, and Gram-anchored dense consistency. These designs aim to connect local cellular morphology with global tissue architecture while stabilizing dense token-level representations across input scales. We further construct a WSI-level benchmark comprising 161 clinically meaningful tasks from 44 public datasets, covering 28,182 patients and 34,394 slides across four clinical domains and nine task categories. All models are evaluated under a fixed patient-level cross-validation protocol with fold-level statistical ranking, enabling reproducible comparisons that are less sensitive to split-dependent variation. Across this benchmark, DaX achieves the highest mean performance across tasks and consistently strong task-level ranking scores, with gains spanning diagnostic pathology, biomarker and molecular profiling, tissue/specimen context, and risk, response, and prognosis. These results support DaX as a transferable visual encoder for computational pathology and provide a standardized evaluation framework for future pathology foundation models. Project page: https://alibaba-damo-academy.github.io/DaX/benchboard/.

Large audio language models (LALMs) extend large language models with an audio encoder and large-scale audio data. However, the scarcity of high-quality annotated audio data remains a fundamental bottleneck for scaling. Through probing signal detectability analysis, we identify fine-grained spectrotemporal perceptual weaknesses in a foundation LALM. To address these challenges, we propose Spectrotemporal Counting (SpectCount), a data-efficient fine-tuning approach based on fully synthetic audio signals generated on-the-fly, without relying on real-world audio, annotations, or pretrained generative models. SpectCount not only resolves the observed weaknesses but also improves performance on diverse auditory benchmarks spanning sound, music, and speech, unseen during fine-tuning. These results suggest that weakness-targeted synthetic signals provide a data-efficient path toward enhanced auditory understanding capabilities in LALMs.

Synthetic aperture radar (SAR) has become indispensable for target interpretation owing to its all-day and all-weather observation capability. In SAR target interpretation, electromagnetic scattering information provides a physically grounded cue beyond visual texture and has been widely exploited for target interpretation. However, existing methods remain dominated by local scattering center representations. Such unordered and component-agnostic representations are highly unstable for aircraft targets. As a result, physically existing components with weak scattering responses are often missed, resulting in the incomplete reconstructed topology structure. To address this limitation, we establish Semantic Scattering Structure Understanding as a new paradigm for SAR aircraft interpretation. Semantic scattering keypoints are defined to associate local electromagnetic responses with physically meaningful aircraft components, while visibility-aware attributes are introduced to retain weakly observable yet physically existed components. The keypoints are further organized into a stable semantic scattering structure. Build upon this, we propose S3U-SAR, a physics-driven framework to localize semantic scattering keypoints and construct the complete representation constrained by multi-dimensional physical priors containing scattering heterogeneity, rigid-body topology, speckle uncertainty. A confidence-gated joint supervision strategy is further introduced to alleviate optimization conflicts. We construct KP-SAR-Aircraft-1.0, the first fine-grained benchmark for semantic scattering structure understanding. Extensive experiments demonstrate that S3U-SAR achieves the best performance compared with baselines. Cross-category and cross-dataset evaluations further verify its robustness and transferability.

Scripted vs spontaneous speech detection is appealing for interview guardrails, but benchmark performance can be inflated by shortcuts tied to corpus identity, channel conditions, and recording artifacts rather than speaking style itself. We present SEAM, a shortcut-aware framework for real-time scriptedness detection that combines uniform preprocessing, seam-aware sampling, non-speech augmentation, and a compact DistilHuBERT backbone. With 8s windows, the model achieves 0.971 +- 0.004 ROC-AUC on an external interview-domain evaluation set. Removing the shortcut-prevention components improves internal held-out metrics but sharply reduces external performance, indicating shortcut learning. Post-training quantization reduces the model footprint to 41.8MB with little loss in external performance. The results demonstrate that robust real-time scriptedness detection depends not only on the backbone, but on shortcut-aware data design and evaluation. We release code and model checkpoints.

We present BiEAR, a human auditory-inspired adaptive binaural front-end for multi-speaker localisation and distance estimation. Inspired by medial olivocochlear (MOC) feedback in human hearing, BiEAR uses a neural controller to adaptively adjust the frequency selectivity of a binaural auditory filterbank during inference. This yields time-frequency adaptive representations for ears, enabling the model to respond to changing acoustic conditions. We evaluate BiEAR on multi-speaker localisation and distance estimation in anechoic and real-room environments. Results show that the adaptive front-end improves localisation accuracy and robustness to unseen speakers and rooms compared with commonly used fixed binaural front-ends. Visualisation and analysis of learned filter adaptations show that BiEAR emphasises informative frequency bands over time. These findings suggest that adaptive, biologically inspired binaural front-ends can improve machine hearing robustness in complex acoustic scenes.

