We investigate the mechanisms of self-distillation in multi-class classification, particularly in the context of linear probing with fixed feature extractors where traditional feature learning explanations do not apply. Our theoretical analysis reveals that multi-round self-distillation effectively performs label averaging among instances with high feature correlations, governed by the eigenvectors of the Gram matrix derived from input features. This process leads to clustered predictions and improved generalization, mitigating the impact of label noise by reducing the model's reliance on potentially corrupted labels. We establish conditions under which multi-round self-distillation achieves 100\% population accuracy despite label noise. Furthermore, we introduce a novel, efficient single-round self-distillation method using refined partial labels from the teacher's top two softmax outputs, referred to as the PLL student model. This approach replicates the benefits of multi-round distillation in a single round, achieving comparable or superior performance--especially in high-noise scenarios--while significantly reducing computational cost.

We study community detection in multiple networks whose nodes and edges are jointly correlated, a scenario that arises naturally in social platforms. Extending the classical Stochastic Block Model (SBM) and its contextual counterpart (CSBM), we introduce the correlated CSBMs, which incorporates both structural and attribute correlations. To build intuition, we first analyze correlated Gaussian Mixture Models, where a distance-based estimator can align nodes across graphs (without edges) even when community labels are initially unknown. For correlated CSBMs, we develop a two-step procedure that matches most nodes via$k$-core matching based on edge information, then refines the matching for remaining nodes by leveraging their attributes, enabling perfect alignment under suitable conditions. By aligning and combining graphs, we identify regimes where community detection is infeasible in a single graph but becomes possible when side information from correlated graphs is incorporated, illustrating how interplay between graph matching and community recovery enhances the inference on graphs.

Test-Time Adaptation (TTA) adjusts models using unlabeled test data to handle dynamic distribution shifts. However, existing methods rely on frequent adaptation and high computational cost, making them unsuitable for resource-constrained edge environments. To address this, we propose SNAP, a sparse TTA framework that reduces adaptation frequency and data usage while preserving accuracy. SNAP maintains competitive accuracy even when adapting based on only 1\% of the incoming data stream, demonstrating its robustness under infrequent updates. Our method introduces two key components: (i) Class and Domain Representative Memory (CnDRM), which identifies and stores a small set of samples that are representative of both class and domain characteristics to support efficient adaptation with limited data; and (ii) Inference-only Batch-aware Memory Normalization (IoBMN), which dynamically adjusts normalization statistics at inference time by leveraging these representative samples, enabling efficient alignment to shifting target domains. Integrated with five state-of-the-art TTA algorithms, SNAP reduces latency by up to 93.12\%, while keeping the accuracy drop below 3.3\%, even across adaptation rates ranging from 1\% to 50\%. This demonstrates its strong potential for practical use on edge devices serving latency-sensitive applications. The source code is available at https://github.com/chahh9808/SNAP.

Multimodal dataset distillation aims to synthesize a small set of image-text pairs that enables efficient training of large-scale vision-language models. While dataset distillation has shown promise in unimodal tasks, extending it to multimodal contrastive learning presents key challenges: learning cross-modal alignment and managing the high computational cost of large encoders. Prior approaches address scalability by freezing the text encoder and update only the image encoder and text projection layer. However, we find this severely limits semantic alignment and becomes a bottleneck for performance scaling. We propose CovMatch, a scalable dataset distillation framework that aligns the cross-covariance of real and synthetic features while regularizing feature distributions within each modality. Unlike prior approaches, CovMatch enables joint optimization of both encoders, leading to stronger cross-modal alignment and improved performance. Evaluated on Flickr30K and COCO, CovMatch outperforms state-of-the-art multimodal distillation methods and achieves up to 6.8\% absolute gains in retrieval accuracy using only 500 synthetic pairs.

