Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for these activation functions is that without them, neural networks only can model a line. However, a novel explanation we propose in this paper for the impracticality of neural networks without activation functions, or linear neural networks, is that they actually reduce both training and testing performance. Having more parameters makes LNNs harder to optimize, and thus they require more training iterations than linear regression to even potentially converge to the optimal solution. We prove this hypothesis through an analysis of the optimization of an LNN and rigorous testing comparing the performance between both LNNs and linear regression on synthethic, noisy datasets.

The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive capabilities and show great potential for data-driven modeling of complex physical systems. However, a critical and yet unaddressed challenge lies in the quantification of inherent uncertainties stemming from multiple sources. Addressing this gap, we introduce a novel method, DiffHybrid-UQ, for effective and efficient uncertainty propagation and estimation in hybrid neural differentiable models, leveraging the strengths of deep ensemble Bayesian learning and nonlinear transformations. Specifically, our approach effectively discerns and quantifies both aleatoric uncertainties, arising from data noise, and epistemic uncertainties, resulting from model-form discrepancies and data sparsity. This is achieved within a Bayesian model averaging framework, where aleatoric uncertainties are modeled through hybrid neural models. The unscented transformation plays a pivotal role in enabling the flow of these uncertainties through the nonlinear functions within the hybrid model. In contrast, epistemic uncertainties are estimated using an ensemble of stochastic gradient descent (SGD) trajectories. This approach offers a practical approximation to the posterior distribution of both the network parameters and the physical parameters. Notably, the DiffHybrid-UQ framework is designed for simplicity in implementation and high scalability, making it suitable for parallel computing environments. The merits of the proposed method have been demonstrated through problems governed by both ordinary and partial differentiable equations.

In this paper, we present a comprehensive survey on online test-time adaptation (OTTA), a paradigm focused on adapting machine learning models to novel data distributions upon batch arrival. Despite the proliferation of OTTA methods recently, the field is mired in issues like ambiguous settings, antiquated backbones, and inconsistent hyperparameter tuning, obfuscating the real challenges and making reproducibility elusive. For clarity and a rigorous comparison, we classify OTTA techniques into three primary categories and subject them to benchmarks using the potent Vision Transformer (ViT) backbone to discover genuinely effective strategies. Our benchmarks span not only conventional corrupted datasets such as CIFAR-10/100-C and ImageNet-C but also real-world shifts embodied in CIFAR-10.1 and CIFAR-10-Warehouse, encapsulating variations across search engines and synthesized data by diffusion models. To gauge efficiency in online scenarios, we introduce novel evaluation metrics, inclusive of FLOPs, shedding light on the trade-offs between adaptation accuracy and computational overhead. Our findings diverge from existing literature, indicating: (1) transformers exhibit heightened resilience to diverse domain shifts, (2) the efficacy of many OTTA methods hinges on ample batch sizes, and (3) stability in optimization and resistance to perturbations are critical during adaptation, especially when the batch size is 1. Motivated by these insights, we pointed out promising directions for future research. The source code is made available: https://github.com/Jo-wang/OTTA_ViT_survey.

Accumulated Local Effects (ALE) is a model-agnostic approach for global explanations of the results of black-box machine learning (ML) algorithms. There are at least three challenges with conducting statistical inference based on ALE: ensuring the reliability of ALE analyses, especially in the context of small datasets; intuitively characterizing a variable's overall effect in ML; and making robust inferences from ML data analysis. In response, we introduce innovative tools and techniques for statistical inference using ALE, establishing bootstrapped confidence intervals tailored to dataset size and introducing ALE effect size measures that intuitively indicate effects on both the outcome variable scale and a normalized scale. Furthermore, we demonstrate how to use these tools to draw reliable statistical inferences, reflecting the flexible patterns ALE adeptly highlights, with implementations available in the 'ale' package in R. This work propels the discourse on ALE and its applicability in ML and statistical analysis forward, offering practical solutions to prevailing challenges in the field.

In the intricate architecture of the mammalian central nervous system, neurons form populations. Axonal bundles communicate between these clusters using spike trains. However, these neuron populations' precise encoding and operations have yet to be discovered. In our analysis, the starting point is a state-of-the-art mechanistic model of a generic neuron endowed with plasticity. From this simple framework emerges a subtle mathematical construct: The representation and manipulation of information can be precisely characterized by an algebra of convex cones. Furthermore, these neuron populations are not merely passive transmitters. They act as operators within this algebraic structure, mirroring the functionality of a low-level programming language. When these populations interconnect, they embody succinct yet potent algebraic expressions. These networks allow them to implement many operations, such as specialization, generalization, novelty detection, dimensionality reduction, inverse modeling, prediction, and associative memory. In broader terms, this work illuminates the potential of matrix embeddings in advancing our understanding in fields like cognitive science and AI. These embeddings enhance the capacity for concept processing and hierarchical description over their vector counterparts.

Federated learning has gained significant attention due to its groundbreaking ability to enable distributed learning while maintaining privacy constraints. However, as a consequence of data heterogeneity among decentralized devices, it inherently experiences significant learning degradation and slow convergence speed. Therefore, it is natural to employ the concept of clustering homogeneous clients into the same group, allowing only the model weights within each group to be aggregated. While most existing clustered federated learning methods employ either model gradients or inference outputs as metrics for client partitioning, with the goal of grouping similar devices together, may still have heterogeneity within each cluster. Moreover, there is a scarcity of research exploring the underlying reasons for determining the appropriate timing for clustering, resulting in the common practice of assigning each client to its own individual cluster, particularly in the context of highly non independent and identically distributed (Non-IID) data. In this paper, we introduce a two-stage decoupling federated learning algorithm with adaptive personalization layers named FedTSDP, where client clustering is performed twice according to inference outputs and model weights, respectively. Hopkins amended sampling is adopted to determine the appropriate timing for clustering and the sampling weight of public unlabeled data. In addition, a simple yet effective approach is developed to adaptively adjust the personalization layers based on varying degrees of data skew. Experimental results show that our proposed method has reliable performance on both IID and non-IID scenarios.