Myocardial perfusion quantification using contrast-enhanced ultrasound offers a bedside non-ionizing alternative to nuclear imaging modalities. However, its clinical adoption is hindered by time-consuming manual labelling. Automated segmentation has proved challenging due to a paucity of in-domain training data. Adapting strategies currently used to optimise large language models for large datasets, we apply neural scaling laws to predict network performance for myocardial segmentation. We extrapolate performance on subsets of the data to determine optimal network size on the CAMUS echocardiography dataset and a 25-patient contrast-enhanced ultrasound (CEUS) dataset. Finally, we validate the clinical utility of our models by comparing the final myocardial perfusion parameters with those obtained by a senior cardiologist. Extrapolation based on the scaling law is predictive of test loss at the full dataset size, allowing us to select two networks that obtained state-of-the-art performance on CAMUS with a 240-fold reduction in parameter count. We observe the gradient of the scaling law transfers from CAMUS to the CEUS dataset with a bias in the predicted losses. The automatically segmented masks perform equivalently to a senior cardiologist in myocardial perfusion quantification. These results establish neural scaling laws as a practical tool for data-driven compute-optimal model design for small imaging datasets.

We introduce ErA (Error-Aware Deep Unrolling Network), an end-to-end frame work for single-image defocus deblurring. ErA jointly learns a compact kerne basis and per-pixel weights, while an error-aware term in Augmented Lagrangian unrolling corrects kernel estimation errors via alternating updates and ResUNet denoisers. It achieves state-of-the-art PSNR/SSIM on DPDD, RealDOF, and RTF, and shows strong generalization on CUHK without ground truth.

Longitudinal medical visual question answering (VQA) requires reasoning about anatomical differences between an image of a current time point and an image of a referred time point. We propose an attention-guided encoder-decoder for this task with chest X-rays. Instead of conventional direct contrast, we propose to include a lightweight affine registration module to reduce nuisance motion by co-registering the current image to the reference image with a small registration regularizer. The registered image pair is fed into the image encoder, followed by a frozen DINO-based mask generator and a trainable adaptive mask generator to produce masks applied to the original image pairs. The masked image pairs are again fed into the image encoder and concatenated with text features as the input to a multimodal transformer-based decoder to generate final answers. To facilitate learning stabilization and clarify the change signal, inspired by DINO-v3, we include additional auxiliary objectives, including a mask rebuilding loss, a pairwise Gram-style consistency loss, and a KoLeo uniformity loss, which enhances the geometry of the representation. On the Medical-Diff-VQA benchmark, the model delivers strong BLEU, ROUGE-L, CIDEr, and METEOR scores while offering intrinsic interpretability through the shared saliency mask. These results support saliency-conditioned generation with mild pre-alignment as a principled framework for longitudinal reasoning in medical VQA. Our training strategy also illustrates the potential of a paradigm in utilizing image foundation models in biomedicine: optimizing both supervised and unsupervised learning objectives simultaneously.

Accurate and scalable flood mapping remains challenging due to limited ground observations, heterogeneous terrain conditions, and the difficulty of enforcing hydrodynamic consistency within data-driven models. This work introduces a physics-guided deep learning framework that integrates multi-modal remote sensing (Sentinel-1 SAR, Sentinel-2 optical imagery, and DEM-derived terrain features) with constraints from the depth-averaged shallow water equations (SWE). The proposed hybrid architecture combines a UNet to capture fine-scale spatial details with a Fourier Neural Operator (FNO) to model basin-scale hydraulic interactions, while physics-informed residual losses ensure mass and momentum consistency. Evaluated across diverse floodplain settings, the hybrid model achieves an Intersection over Union of 0.82 and an F1 score of 0.90 for flood extent prediction, outperforming UNet-only and FNO-only baselines. Using hydrodynamic simulations as reference data, the model achieves an RMSE of 0.21 m for water depth and 0.15 m/s for flow velocity. Physics consistency is maintained, with low residuals and mass imbalance below 2.1%. Ablation studies confirm that removing physicsbased regularization significantly degrades performance, underscoring the value of physical constraints for stability and generalization. These results demonstrate that embedding hydrodynamic principles into deep learning yields more accurate, reliable, and physically coherent flood predictions, offering strong potential for operational monitoring and large-scale deployment.