In the era of large-scale foundation models, fully fine-tuning pretrained networks for each downstream task is often prohibitively resource-intensive. Prompt tuning offers a lightweight alternative by introducing tunable prompts while keeping the backbone frozen. However, existing visual prompt tuning methods often fail to specialize the prompts or enrich the representation space--especially when applied to self-supervised backbones. We show that these limitations become especially pronounced in challenging tasks and data-scarce settings, where effective adaptation is most critical. In this work, we introduce VIPAMIN, a visual prompt initialization strategy that enhances adaptation of self-supervised models by (1) aligning prompts with semantically informative regions in the embedding space, and (2) injecting novel representational directions beyond the pretrained subspace. Despite its simplicity--requiring only a single forward pass and lightweight operations--VIPAMIN consistently improves performance across diverse tasks and dataset sizes, setting a new state of the art in visual prompt tuning.

We study community detection in multiple networks with jointly correlated node attributes and edges. This setting arises naturally in applications such as social platforms, where a shared set of users may exhibit both correlated friendship patterns and correlated attributes across different platforms. Extending the classical Stochastic Block Model (SBM) and its contextual counterpart (Contextual SBM or CSBM), we introduce the correlated CSBM, which incorporates structural and attribute correlations across graphs. To build intuition, we first analyze correlated Gaussian Mixture Models, wherein only correlated node attributes are available without edges, and identify the conditions under which an estimator minimizing the distance between attributes achieves exact matching of nodes across the two databases. For the correlated CSBMs, we develop a two-step procedure that first appliesk-core matching to most nodes using edge information, then refines the matching for the remaining unmatched nodes by leveraging their attributes with a distance-based estimator. We identify the conditions under which the algorithm recovers the exact node correspondence, enabling us to merge the correlated edges and average the correlated attributes for enhanced community detection. Crucially, by aligning and combining graphs, we identify regimes in which community detection is impossible in a single graph but becomes feasible when side information from correlated graphs is incorporated. Our results illustrate how the interplay between graph matching and community recovery can boost performance, broadening the scope of multi-graph, attribute-based community detection.

Data subset selection aims to find a smaller yet informative subset of a large dataset that can approximate the full-dataset training, addressing challenges associated with training neural networks on large-scale datasets. However, existing methods tend to specialize in either high or low selection ratio regimes, lacking a universal approach that consistently achieves competitive performance across a broad range of selection ratios. We introduce a universal and efficient data subset selection method, Best Window Selection (BWS), by proposing a method to choose the best window subset from samples ordered based on their difficulty scores. This approach offers flexibility by allowing the choice of window intervals that span from easy to difficult samples. Furthermore, we provide an efficient mechanism for selecting the best window subset by evaluating its quality using kernel ridge regression. Our experimental results demonstrate the superior performance of BWS compared to other baselines across a broad range of selection ratios over datasets, including CIFAR-10/100 and ImageNet, and the scenarios involving training from random initialization or fine-tuning of pre-trained models.

Dataset distillation aims to synthesize a small number of images per class (IPC) from a large dataset to approximate full dataset training with minimal performance loss. While effective in very small IPC ranges, many distillation methods become less effective, even underperforming random sample selection, as IPC increases. Our examination of state-of-the-art trajectory-matching based distillation methods across various IPC scales reveals that these methods struggle to incorporate the complex, rare features of harder samples into the synthetic dataset even with the increased IPC, resulting in a persistent coverage gap between easy and hard test samples. Motivated by such observations, we introduce SelMatch, a novel distillation method that effectively scales with IPC. SelMatch uses selection-based initialization and partial updates through trajectory matching to manage the synthetic dataset's desired difficulty level tailored to IPC scales. When tested on CIFAR-10/100 and TinyImageNet, SelMatch consistently outperforms leading selection-only and distillation-only methods across subset ratios from 5% to 30%.

Graph matching problem aims to identify node correspondence between two or more correlated graphs. Previous studies have primarily focused on models where only edge information is provided. However, in many social networks, not only the relationships between users, represented by edges, but also their personal information, represented by features, are present. In this paper, we address the challenge of identifying node correspondence in correlated graphs, where additional node features exist, as in many real-world settings. We propose a two-step procedure, where we initially match a subset of nodes only using edge information, and then match the remaining nodes using node features. We derive information-theoretic limits for exact graph matching on this model. Our approach provides a comprehensive solution to the real-world graph matching problem by providing systematic ways to utilize both edge and node information for exact matching of the graphs.

