While most existing federated learning (FL) approaches assume a fixed set of clients in the system, in practice, clients can dynamically leave or join the system depending on their needs or interest in the specific task. This dynamic FL setting introduces several key challenges: (1) the objective function dynamically changes depending on the current set of clients, unlike traditional FL approaches that maintain a static optimization goal; (2) the current global model may not serve as the best initial point for the next FL rounds and could potentially lead to slow adaptation, given the possibility of clients leaving or joining the system. In this paper, we consider a dynamic optimization objective in FL that seeks the optimal model tailored to the currently active set of clients. Building on our probabilistic framework that provides direct insights into how the arrival and departure of different types of clients influence the shifts in optimal points, we establish an upper bound on the optimality gap, accounting for factors such as stochastic gradient noise, local training iterations, non-IIDness of data distribution, and deviations between optimal points caused by dynamic client pattern. The proposed approach is validated on various datasets and FL algorithms, demonstrating robust performance across diverse client arrival and departure patterns, underscoring its effectiveness in dynamic FL environments. Federated learning (FL) is a decentralized machine learning paradigm that facilitates collaborative model training across multiple clients, such as smartphones and Internet of Things (IoT) clients, without exchanging individual data. Instead of transmitting raw data to the central server, each client performs local training using its proprietary data, sending only model updates to the server.

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple samples from the posterior which is time-consuming. In this work, by analyzing the probability density evolution of the conditional reverse diffusion process, we prove that the posterior mean can be achieved by tracking the mean of each reverse diffusion step. Based on that, we establish a framework termed reverse mean propagation (RMP) that targets the posterior mean directly. We show that RMP can be implemented by solving a variational inference problem, which can be further decomposed as minimizing a reverse KL divergence at each reverse step. We further develop an algorithm that optimizes the reverse KL divergence with natural gradient descent using score functions and propagates the mean at each reverse step. Experiments demonstrate the validity of the theory of our framework and show that our algorithm outperforms state-of-the-art algorithms on reconstruction performance with lower computational complexity in various inverse problems.

The Greenland Ice Sheet (GrIS) has emerged as a significant contributor to global sea level rise, primarily due to increased meltwater runoff. Supraglacial lakes, which form on the ice sheet surface during the summer months, can impact ice sheet dynamics and mass loss; thus, better understanding these lakes' seasonal evolution and dynamics is an important task. This study presents a computationally efficient time series classification approach that uses Gaussian Mixture Models (GMMs) of the Reconstructed Phase Spaces (RPSs) to identify supraglacial lakes based on their seasonal evolution: 1) those that refreeze at the end of the melt season, 2) those that drain during the melt season, and 3) those that become buried, remaining liquid insulated a few meters beneath the surface. Our approach uses time series data from the Sentinel-1 and Sentinel-2 satellites, which utilize microwave and visible radiation, respectively. Evaluated on a GrIS-wide dataset, the RPS-GMM model, trained on a single representative sample per class, achieves 85.46% accuracy with Sentinel-1 data alone and 89.70% with combined Sentinel-1 and Sentinel-2 data. This performance significantly surpasses existing machine learning and deep learning models which require a large training data. The results demonstrate the robustness of the RPS-GMM model in capturing the complex temporal dynamics of supraglacial lakes with minimal training data.

Temporal point processes (TPPs) are effective for modeling event occurrences over time, but they struggle with sparse and uncertain events in federated systems, where privacy is a major concern. To address this, we propose \textit{FedPP}, a Federated neural nonparametric Point Process model. FedPP integrates neural embeddings into Sigmoidal Gaussian Cox Processes (SGCPs) on the client side, which is a flexible and expressive class of TPPs, allowing it to generate highly flexible intensity functions that capture client-specific event dynamics and uncertainties while efficiently summarizing historical records. For global aggregation, FedPP introduces a divergence-based mechanism that communicates the distributions of SGCPs' kernel hyperparameters between the server and clients, while keeping client-specific parameters local to ensure privacy and personalization. FedPP effectively captures event uncertainty and sparsity, and extensive experiments demonstrate its superior performance in federated settings, particularly with KL divergence and Wasserstein distance-based global aggregation.

The demand of modeling and forecasting high-dimensional matrix time series brings the opportunities with challenges. Let Y t " p y i,j,tq be a p ˆ q matrix recorded at time t, where y i,j,trepresents the value of, for example, the j -th variable on the i -th individual at time t . A popular approach to model Y t in the existing literature is via the so-called Tucker decomposition, namely the matrix Tucker-factor model. See, for example, Wang et al. (2019), Chen et al. (2020) and Chen and Chen (2022). It represents a high-dimensional matrix time series as a linear combination of a lower-dimensional matrix process. The Tucker decomposition can be viewed as a natural extension of the factor model for vector time series considered in Lam and Yao (2012) and Chang et al. (2015). Similarly we can only identify the factor loading spaces (the linear spaces spanned by the columns of the factor loading matrices) in the matrix Tucker-factor model while the factor loading matrices themselves are not uniquely defined. Parallel to the Tucker decomposition for matrix time series Y t, Chang et al. (2023) and Han et al. (2024) consider to model Y t via the so-called canonical polyadic (CP) decomposition, namely the matrix CP-factor model. It provides a more comprehensive dimensionality reduction as the dynamic structure of a matrix time series is driven by a vector process rather than a matrix process. Furthermore the factor loading matrices in the matrix CP-factor model can be identified uniquely upto the column reflection and permutation indeterminacy under some regularity conditions. The CP-factor model for matrix time series specified in Chang et al. (2023) admits the form Y t " AX tB J ` ε t, t ě 1, (1) where X t " diag p x tq with x t " p x t, 1, .. .

