This paper conducts a comprehensive study of the learning curves of kernel ridge regression (KRR) under minimal assumptions. Our contributions are three-fold: 1) we analyze the role of key properties of the kernel, such as its spectral eigen-decay, the characteristics of the eigenfunctions, and the smoothness of the kernel; 2) we demonstrate the validity of the Gaussian Equivalent Property (GEP), which states that the generalization performance of KRR remains the same when the whitened features are replaced by standard Gaussian vectors, thereby shedding light on the success of previous analyzes under the Gaussian Design Assumption; 3) we derive novel bounds that improve over existing bounds across a broad range of setting such as (in)dependent feature vectors and various combinations of eigen-decay rates in the over/underparameterized regimes.

We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we connect this approach to rank-$1$ canonical tensor decomposition. By generalizing it to a rank-$r$ canonical probability decomposition, we develop an improved model that predicts multiple tokens simultaneously. This model can also be interpreted as a mixture of experts, allowing us to leverage successful techniques from that domain for efficient and robust training. Importantly, the overall overhead for training and sampling remains low. Our method demonstrates significant improvements in inference speed for both text and code generation tasks, proving particularly beneficial within the self-speculative decoding paradigm. It maintains its effectiveness across various model sizes and training epochs, highlighting its robustness and scalability.

Federated Learning (FL) is an evolving paradigm that enables multiple parties to collaboratively train models without sharing raw data. Among its variants, Vertical Federated Learning (VFL) is particularly relevant in real-world, cross-organizational collaborations, where distinct features of a shared instance group are contributed by different parties. In these scenarios, parties are often linked using fuzzy identifiers, leading to a common practice termed as multi-party fuzzy VFL. Existing models generally address either multi-party VFL or fuzzy VFL between two parties. Extending these models to practical multi-party fuzzy VFL typically results in significant performance degradation and increased costs for maintaining privacy. To overcome these limitations, we introduce the Federated Transformer (FeT), a novel framework that supports multi-party VFL with fuzzy identifiers. FeT innovatively encodes these identifiers into data representations and employs a transformer architecture distributed across different parties, incorporating three new techniques to enhance performance. Furthermore, we have developed a multi-party privacy framework for VFL that integrates differential privacy with secure multi-party computation, effectively protecting local representations while minimizing associated utility costs. Our experiments demonstrate that the FeT surpasses the baseline models by up to 46\% in terms of accuracy when scaled to 50 parties. Additionally, in two-party fuzzy VFL settings, FeT also shows improved performance and privacy over cutting-edge VFL models.

Thermal Infrared (TIR) imaging provides robust perception for navigating in challenging outdoor environments but faces issues with poor texture and low image contrast due to its 14/16-bit format. Conventional methods utilize various tone-mapping methods to enhance contrast and photometric consistency of TIR images, however, the choice of tone-mapping is largely dependent on knowing the task and temperature dependent priors to work well. In this paper, we present Thermal Chameleon Network (TCNet), a task-adaptive tone-mapping approach for RAW 14-bit TIR images. Given the same image, TCNet tone-maps different representations of TIR images tailored for each specific task, eliminating the heuristic image rescaling preprocessing and reliance on the extensive prior knowledge of the scene temperature or task-specific characteristics. TCNet exhibits improved generalization performance across object detection and monocular depth estimation, with minimal computational overhead and modular integration to existing architectures for various tasks. Project Page: https://github.com/donkeymouse/ThermalChameleon

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional descriptions from high-dimensional data, facilitating comprehension and analysis. We address the challenges posed by real-world data that defy conventional assumptions, such as complex interactions within neural systems or high-dimensional dynamical systems. Leveraging insights from both theoretical physics and machine learning, this work unifies diverse reduction methods under a comprehensive framework, the Deep Variational Multivariate Information Bottleneck. This framework enables the design of tailored reduction algorithms based on specific research questions. We explore and assert the efficacy of simultaneous reduction approaches over their independent reduction counterparts, demonstrating their superiority in capturing covariation between multiple modalities, while requiring less data. We also introduced novel techniques, such as the Deep Variational Symmetric Information Bottleneck, for general nonlinear simultaneous reduction. We show that the same principle of simultaneous reduction is the key to efficient estimation of mutual information. We show that our new method is able to discover the coordinates of high-dimensional observations of dynamical systems. Through analytical investigations and empirical validations, we shed light on the intricacies of dimensionality reduction methods, paving the way for enhanced data analysis across various domains. We underscore the potential of these methodologies to extract meaningful insights from complex datasets, driving advancements in fundamental research and applied sciences. As these methods evolve, they promise to deepen our understanding of complex systems and inform more effective data analysis strategies.