Numerous medical imaging problems must be solved under limited labels and constrained compute, yet it remains unclear whether performance gains are driven mainly by more expressive models or by better representation of clinically meaningful anatomy. We study this question through a low-data anatomy-aware benchmark for 5-class cardiac pathology prediction on the public ACDC MRI dataset. Using segmentation-derived patient descriptors from the right ventricle, myocardium, and left ventricle, we compare anatomy-specific and multi-structure representations across linear, kernel, and tree-based classifiers. We find that under limited label settings, representation dominates complexity. These results suggest that in resource-constrained healthcare settings, identifying and representing the most informative anatomy may matter more than the increasing complexity of the model alone.

Generative models for counterfactual outcomes have great potential to support decision-making under complex interventions, but existing approaches are limited by unstable estimation, poor generalization across environments, and bias from nuisance model misspecification. We introduce ADIGen, a framework for automatic, debiased, and invariant counterfactual generation under general interventions, including high-dimensional interventions and outcomes. ADIGen combines Riesz regression to avoid unstable density-ratio estimation, causal invariance to improve generalization under distribution shift, and orthogonal statistical learning to obtain doubly robust guarantees against nuisance model misspecification. We provide excess-risk bounds showing that ADIGen controls counterfactual risk under general interventions, with a product-bias nuisance remainder and an invariant risk bound across environments.

The kappa statistic is the most widely used measure of inter-rater agreement for categorical data. Despite its popularity, applied researchers often encounter two major hurdles: (i) determining the sample size required to achieve a desired level of agreement with given power, and (ii) computing appropriate kappa coefficients with proper interpretation. Existing R packages such as irr and kappaSize provide these functionalities but require programming skills and lack an integrated, user-friendly interface. We present CATEKAPPA, an R package that bridges this gap by combining sample size planning (via kappaSize) and agreement analysis (via irr) into a single Shiny-based web application. The package supports Cohen's kappa for two raters, Fleiss' kappa for three or more raters, and Light's kappa, and provides automatic interpretation using the Landis & Koch scale. Users can either launch an interactive graphical interface or use command-line functions for scripting. The package is freely available on CRAN.

Vulnerable road users (VRUs) account for approximately half of urban traffic deaths globally, with intersections concentrating a disproportionate share of these casualties. Recent reviews of sensing technology for VRU protection have cataloged dozens of single-sensor and dual-sensor deployments, yet none of the surveyed systems couples multi-modal sensing with edge-side near-miss analytics and bidirectional vehicle-to-everything (V2X) and pedestrian-to-everything (P2X) messaging in a single intersection cabinet. This paper presents an integrated framework for VRU protection at signalized intersections, combining LiDAR, radar, RGB camera, and thermal camera at the perception layer, edge-based prediction and surrogate-safety analytics at the computation layer, V2X and P2X messaging at the communication layer, and adaptive signal control at the actuation layer. The framework is grounded in an empirical case study using R-LiViT, the first publicly released roadside LiDAR-Visual-Thermal dataset, which provides 200 multi-modal sequences and 2,400 annotated RGB-T frames at three German intersections. Analysis of 53,319 detection annotations reveals that VRUs comprise approximately 49% of all road-user observations, that day-to-night density drops by 38% for pedestrians and 45% for vehicles while the night distribution shows a higher close-proximity share, that per-frame close-proximity event counts vary approximately 10-fold across the eight unique locations at three intersections, and that 83% of pedestrian bounding boxes are small in image space, indicating that VRUs are typically far from any single sensor. These findings support multi-modal sensing, edge-side analytics, and adaptive context-sensitive deployment rather than uniform single-sensor solutions.

Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional. We propose DeSI (Deep Single-Index Fréchet Regression), a semiparametric framework for regression with metric space-valued outputs and multivariate inputs that assumes a single-index structure for the conditional Fréchet mean. DeSI estimates an interpretable index direction, which quantifies the relative importance of inputs, using a deep neural network, and performs Fréchet regression along the resulting one-dimensional index in the target metric space. This structure mitigates the curse of dimensionality while retaining interpretability, which stands in contrast to standard deep neural networks. We establish theoretical guarantees for DeSI, including uniform approximation and convergence rates, and demonstrate its strong predictive performance through simulations on distributions, networks, and symmetric positive-definite matrices, as well as an application to compositional mood data from New Jersey.

