Class-attribute Priors: Adapting Optimization to Heterogeneity and Fairness Objective

Modern classification problems exhibit heterogeneities across individual classes: Each class may have unique attributes, such as sample size, label quality, or predictability (easy vs difficult), and variable importance at test-time. Without care, these heterogeneities impede the learning process, most notably, when optimizing fairness objectives. Confirming this, under a gaussian mixture setting, we show that the optimal SVM classifier for balanced accuracy needs to be adaptive to the class attributes. This motivates us to propose CAP: An effective and general method that generates a class-specific learning strategy (e.g. hyperparameter) based on the attributes of that class. This way, optimization process better adapts to heterogeneities. CAP leads to substantial improvements over the naive approach of assigning separate hyperparameters to each class. We instantiate CAP for loss function design and post-hoc logit adjustment, with emphasis on label-imbalanced problems. We show that CAP is competitive with prior art and its flexibility unlocks clear benefits for fairness objectives beyond balanced accuracy. Finally, we evaluate CAP on problems with label noise as well as weighted test objectives to showcase how CAP can jointly adapt to different heterogeneities.

FedYolo: Augmenting Federated Learning with Pretrained Transformers

The growth and diversity of machine learning applications motivate a rethinking of learning with mobile and edge devices. How can we address diverse client goals and learn with scarce heterogeneous data? While federated learning aims to address these issues, it has challenges hindering a unified solution. Large transformer models have been shown to work across a variety of tasks achieving remarkable few-shot adaptation. This raises the question: Can clients use a single general-purpose model, rather than custom models for each task, while obeying device and network constraints? In this work, we investigate pretrained transformers (PTF) to achieve these on-device learning goals and thoroughly explore the roles of model size and modularity, where the latter refers to adaptation through modules such as prompts or adapters. Focusing on federated learning, we demonstrate that: (1) Larger scale shrinks the accuracy gaps between alternative approaches and improves heterogeneity robustness. Scale allows clients to run more local SGD epochs which can significantly reduce the number of communication rounds. At the extreme, clients can achieve respectable accuracy locally highlighting the potential of fully-local learning. (2) Modularity, by design, enables $>$100$\times$ less communication in bits. Surprisingly, it also boosts the generalization capability of local adaptation methods and the robustness of smaller PTFs. Finally, it enables clients to solve multiple unrelated tasks simultaneously using a single PTF, whereas full updates are prone to catastrophic forgetting. These insights on scale and modularity motivate a new federated learning approach we call "You Only Load Once" (FedYolo): The clients load a full PTF model once and all future updates are accomplished through communication-efficient modules with limited catastrophic-forgetting, where each task is assigned to its own module.

Max-Margin Token Selection in Attention Mechanism

Attention mechanism is a central component of the transformer architecture which led to the phenomenal success of large language models. However, the theoretical principles underlying the attention mechanism are poorly understood, especially its nonconvex optimization dynamics. In this work, we explore the seminal softmax-attention model $f(\boldsymbol{X})=\langle \boldsymbol{Xv}, \texttt{softmax}(\boldsymbol{XWp})\rangle$, where $\boldsymbol{X}$ is the token sequence and $(\boldsymbol{v},\boldsymbol{W},\boldsymbol{p})$ are trainable parameters. We prove that running gradient descent on $\boldsymbol{p}$, or equivalently $\boldsymbol{W}$, converges in direction to a max-margin solution that separates $\textit{locally-optimal}$ tokens from non-optimal ones. This clearly formalizes attention as an optimal token selection mechanism. Remarkably, our results are applicable to general data and precisely characterize $\textit{optimality}$ of tokens in terms of the value embeddings $\boldsymbol{Xv}$ and problem geometry. We also provide a broader regularization path analysis that establishes the margin maximizing nature of attention even for nonlinear prediction heads. When optimizing $\boldsymbol{v}$ and $\boldsymbol{p}$ simultaneously with logistic loss, we identify conditions under which the regularization paths directionally converge to their respective hard-margin SVM solutions where $\boldsymbol{v}$ separates the input features based on their labels. Interestingly, the SVM formulation of $\boldsymbol{p}$ is influenced by the support vector geometry of $\boldsymbol{v}$. Finally, we verify our theoretical findings via numerical experiments and provide insights.