Federated learning (FL) provides an efficient paradigm to jointly train a global model leveraging data from distributed users. As local training data comes from different users who may not be trustworthy, several studies have shown that FL is vulnerable to poisoning attacks. Meanwhile, to protect the privacy of local users, FL is usually trained in a differentially private way (DPFL). Thus, in this paper, we ask: What are the underlying connections between differential privacy and certified robustness in FL against poisoning attacks? Can we leverage the innate privacy property of DPFL to provide certified robustness for FL? Can we further improve the privacy of FL to improve such robustness certification? We first investigate both user-level and instance-level privacy of FL and provide formal privacy analysis to achieve improved instance-level privacy. We then provide two robustness certification criteria: certified prediction and certified attack inefficacy for DPFL on both user and instance levels. Theoretically, we provide the certified robustness of DPFL based on both criteria given a bounded number of adversarial users or instances. Empirically, we conduct extensive experiments to verify our theories under a range of poisoning attacks on different datasets. We find that increasing the level of privacy protection in DPFL results in stronger certified attack inefficacy; however, it does not necessarily lead to a stronger certified prediction. Thus, achieving the optimal certified prediction requires a proper balance between privacy and utility loss.

Federated learning (FL) enables distributed resource-constrained devices to jointly train shared models while keeping the training data local for privacy purposes. Vertical FL (VFL), which allows each client to collect partial features, has attracted intensive research efforts recently. We identified the main challenges that existing VFL frameworks are facing: the server needs to communicate gradients with the clients for each training step, incurring high communication cost that leads to rapid consumption of privacy budgets. To address these challenges, in this paper, we introduce a VFL framework with multiple heads (VIM), which takes the separate contribution of each client into account, and enables an efficient decomposition of the VFL optimization objective to sub-objectives that can be iteratively tackled by the server and the clients on their own. In particular, we propose an Alternating Direction Method of Multipliers (ADMM)-based method to solve our optimization problem, which allows clients to conduct multiple local updates before communication, and thus reduces the communication cost and leads to better performance under differential privacy (DP). We provide the user-level DP mechanism for our framework to protect user privacy. Moreover, we show that a byproduct of VIM is that the weights of learned heads reflect the importance of local clients. We conduct extensive evaluations and show that on four vertical FL datasets, VIM achieves significantly higher performance and faster convergence compared with the state-of-the-art. We also explicitly evaluate the importance of local clients and show that VIM enables functionalities such as client-level explanation and client denoising. We hope this work will shed light on a new way of effective VFL training and understanding.

Quantification of behavior is critical in applications ranging from neuroscience, veterinary medicine and animal conservation efforts. A common key step for behavioral analysis is first extracting relevant keypoints on animals, known as pose estimation. However, reliable inference of poses currently requires domain knowledge and manual labeling effort to build supervised models. We present a series of technical innovations that enable a new method, collectively called SuperAnimal, to develop unified foundation models that can be used on over 45 species, without additional human labels. Concretely, we introduce a method to unify the keypoint space across differently labeled datasets (via our generalized data converter) and for training these diverse datasets in a manner such that they don't catastrophically forget keypoints given the unbalanced inputs (via our keypoint gradient masking and memory replay approaches). These models show excellent performance across six pose benchmarks. Then, to ensure maximal usability for end-users, we demonstrate how to fine-tune the models on differently labeled data and provide tooling for unsupervised video adaptation to boost performance and decrease jitter across frames. If the models are fine-tuned, we show SuperAnimal models are 10-100$\times$ more data efficient than prior transfer-learning-based approaches. We illustrate the utility of our models in behavioral classification in mice and gait analysis in horses. Collectively, this presents a data-efficient solution for animal pose estimation.

Diffusion-based generative models have achieved remarkable success in various domains. It trains a shared model on denoising tasks that encompass different noise levels simultaneously, representing a form of multi-task learning (MTL). However, analyzing and improving diffusion models from an MTL perspective remains under-explored. In particular, MTL can sometimes lead to the well-known phenomenon of negative transfer, which results in the performance degradation of certain tasks due to conflicts between tasks. In this paper, we first aim to analyze diffusion training from an MTL standpoint, presenting two key observations: (O1) the task affinity between denoising tasks diminishes as the gap between noise levels widens, and (O2) negative transfer can arise even in diffusion training. Building upon these observations, we aim to enhance diffusion training by mitigating negative transfer. To achieve this, we propose leveraging existing MTL methods, but the presence of a huge number of denoising tasks makes this computationally expensive to calculate the necessary per-task loss or gradient. To address this challenge, we propose clustering the denoising tasks into small task clusters and applying MTL methods to them. Specifically, based on (O2), we employ interval clustering to enforce temporal proximity among denoising tasks within clusters. We show that interval clustering can be solved using dynamic programming, utilizing signal-to-noise ratio, timestep, and task affinity for clustering objectives. Through this, our approach addresses the issue of negative transfer in diffusion models by allowing for efficient computation of MTL methods. We validate the efficacy of proposed clustering and its integration with MTL methods through various experiments, demonstrating 1) improved generation quality and 2) faster training convergence of diffusion models.