While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses. We develop a stability-based framework that requires only a finite $L_p$ moment condition. Our first contribution is sharp concentration inequalities for functions of independent random variables under $L_p$ constraints, extending McDiarmid's bounded-differences techniques beyond the classical regime. Leveraging these results, we derive sharp high-probability generalization bounds across a range of learning paradigms, including empirical risk minimization, transductive regression, and meta-learning. These guarantees show that $L_p$ stability suffices for robust generalization even when boundedness fails, substantially weakening the standard assumptions in the stability literature.

The transformer's emergent ability to perform in-context learning (ICL) has sparked a wide range of studies designed to understand its underlying mechanisms. Existing works often study how training task diversity, defined either as the number of ICL training task vectors or as the number of function classes from which the task vectors are drawn, shapes both the learning dynamics and generalization capabilities of ICL. While both definitions have uncovered many interesting phenomena, many observations under the latter definition remain theoretically unexplained. This paper presents a minimal analytical model under which these phenomena provably emerge from the properties of the training data. By modeling the training task vectors as a mixture of low-rank Gaussians, we show how training task diversity, defined by the number of non-overlapping columns between subspaces that parameterize the covariance matrices, improves both the generalization and optimization trajectory of ICL with linear attention. In particular, we show that our model can explain (i) why training with task diversity shortens the ICL plateau and (ii) why ICL appears to achieve out-of-distribution generalization. We conclude by empirically demonstrating how our results extend to nonlinear transformers and nonlinear function classes. Overall, our work presents a tractable framework to unify existing observations.

We study finite-sample change detection for one-dimensional noisy dynamical systems using partition-based empirical approximations of stationary behaviour. Given observations from an interval-valued process, we partition the state space, estimate a finite transition matrix from observed transitions between partition elements, and apply a small Doeblin-type regularisation to ensure a unique stationary distribution. From an initial reference segment, we compute a baseline empirical stationary distribution \(\widehatπ_{0,ρ}\). For each later sliding window, we compute \(\widehatπ_{t,ρ}\) and define the score \[ S_t=\|\widehatπ_{t,ρ}-\widehatπ_{0,ρ}\|_1. \] Large values of \(S_t\) indicate a change in stationary behaviour relative to the baseline. The statistic detects changes in invariant density or stationary law, but not all possible changes in transition dynamics. Under explicit assumptions on empirical transition concentration, finite-state stationary distribution stability, partition approximation, regularisation bias, and noise stability, we derive a finite-sample bound for the empirical stationary density. The bound separates sampling error, regularisation bias, partition approximation error, and noise bias. We then obtain a single-window false-alarm guarantee and a sufficient detection condition when the invariant density changes by more than the estimation error. We illustrate the method on synthetic noisy beta-map change-point experiments.

Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the behavior of shallow architectures, the statistical generalization properties of deep neural networks (DNNs), especially in regression tasks, remain far less understood. In this paper, we make significant progress toward closing this gap by providing a comprehensive generalization analysis of DNNs trained using gradient-based methods. First, we establish, for the first time, a crucial connection between the learning dynamics of a DNN with smooth activation functions trained via gradient-based methods and those of kernel methods, showing that gradient-based methods on over-parameterized DNNs can fully inherit the favorable learning dynamics of their kernel counterparts. Building on this connection and the well-established optimality of kernel methods, we derive the first known minimax-optimal rates for the excess population risk of both gradient descent (GD) and stochastic gradient descent (SGD), under the assumption that network width scales polynomially with the sample size. Our results demonstrate that, with sufficient width, DNNs trained by GD or SGD can achieve generalization performance comparable to kernel-based methods.

Recent progress has been made in understanding the statistical generalization performance of gradient descent methods for overparameterized neural networks within the neural tangent kernel (NTK) regime. However, most of the existing work on regression problems is limited to shallow network architectures, leaving a notable gap in the theory of deep neural networks. This paper addresses this gap by presenting a comprehensive generalization analysis for deep ReLU networks trained using gradient descent (GD) and stochastic gradient descent (SGD). Specifically, we establish the first known minimax-optimal rates of excess population risk for both GD and SGD with deep ReLU networks, under the assumption that the network width scales polynomially with respect to the network depth and training sample size. Our results demonstrate that with sufficient width, gradient descent methods for deep ReLU networks can achieve optimal generalization rates on par with kernel methods.

