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We introduce the concept of inverse feasibility for linear forward models as a tool to enhance OTA FL algorithms. Inverse feasibility is defined as an upper bound on the condition number of the forward operator as a function of its parameters. We analyze an existing OTA FL model using this definition, identify areas for improvement, and propose a new OTA FL model. Numerical experiments illustrate the main implications of the theoretical results. The proposed framework, which is based on inverse problem theory, can potentially complement existing notions of security and privacy by providing additional desirable characteristics to networks.

In-context learning has emerged as a groundbreaking ability of Large Language Models (LLMs) and revolutionized various fields by providing a few task-relevant demonstrations in the prompt. However, trustworthy issues with LLM's response, such as hallucination, have also been actively discussed. Existing works have been devoted to quantifying the uncertainty in LLM's response, but they often overlook the complex nature of LLMs and the uniqueness of in-context learning. In this work, we delve into the predictive uncertainty of LLMs associated with in-context learning, highlighting that such uncertainties may stem from both the provided demonstrations (aleatoric uncertainty) and ambiguities tied to the model's configurations (epistemic uncertainty). We propose a novel formulation and corresponding estimation method to quantify both types of uncertainties. The proposed method offers an unsupervised way to understand the prediction of in-context learning in a plug-and-play fashion. Extensive experiments are conducted to demonstrate the effectiveness of the decomposition. The code and data are available at: \url{//github.com/lingchen0331/UQ_ICL}.

This paper presents a new generalization error analysis for Decentralized Stochastic Gradient Descent (D-SGD) based on algorithmic stability. The obtained results overhaul a series of recent works that suggested an increased instability due to decentralization and a detrimental impact of poorly-connected communication graphs on generalization. On the contrary, we show, for convex, strongly convex and non-convex functions, that D-SGD can always recover generalization bounds analogous to those of classical SGD, suggesting that the choice of graph does not matter. We then argue that this result is coming from a worst-case analysis, and we provide a refined data-dependent generalization bound for general convex functions. This new bound reveals that the choice of graph can in fact improve the worst-case bound in certain regimes, and that surprisingly, a poorly-connected graph can even be beneficial.

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self-attention, positional encoding and feed-forward layer, affect its expressive power, and we study their combined effects through establishing explicit approximation rates. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads, and these insights also provide natural suggestions for alternative architectures.

The paper presents an approach to the modelling of epistemic uncertainty in Conjunction Data Messages (CDM) and the classification of conjunction events according to the confidence in the probability of collision. The approach proposed in this paper is based on the Dempster-Shafer Theory (DSt) of evidence and starts from the assumption that the observed CDMs are drawn from a family of unknown distributions. The Dvoretzky-Kiefer-Wolfowitz (DKW) inequality is used to construct robust bounds on such a family of unknown distributions starting from a time series of CDMs. A DSt structure is then derived from the probability boxes constructed with DKW inequality. The DSt structure encapsulates the uncertainty in the CDMs at every point along the time series and allows the computation of the belief and plausibility in the realisation of a given probability of collision. The methodology proposed in this paper is tested on a number of real events and compared against existing practices in the European and French Space Agencies. We will show that the classification system proposed in this paper is more conservative than the approach taken by the European Space Agency but provides an added quantification of uncertainty in the probability of collision.

Modern policy optimization methods in reinforcement learning, such as TRPO and PPO, owe their success to the use of parameterized policies. However, while theoretical guarantees have been established for this class of algorithms, especially in the tabular setting, the use of general parameterization schemes remains mostly unjustified. In this work, we introduce a novel framework for policy optimization based on mirror descent that naturally accommodates general parameterizations. The policy class induced by our scheme recovers known classes, e.g., softmax, and generates new ones depending on the choice of mirror map. Using our framework, we obtain the first result that guarantees linear convergence for a policy-gradient-based method involving general parameterization. To demonstrate the ability of our framework to accommodate general parameterization schemes, we provide its sample complexity when using shallow neural networks, show that it represents an improvement upon the previous best results, and empirically validate the effectiveness of our theoretical claims on classic control tasks.

Variable projection methods prove highly efficient in solving separable nonlinear least squares problems by transforming them into a reduced nonlinear least squares problem, typically solvable via the Gauss-Newton method. When solving large-scale separable nonlinear inverse problems with general-form Tikhonov regularization, the computational demand for computing Jacobians in the Gauss-Newton method becomes very challenging. To mitigate this, iterative methods, specifically LSQR, can be used as inner solvers to compute approximate Jacobians. This article analyzes the impact of these approximate Jacobians within the variable projection method and introduces stopping criteria to ensure convergence. We also present numerical experiments where we apply the proposed method to solve a blind deconvolution problem to illustrate and confirm our theoretical results.

This study assesses deep learning models for audio classification in a clinical setting with the constraint of small datasets reflecting real-world prospective data collection. We analyze CNNs, including DenseNet and ConvNeXt, alongside transformer models like ViT, SWIN, and AST, and compare them against pre-trained audio models such as YAMNet and VGGish. Our method highlights the benefits of pre-training on large datasets before fine-tuning on specific clinical data. We prospectively collected two first-of-their-kind patient audio datasets from stroke patients. We investigated various preprocessing techniques, finding that RGB and grayscale spectrogram transformations affect model performance differently based on the priors they learn from pre-training. Our findings indicate CNNs can match or exceed transformer models in small dataset contexts, with DenseNet-Contrastive and AST models showing notable performance. This study highlights the significance of incremental marginal gains through model selection, pre-training, and preprocessing in sound classification; this offers valuable insights for clinical diagnostics that rely on audio classification.

The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.

Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering and recommendation systems, etc. According to the graph types, the existing KGR models can be roughly divided into three categories, \textit{i.e.,} static models, temporal models, and multi-modal models. The early works in this domain mainly focus on static KGR and tend to directly apply general knowledge graph embedding models to the reasoning task. However, these models are not suitable for more complex but practical tasks, such as inductive static KGR, temporal KGR, and multi-modal KGR. To this end, multiple works have been developed recently, but no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the preliminaries, summaries of KGR models, and typical datasets are introduced and discussed consequently. Moreover, we discuss the challenges and potential opportunities. The corresponding open-source repository is shared on GitHub: //github.com/LIANGKE23/Awesome-Knowledge-Graph-Reasoning.