We study the statistical decision process of detecting the low-rank signal from various signal-plus-noise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by entrywise pre-transforming the data matrix if the noise is non-Gaussian, generalizing the known results for the spiked random matrix models with rank-1 signals. As an intermediate step, we find out sharp phase transition thresholds for the extreme eigenvalues of spiked random matrices, which generalize the Baik-Ben Arous-Péché (BBP) transition. We also prove the central limit theorem for the linear spectral statistics for the spiked random matrices and propose a hypothesis test based on it, which does not depend on the distribution of the signal or the noise. When the noise is non-Gaussian noise, the test can be improved with an entrywise transformation to the data matrix with additive noise. We also introduce an algorithm that estimates the rank of the signal when it is not known a priori.

Crowdsourcing system has emerged as an effective platform for labeling data with relatively low cost by using non-expert workers. Inferring correct labels from multiple noisy answers on data, however, has been a challenging problem, since the quality of the answers varies widely across tasks and workers. Many existing works have assumed that there is a fixed ordering of workers in terms of their skill levels, and focused on estimating worker skills to aggregate the answers from workers with different weights. In practice, however, the worker skill changes widely across tasks, especially when the tasks are heterogeneous. In this paper, we consider a new model, called$d$-type specialization model, in which each task and worker has its own (unknown) type and the reliability of each worker can vary in the type of a given task and that of a worker. We allow that the number$d$of types can scale in the number of tasks. In this model, we characterize the optimal sample complexity to correctly infer the labels within any given accuracy, and propose label inference algorithms achieving the order-wise optimal limit even when the types of tasks or those of workers are unknown. We conduct experiments both on synthetic and real datasets, and show that our algorithm outperforms the existing algorithms developed based on more strict model assumptions.

Crowdsourcing has emerged as an effective platform for labeling large amounts of data in a cost- and time-efficient manner. Most previous work has focused on designing an efficient algorithm to recover only the ground-truth labels of the data. In this paper, we consider multi-choice crowdsourcing tasks with the goal of recovering not only the ground truth, but also the most confusing answer and the confusion probability. The most confusing answer provides useful information about the task by revealing the most plausible answer other than the ground truth and how plausible it is. To theoretically analyze such scenarios, we propose a model in which there are the top two plausible answers for each task, distinguished from the rest of the choices. Task difficulty is quantified by the probability of confusion between the top two, and worker reliability is quantified by the probability of giving an answer among the top two. Under this model, we propose a two-stage inference algorithm to infer both the top two answers and the confusion probability. We show that our algorithm achieves the minimax optimal convergence rate. We conduct both synthetic and real data experiments and demonstrate that our algorithm outperforms other recent algorithms. We also show the applicability of our algorithms in inferring the difficulty of tasks and in training neural networks with top-two soft labels.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

The nonconvex formulation of the matrix completion problem has received significant attention in recent years due to its affordable complexity compared to the convex formulation. Gradient Descent (GD) is a simple yet efficient baseline algorithm for solving nonconvex optimization problems. The success of GD has been witnessed in many different problems in both theory and practice when it is combined with random initialization. However, previous works on matrix completion require either careful initialization or regularizers to prove the convergence of GD. In this paper, we study the rank-1 symmetric matrix completion and prove that GD converges to the ground truth when small random initialization is used. We show that in a logarithmic number of iterations, the trajectory enters the region where local convergence occurs. We provide an upper bound on the initialization size that is sufficient to guarantee the convergence, and show that a larger initialization can be used as more samples are available. We observe that the implicit regularization effect of GD plays a critical role in the analysis, and for the entire trajectory, it prevents each entry from becoming much larger than the others.