This paper presents an open-economy macroeconomic equilibrium model for Proof-of-Stake (PoS) networks with fee-burn mechanics (EIP-1559) that formalizes the strategic interplay between a Kelly-optimizing rational institutional investor and a utility-driven retail consumer. We analyze network dynamics across two behavioral regimes. In The Unbounded Accumulation Model, the consumer purely accumulates tokens, creating an exclusive buy-side pressure that interacts with institutional portfolio rebalancing to fuel an ever-expanding speculative bubble and generate compounding excess returns for investors. Conversely, in The Utility-Consumption Model, the consumer dynamically buys and sells tokens to balance crypto wealth against real-world fiat consumption. Within this framework, we derive an explicit steady-state equilibrium price for ETH, demonstrating how token valuation anchors to a stable fundamental baseline that scales directly with network adoption while completely dissolving the institutional yield premium. Our numerical simulations show that while exogenous traditional finance (TradFi) shocks propagate through portfolio rebalancing to drive high token price volatility, network inflation remains highly stable. Furthermore, we prove that network security is insulated from institutional monopoly by counter-cyclical consumer behavior. Our findings reveal that institutional excess wealth creation in PoS ecosystems is not native to the staking protocol itself, but is strictly driven by the leveraged extraction of the retail consumer's continuous demand for transactional utility.

This paper develops a binary-gamble framework for characterizing risk sensitivity and loss aversion in Cumulative Prospect Theory (CPT). The proposed probabilistic risk-sensitivity metric is defined as a probability-threshold ratio that determines acceptance and preference thresholds in choice problems involving either a certain outcome and a binary gamble or two binary gambles. We show how standard notions of symmetric and non-symmetric bet aversion can be recovered within this framework, and we compare the resulting threshold-based conditions with utility premia, probability premia, and Arrow--Pratt curvature measures. The analysis clarifies when these criteria coincide and when they diverge, particularly for increasing aversion conditions, binary gambles with unequal probability distributions, and settings involving probability weighting functions. We also identify technical restrictions that arise when CPT-utility functions are used to represent loss aversion at the reference point. The resulting framework provides a decision-theoretic interpretation of risk sensitivity that is directly tied to probability thresholds and complements existing premium-based approaches.

Breast cancer remains one of the leading causes of cancer-related mortality among women worldwide, making early detection essential for effective treatment. Mammography is the primary screening modality; however, accurate delineation of suspicious lesions remains challenging and subject to inter-observer variability. Automated segmentation methods can assist radiologists by providing consistent and efficient lesion localization. This study presents DSU-Net, an attention-enhanced Dense Skip U-Net architecture for automated breast lesion segmentation in mammographic images. The proposed framework integrates dense skip connections and attention mechanisms to improve feature propagation, preserve spatial information, and enhance lesion boundary delineation. Experiments were conducted using the Curated Breast Imaging Subset of the Digital Database for Screening Mammography (CBIS-DDSM). To address severe foreground-background imbalance, a composite loss function combining Dice loss, focal loss, and binary cross-entropy loss was employed during training. The proposed model achieved a Dice Similarity Coefficient of 0.9421, an Intersection over Union of 0.8905, an accuracy of 0.9711, and an AUC-ROC of 0.9878 on the validation dataset. Qualitative evaluation demonstrated accurate delineation of lesions with varying sizes and morphologies, while quantitative results confirmed robust discrimination between lesion and background regions. These findings demonstrate that DSU-Net provides accurate and reliable breast lesion segmentation in mammographic images and highlights the potential of attention-guided deep learning for computer-aided breast cancer screening and diagnosis.

We advance a new probabilistic supervised learning approach that permits reliable, automated, and early individualised prediction of the severity with which a disease will develop in a prospective patient. The prediction capacity is illustrated via the pre-transplant prediction of the score of severity of Veno Occlusive Disease (or VOD) in the digital twin (DT) of the considered prospective patient, where this score parametrises the severity with which VOD will develop in this patient, after they undergo their Bone Marrow Transplant. The learning of the relationship between the pre-transplant variables, and a severity score variable is undertaken by modelling this relationship as a (random) function that is treated as a sample function of an adequately-chosen stochastic process. The parameters of this underlying process are learnt using a training dataset that is generated using the real-time evolution of retrospective patients in a cohort, with this training dataset subsequently augmented in size by a probabilistic inverse learning of the score of prospective patients. The augmented training set, then permits the learning of the function that capacitates - at the pre-transplant stage - automated prediction of the score of the severity of VOD that characterises the DT of a physical patient in their unique pre-transplant state. This score is subsequently fed back to the real prospective patient as the severity with which VOD will develop in them, after this patient undergoes their transplant. Such a score then permits the treating Haematologist-Oncologists to decide on the treatment regimen, which in this illustration reduces to deciding on treating the patient with Defibrotide. An AI facility is developed to undertake such automated prediction, with the physician inputting the data on the pre-transplant state that characterises the DT of the prospective patient under consideration.