We study the dynamics in high dimensions of online stochastic gradient descent for the multi-spiked tensor model. This multi-index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate $r$ unknown signal vectors within the $N$-dimensional unit sphere through maximum likelihood estimation from noisy observations of a $p$-tensor. We determine the number of samples and the conditions on the signal-to-noise ratios (SNRs) required to efficiently recover the unknown spikes from natural random initializations. We show that full recovery of all spikes is possible provided a number of sample scaling as $N^{p-2}$, matching the algorithmic threshold identified in the rank-one case [Ben Arous, Gheissari, Jagannath 2020, 2021]. Our results are obtained through a detailed analysis of a low-dimensional system that describes the evolution of the correlations between the estimators and the spikes, while controlling the noise in the dynamics. We find that the spikes are recovered sequentially in a process we term "sequential elimination": once a correlation exceeds a critical threshold, all correlations sharing a row or column index become sufficiently small, allowing the next correlation to grow and become macroscopic. The order in which correlations become macroscopic depends on their initial values and the corresponding SNRs, leading to either exact recovery or recovery of a permutation of the spikes. In the matrix case, when $p=2$, if the SNRs are sufficiently separated, we achieve exact recovery of the spikes, whereas equal SNRs lead to recovery of the subspace spanned by the spikes.

This research paper presents the development of an AI model utilizing YOLOv8 for real-time weapon detection, aimed at enhancing safety in public spaces such as schools, airports, and public transportation systems. As incidents of violence continue to rise globally, there is an urgent need for effective surveillance technologies that can quickly identify potential threats. Our approach focuses on leveraging advanced deep learning techniques to create a highly accurate and efficient system capable of detecting weapons in real-time video streams. The model was trained on a comprehensive dataset containing thousands of images depicting various types of firearms and edged weapons, ensuring a robust learning process. We evaluated the model's performance using key metrics such as precision, recall, F1-score, and mean Average Precision (mAP) across multiple Intersection over Union (IoU) thresholds, revealing a significant capability to differentiate between weapon and non-weapon classes with minimal error. Furthermore, we assessed the system's operational efficiency, demonstrating that it can process frames at high speeds suitable for real-time applications. The findings indicate that our YOLOv8-based weapon detection model not only contributes to the existing body of knowledge in computer vision but also addresses critical societal needs for improved safety measures in vulnerable environments. By harnessing the power of artificial intelligence, this research lays the groundwork for developing practical solutions that can be deployed in security settings, ultimately enhancing the protective capabilities of law enforcement and public safety agencies.

Performative prediction (PP) is a framework that captures distribution shifts that occur during the training of machine learning models due to their deployment. As the trained model is used, its generated data could cause the model to evolve, leading to deviations from the original data distribution. The impact of such model-induced distribution shifts in the federated learning (FL) setup remains unexplored despite being increasingly likely to transpire in real-life use cases. Although Jin et al. (2024) recently extended PP to FL in a straightforward manner, the resulting model only converges to a performative stable point, which may be far from optimal. The methods in Izzo et al. (2021); Miller et al. (2021) can find a performative optimal point in centralized settings, but they require the performative risk to be convex and the training data to be noiseless, assumptions often violated in realistic FL systems. This paper overcomes all of these shortcomings and proposes Performative robust optimal Federated Learning (ProFL), an algorithm that finds performative optimal points in FL from noisy and contaminated data. We present the convergence analysis under the Polyak-Lojasiewicz condition, which applies to non-convex objectives. Extensive experiments on multiple datasets validate our proposed algorithms' efficiency.

We present a probabilistic ranking model to identify the optimal treatment in multiple-response experiments. In contemporary practice, treatments are applied over individuals with the goal of achieving multiple ideal properties on them simultaneously. However, often there are competing properties, and the optimality of one cannot be achieved without compromising the optimality of another. Typically, we still want to know which treatment is the overall best. In our framework, we first formulate overall optimality in terms of treatment ranks. Then we infer the latent ranking that allow us to report treatments from optimal to least optimal, provided ideal desirable properties. We demonstrate through simulations and real data analysis how we can achieve reliability of inferred ranks in practice. We adopt a Bayesian approach and derive an associated Markov Chain Monte Carlo algorithm to fit our model to data. Finally, we discuss the prospects of adoption of our method as a standard tool for experiment evaluation in trials-based research.

Model selection is the process of choosing from a class of candidate models given data. For instance, methods such as the LASSO and sparse identification of nonlinear dynamics (SINDy) formulate model selection as finding a sparse solution to a linear system of equations determined by training data. However, absent strong assumptions, such methods are highly unstable: if a single data point is removed from the training set, a different model may be selected. This paper presents a new approach to stabilizing model selection that leverages a combination of bagging and an "inflated" argmax operation. Our method selects a small collection of models that all fit the data, and it is stable in that, with high probability, the removal of any training point will result in a collection of selected models that overlaps with the original collection. In addition to developing theoretical guarantees, we illustrate this method in (a) a simulation in which strongly correlated covariates make standard LASSO model selection highly unstable and (b) a Lotka-Volterra model selection problem focused on identifying how competition in an ecosystem influences species' abundances. In both settings, the proposed method yields stable and compact collections of selected models, outperforming a variety of benchmarks.