Crowdsourcing has emerged as an effective platform to label data with low cost by using non-expert workers. However, inferring correct labels from multiple noisy answers on data has been a challenging problem, since the quality of answers varies widely across tasks and workers. Many existing prior works have assumed a simple model where the order of workers in terms of their reliabilities is fixed across tasks, and focused on estimating the worker reliabilities to aggregate responses with different weights. We propose a highly general crowdsourcing model in which the reliability of each worker can vary depending on the type of a given task, where the number of types d can scale in the number of tasks. In this model, we characterize the optimal sample complexity to correctly infer the unknown labels within any given accuracy, and propose an algorithm achieving the order-wise optimal result. We conduct experiments on synthetic and real datasets, and show that our algorithm outperforms the existing ones developed based on strict model assumptions.1

We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We prove a central limit theorem for the linear spectral statistics of general rank-one spiked Wigner matrices, and based on the central limit theorem, we propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does not require prior knowledge about the distribution of the signal or the noise. When the noise is Gaussian, the proposed test is optimal in the sense that its error matches that of the likelihood ratio test, which minimizes the sum of the Type-I and Type-II errors. If the density of the noise is known and non-Gaussian, the error of the test can be lowered by applying an entrywise transformation to the data matrix.

We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik–Ben Arous–Péché (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.

We consider crowdsourced labeling under a$d$-type worker-task specialization model, where each worker and task is associated with one particular type among a finite set of types and a worker provides a more reliable answer to tasks of the matched type than to tasks of unmatched types. We design an inference algorithm that recovers binary task labels (up to any given recovery accuracy) by using worker clustering, worker skill estimation and weighted majority voting. The designed inference algorithm does not require any information about worker/task types, and achieves any targeted recovery accuracy with the best known performance (minimum number of queries per task).11This work was supported in part by National Research Foundation of Korea under Grant 2017R1E1A1A01076340; in part by the Ministry of Science and ICT, South Korea, under the ITRC support program under Grant IITP-2021-2018-0-01402; and in part by the Institute of Information and Communications Technology Planning & Evaluation (IITP) grant funded by the Korea Government MSIT under Grant 2020-0-00626.

Despite remarkable performance in producing realistic samples, Generative Adversarial Networks (GANs) often produce low-quality samples near low-density regions of the data manifold, e.g., samples of minor groups. Many techniques have been developed to improve the quality of generated samples, either by post-processing generated samples or by pre-processing the empirical data distribution, but at the cost of reduced diversity. To promote diversity in sample generation without degrading the overall quality, we propose a simple yet effective method to diagnose and emphasize underrepresented samples during training of a GAN. The main idea is to use the statistics of the discrepancy between the data distribution and the model distribution at each data instance. Based on the observation that the underrepresented samples have a high average discrepancy or high variability in discrepancy, we propose a method to emphasize those samples during training of a GAN. Our experimental results demonstrate that the proposed method improves GAN performance on various datasets, and it is especially effective in improving the quality and diversity of sample generation for minor groups.

We consider a query-based data acquisition problem for binary classification of unknown labels, which has diverse applications in communications, crowdsourcing, recommender systems and active learning. To ensure reliable recovery of unknown labels with as few number of queries as possible, we consider an effective query type that asks “group attribute” of a chosen subset of objects. In particular, we consider the problem of classifying m binary labels with XOR queries that ask whether the number of objects having a given attribute in the chosen subset of size d is even or odd. The subset size d, which we call query degree, can be varying over queries. We consider a general noise model where the accuracy of answers on queries changes depending both on the worker (the data provider) and query degree d. For this general model, we characterize the information-theoretic limit on the optimal number of queries to reliably recover m labels in terms of a given combination of degree-d queries and noise parameters. Further, we propose an efficient inference algorithm that achieves this limit even when the noise parameters are unknown.

We consider the crowdsourced classification of m binary labels with XOR queries that ask whether the number of objects having a given attribute in the chosen subset of size d is even or odd. The subset size d, which we call query degree, can be varying over queries. Since a worker needs to make more efforts to answer a query of a higher degree, we consider a noise model where the accuracy of worker's answer changes depending both on the worker reliability and query degree d. For this general model, we characterize the information-theoretic limit on the optimal number of queries to reliably recover m labels in terms of a given combination of degree-d queries and noise parameters. Further, we propose an efficient inference algorithm that achieves this limit even when the noise parameters are unknown.1

We consider the problem of detecting the presence of the signal in a rank-one signal-plus-noise data matrix. In case the signal-to-noise ratio is under the threshold below which a reliable detection is impossible, we propose a hypothesis test based on the linear spectral statistics of the data matrix. When the noise is Gaussian, the error of the proposed test is optimal as it matches the error of the likelihood ratio test that minimizes the sum of the Type-I and Type-II errors. The test is data-driven and does not depend on the distribution of the signal or the noise. If the density of the noise is known, it can be further improved by an entrywise transformation to lower the error of the test.

