Sample-wise learning curves plot performance versus training set size. They are useful for studying scaling laws and speeding up hyperparameter tuning and model selection. Learning curves are often assumed to be well-behaved: monotone (i.e.

The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step random walk transition kernels.

Ev ing modern en task in arts controlled for rely a wide on settings, e range xpensi of v understanding e vis input ual models.

We propose a novel gradient-based framework for learning parameterized quantum circuits (PQCs) in the presence of Pauli noise in gate operation. The key innovation in our framework is the simultaneous optimization of model parameters and learning of an inverse noise channel, specifically designed to mitigate Pauli noise. Our parametrized inverse noise model utilizes the Pauli-Lindblad equation and relies on the principle underlying the Probabilistic Error Cancellation (PEC) protocol to learn an effective and scalable mechanism for noise mitigation. In contrast to conventional approaches that apply predetermined inverse noise models during execution, our method systematically mitigates Pauli noise by dynamically updating the inverse noise parameters in conjunction with the model parameters, facilitating task-specific noise adaptation throughout the learning process. We employ proximal stochastic gradient descent (proximal SGD) to ensure that updates are bounded within a feasible range to ensure stability. This approach allows the model to converge efficiently to a stationary point, balancing the trade-off between noise mitigation and computational overhead, resulting in a highly adaptable quantum model that performs robustly in noisy quantum environments.

Contrastive learning has proven to be highly efficient and adaptable in shaping representation spaces across diverse modalities by pulling similar samples together and pushing dissimilar ones apart. However, two key limitations persist: (1) Without explicit regulation of the embedding distribution, semantically related instances can inadvertently be pushed apart unless complementary signals guide pair selection, and (2) excessive reliance on large in-batch negatives and tailored augmentations hinders generalization. To address these limitations, we propose Variational Supervised Contrastive Learning (VarCon), which reformulates supervised contrastive learning as variational inference over latent class variables and maximizes a posterior-weighted evidence lower bound (ELBO) that replaces exhaustive pair-wise comparisons for efficient class-aware matching and grants fine-grained control over intra-class dispersion in the embedding space. Trained exclusively on image data, our experiments on CIFAR-10, CIFAR-100, ImageNet100, and ImageNet-1K show that VarCon (1) achieves state-of-the-art performance for contrastive learning frameworks, reaching 79.36% Top-1 accuracy on ImageNet1K and 78.29% on CIFAR-100 with a ResNet-50 encoder while converging in just 200 epochs; (2) yields substantially clearer decision boundaries and semantic organization in the embedding space, as evidenced by KNN classification, hierarchical clustering results, and transfer-learning assessments; and (3) demonstrates superior performance in few-shot learning than supervised baseline and superior robustness across various augmentation strategies.

Recent deep clustering models have produced impressive clustering performance. However, a common issue with existing methods is the disparity between global and local feature structures. While local structures typically show strong consistency and compactness within class samples, global features often present intertwined boundaries and poorly separated clusters. Motivated by this observation, we propose DCBoost, a parameter-free plug-in designed to enhance the global feature structures of current deep clustering models. By harnessing reliable local structural cues, our method aims to elevate clustering performance effectively. Specifically, we first identify high-confidence samples through adaptive k-nearest neighborsbased consistency filtering, aiming to select a sufficient number of samples with high label reliability to serve as trustworthy anchors for self-supervision. Subsequently, these samples are utilized to compute a discriminative loss, which promotes both intra-class compactness and inter-class separability, to guide network optimization. Extensive experiments across various benchmark datasets showcase that our DCBoost significantly improves the clustering performance of diverse existing deep clustering models. Notably, our method improves the performance of current state-of-the-art baselines (e.g., ProPos) by more than 3% on average and amplifies the silhouette coefficient by over 7 .

In recommendation systems, implicit feedback data can be automatically recorded and is more common than explicit feedback data. However, implicit feedback poses two challenges for relevance prediction, namely (a) positive-unlabeled (PU): negative feedback does not necessarily imply low relevance and (b) missing not at random (MNAR): items that are popular or frequently recommended tend to receive more clicks than other items, even if the user does not have a significant interest in them. Existing methods either overlook the MNAR issue or fail to account for the inherent mechanism of the PU issue. As a result, they may lead to inaccurate relevance predictions or inflated biases and variances. In this paper, we formulate the implicit feedback problem as a counterfactual estimation problem with missing treatment variables.

Effective modeling of endangered marine mammal species, such as the North Atlantic Right Whale, is critical for balancing marine conservation with the growing blue economy. Passive acoustic monitoring data collected by autonomous underwater vehicles provide new opportunities for localized marine species detection and oceanographic sensing, but introduce complex statistical challenges such as zero inflation, imperfect detection, and intricate dependence structures. In response, we propose the Deep Zero-Inflated Bernoulli (DeepZIB) model--a deep statistical method which jointly models latent species presence and conditional detection probabilities while learning complex habitat relationships from heterogeneous covariate information. We establish theoretical results on the model's structural properties and conduct simulation experiments to demonstrate its ability to recover underlying parameters and latent presence fields. Application to real-world passive acoustic monitoring data on the North Atlantic Right Whale along the U.S. East Coast demonstrates improved model adequacy and predictive performance in capturing the species' dynamic and spatially varying habitat. A key advantage of DeepZIB is its ability to generate high-resolution, spatially and temporally varying presence maps, providing valuable insights for targeted and risk-aware management of blue economy industries, ranging from offshore and marine energy, to fisheries management and maritime transport.

We introduce a new convex optimization framework for logistic scalar-on-matrix regression which incorporates nuclear and $\ell_1$ norm penalties to enforce simultaneously low-rank and sparse structures in the estimated coefficient matrix. The proposed method enables interpretable modeling of high-dimensional matrix-valued predictors in the presence of binary responses. We derive a custom algorithm based on the Alternating Direction Method of Multipliers (ADMM) to efficiently solve the resulting convex optimization problem and establish the theoretical properties of the obtained solution. Numerical experiments clearly demonstrate the effectiveness of our method in recovering meaningful predictive patterns. Finally, we apply our method to the brain imaging data to identify structures in functional brain connectivity matrices that are characteristic of subjects with a family history of alcohol use disorders (AUDs).

Clustering is widely used for exploratory analysis and scientific discovery, driving insights from market segmentation to biological data analysis, but its outputs can be difficult to interpret, audit, and reproduce as modern datasets become increasingly large and complex. Reliable use of clustering requires understanding which features drive the discovered structure, yet feature-level explanations for clustering remain scarce compared with methods in supervised learning. Furthermore, existing clustering feature importance scores are often tied to specific algorithms and data assumptions. To address these challenges, we propose Cluster LOCO (Leave-One-Covariate-Out), a family of model-agnostic feature importance scores for clustering. Cluster LOCO is built on feature occlusion and clustering generalizability, defined as whether cluster labels learned on one subset of the data can be accurately predicted on held-out samples. For any chosen clustering algorithm, Cluster LOCO quantifies a feature's importance by measuring how much its removal degrades generalizability. We first introduce Cluster LOCO-Split, which relies on data splitting, and then extend it to Cluster LOCO-MP, a minipatch ensemble-based version designed for large-scale data. Across synthetic simulations and an application to cell-type discovery in single-cell transcriptomics, we show that Cluster LOCO more reliably recovers informative features than existing clustering feature importance methods.