Aiming to incrementally learn new classes with only few samples while preserving the knowledge of base (old) classes, few-shot class-incremental learning (FSCIL) faces several challenges, such as overfitting and catastrophic forgetting. Such a challenging problem is often tackled by fixing a feature extractor trained on base classes to reduce the adverse effects of overfitting and forgetting. Under such formulation, our primary focus is representation learning on base classes to tackle the unique challenge of FSCIL: simultaneously achieving the transferability and the discriminability of the learned representation. Building upon the recent efforts for enhancing transferability, such as promoting the spread of features, we find that trying to secure the spread of features within a more confined feature space enables the learned representation to strike a better balance between transferability and discriminability. Thus, in stark contrast to prior beliefs that the inter-class distance should be maximized, we claim that the closer different classes are, the better for FSCIL. The empirical results and analysis from the perspective of information bottleneck theory justify our simple yet seemingly counter-intuitive representation learning method, raising research questions and suggesting alternative research directions. The code is available at https://github.com/JungHunOh/CLOSER_ECCV2024.

Recent advances in artificial intelligence have been fueled by the development of foundation models such as BERT, GPT, T5, and Vision Transformers. These models are first pretrained on vast and diverse datasets and then adapted to specific downstream tasks, often with significantly less data. However, the mechanisms behind the success of this ubiquitous pretrain-then-adapt paradigm remain underexplored, particularly the characteristics of pretraining checkpoints that lend themselves to good downstream adaptation. We introduce a Bayesian model selection criterion, called the downstream free energy, which quantifies a checkpoint's adaptability by measuring the concentration of nearby favorable parameters for the downstream task. We demonstrate that this free energy criterion can be effectively implemented without access to the downstream data or prior knowledge of the downstream task. Furthermore, we provide empirical evidence that the free energy criterion reliably correlates with improved fine-tuning performance, offering a principled approach to predicting model adaptability. The advent of foundation models has significantly reshaped the landscape of modern machine learning (Bommasani et al., 2021).

Federated learning has emerged in the last decade as a distributed optimization paradigm due to the rapidly increasing number of portable devices able to support the heavy computational needs related to the training of machine learning models. Federated learning utilizes gradient-based optimization to minimize a loss objective shared across participating agents. To the best of our knowledge, the literature mostly lacks elegant solutions that naturally harness the reciprocal statistical similarity between clients to redesign the optimization procedure. To address this gap, by conceiving the federated network as a similarity graph, we propose a novel modified framework wherein each client locally performs a perturbed gradient step leveraging prior information about other statistically affine clients. We theoretically prove that our procedure, due to a suitably introduced adaptation in the update rule, achieves a quantifiable speedup concerning the exponential contraction factor in the strongly convex case compared with popular algorithms FedAvg and FedProx, here analyzed as baselines. Lastly, we legitimize our conclusions through experimental results on the CIFAR10 and FEMNIST datasets, where we show that our algorithm speeds convergence up to a margin of 30 global rounds compared with FedAvg while modestly improving generalization on unseen data in heterogeneous settings.

Knowledge distillation leverages a teacher model to improve the training of a student model. A persistent challenge is that a better teacher does not always yield a better student, to which a common mitigation is to use additional supervision from several ``intermediate'' teachers. One empirically validated variant of this principle is progressive distillation, where the student learns from successive intermediate checkpoints of the teacher. Using sparse parity as a sandbox, we identify an implicit curriculum as one mechanism through which progressive distillation accelerates the student's learning. This curriculum is available only through the intermediate checkpoints but not the final converged one, and imparts both empirical acceleration and a provable sample complexity benefit to the student. We then extend our investigation to Transformers trained on probabilistic context-free grammars (PCFGs) and real-world pre-training datasets (Wikipedia and Books). Through probing the teacher model, we identify an analogous implicit curriculum where the model progressively learns features that capture longer context. Our theoretical and empirical findings on sparse parity, complemented by empirical observations on more complex tasks, highlight the benefit of progressive distillation via implicit curriculum across setups.

A central problem related to transformers can be stated as follows: given two $n \times d$ matrices $Q$ and $K$, and a non-negative function $f$, define the matrix $A$ as follows: (1) apply the function $f$ to each entry of the $n \times n$ matrix $Q K^T$, and then (2) normalize each of the row sums of $A$ to be equal to $1$. The matrix $A$ can be computed in $O(n^2 d)$ time assuming $f$ can be applied to a number in constant time, but the quadratic dependence on $n$ is prohibitive in applications where it corresponds to long context lengths. For a large class of functions $f$, we show how to find all the ``large attention scores", i.e., entries of $A$ which are at least a positive value $\varepsilon$, in time with linear dependence on $n$ (i.e., $n \cdot \textrm{poly}(d/\varepsilon)$) for a positive parameter $\varepsilon > 0$. Our class of functions include all functions $f$ of the form $f(x) = |x|^p$, as explored recently in transformer models. Using recently developed tools from randomized numerical linear algebra, we prove that for any $K$, there is a ``universal set" $U \subset [n]$ of size independent of $n$, such that for any $Q$ and any row $i$, the large attention scores $A_{i,j}$ in row $i$ of $A$ all have $j \in U$. We also find $U$ in $n \cdot \textrm{poly}(d/\varepsilon)$ time. Notably, we (1) make no assumptions on the data, (2) our workspace does not grow with $n$, and (3) our algorithms can be computed in streaming and parallel settings. We call the attention mechanism that uses only the subset of keys in the universal set as LevAttention since our algorithm to identify the universal set $U$ is based on leverage scores. We empirically show the benefits of our scheme for vision transformers, showing how to train new models that use our universal set while training as well, showing that our model is able to consistently select ``important keys'' during training.