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separability condition in this work is more relaxed than the widely used linear separability. Moreover, the constructed neural network guarantees perfect classification for any datasets sampled from a separable probability distribution. This generalization capability comes from the saturation of sigmoid function that exploits small margins near the boundaries of intervals formed by the separable probability distribution1.

We propose a non-adaptive unequal error protection (UEP) querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the outputs of a binary symmetric channel the 20 questions problem can be mapped to an equivalent problem of channel coding with UEP. A new non-adaptive querying strategy based on UEP superposition coding is introduced whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). In fact, we show that the proposed non-adaptive UEP querying policy achieves the same order convergence rate as the adaptive policy.

We consider query-based data acquisition and the corresponding information recovery problem, where the goal is to recover k binary variables (information bits) from parity measurements of those variables. The queries and the corresponding parity measurements are designed using the encoding rule of Fountain codes. By using Fountain codes, we can design potentially limitless number of queries, and corresponding parity measurements, and guarantee that the original k information bits can be recovered with high probability from any sufficiently large set of measurements of size n. In the query design, the average number of information bits that is associated with one parity measurement is called query difficulty (d̅) and the minimum number of measurements required to recover the k information bits for a fixed d̅ is called sample complexity (n). We analyze the fundamental trade-offs between the query difficulty and the sample complexity, and show that the sample complexity of n = c max{k,(k log k)/d̅} for some constant c > 0 is necessary and sufficient to recover k information bits with high probability as k→∞.

In this paper, we propose an open-loop unequal-error-protection querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel, the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A new non-adaptive querying strategy based on UEP superposition coding is introduced, whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). With the proposed querying strategy, the rate of exponential decrease in the number of queries matches the rate of a closed-loop adaptive scheme, where queries are sequentially designed with the benefit of feedback. Furthermore, the achievable error exponent is significantly better than that of random block codes employing equal error protection.

We show a direct relationship between the variance and the differential entropy for subclasses of symmetric and asymmetric unimodal distributions by providing an upper bound on variance in terms of entropy power. Combining this bound with the well-known entropy power lower bound on variance, we prove that the variance of the appropriate subclasses of unimodal distributions can be bounded below and above by the scaled entropy power. As the differential entropy decreases, the variance is sandwiched between two exponentially decreasing functions in the differential entropy. This establishes that for the subclasses of unimodal distributions, the differential entropy can be used as a surrogate for concentration of the distribution.

In this paper, we propose an unequal error protection coding strategy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A superposition coding strategy with UEP is introduced that has error exponent that is significantly better than that of the UEP repetition code introduced by Variani et al. [1].

The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on CN/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N -length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to CN/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C2, where V is the respective channel dispersion quantity.

We investigate superadditivity in the maximum achievable rate of reliable classical communication over a quantum channel. The maximum number of classical information bits extracted per use of the quantum channel strictly increases as the number of channel outputs jointly measured at the receiver increases. This phenomenon is called superadditivity. We provide an explanation of this phenomenon by comparing a quantum channel with a classical discrete memoryless channel (DMC) under concatenated codes. We also give a lower bound on the maximum accessible information per channel use at a finite length of quantum measurements in terms of V, which is the quantum version of channel dispersion, and C, the classical capacity of the quantum channel.

We study the general coherent-state hypothesis testing problem and the capacity of the pure-loss optical channel with a coherent processing receiver (a receiver that uses coherent feedback control and direct detection). We describe the binary hypothesis minimum probability of error receiver as optimizing the communication efficiency at each instant, based on recursively updated knowledge of the receiver. Using this viewpoint, we give a natural generalization of the designs to general M-ary hypothesis testing problems. We analyze the information capacity with coherent receivers, and compare the result with that with direct detection receivers and with arbitrary quantum receivers (the Holevo limit), using the appropriate scalings in the low photon number regime.