Margin Maximization in Attention Mechanism

Attention mechanism is a central component of the transformer architecture which led to the phenomenal success of large language models. However, the theoretical principles underlying the attention mechanism are poorly understood, especially its nonconvex optimization dynamics. In this work, we explore the seminal softmax-attention model $f(\boldsymbol{X})=\langle \boldsymbol{Xv}, \texttt{softmax}(\boldsymbol{XWp})\rangle$, where, $\boldsymbol{X}$ is the token sequence and $(\boldsymbol{v},\boldsymbol{W},\boldsymbol{p})$ are tunable parameters. We prove that running gradient descent on $\boldsymbol{p}$, or equivalently $\boldsymbol{W}$, converges in direction to a max-margin solution that separates $\textit{locally-optimal}$ tokens from non-optimal ones. This clearly formalizes attention as a token separation mechanism. Remarkably, our results are applicable to general data and precisely characterize $\textit{optimality}$ of tokens in terms of the value embeddings $\boldsymbol{Xv}$ and problem geometry. We also provide a broader regularization path analysis that establishes the margin maximizing nature of attention even for nonlinear prediction heads. When optimizing $\boldsymbol{v}$ and $\boldsymbol{p}$ simultaneously with logistic loss, we identify conditions under which the regularization paths directionally converge to their respective hard-margin SVM solutions where $\boldsymbol{v}$ separates the input features based on their labels. Interestingly, the SVM formulation of $\boldsymbol{p}$ is influenced by the support vector geometry of $\boldsymbol{v}$. Finally, we verify our theoretical findings via numerical experiments and provide insights.

Learning on Manifolds: Universal Approximations Properties using Geometric Controllability Conditions for Neural ODEs

In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural ordinary differential equations (ODEs), however, typically fail to satisfy these manifold constraints and perform poorly for these applications. To address this shortcoming, in this paper we study a class of neural ordinary differential equations that, by design, leave a given manifold invariant, and characterize their properties by leveraging the controllability properties of control affine systems. In particular, using a result due to Agrachev and Caponigro on approximating diffeomorphisms with flows of feedback control systems, we show that any map that can be represented as the flow of a manifold-constrained dynamical system can also be approximated using the flow of manifold-constrained neural ODE, whenever a certain controllability condition is satisfied. Additionally, we show that this universal approximation property holds when the neural ODE has limited width in each layer, thus leveraging the depth of network instead for approximation. We verify our theoretical findings using numerical experiments on PyTorch for the manifolds S2 and the 3-dimensional orthogonal group SO(3), which are model manifolds for mechanical systems such as spacecrafts and satellites. We also compare the performance of the manifold invariant neural ODE with classical neural ODEs that ignore the manifold invariant properties and show the superiority of our approach in terms of accuracy and sample complexity.

AutoBalance: Optimized Loss Functions for Imbalanced Data

Imbalanced datasets are commonplace in modern machine learning problems. The presence of under-represented classes or groups with sensitive attributes results in concerns about generalization and fairness. Such concerns are further exacerbated by the fact that large capacity deep nets can perfectly fit the training data and appear to achieve perfect accuracy and fairness during training, but perform poorly during test. To address these challenges, we propose AutoBalance, a bi-level optimization framework that automatically designs a training loss function to optimize a blend of accuracy and fairness-seeking objectives. Specifically, a lower-level problem trains the model weights, and an upper-level problem tunes the loss function by monitoring and optimizing the desired objective over the validation data. Our loss design enables personalized treatment for classes/groups by employing a parametric cross-entropy loss and individualized data augmentation schemes. We evaluate the benefits and performance of our approach for the application scenarios of imbalanced and group-sensitive classification. Extensive empirical evaluations demonstrate the benefits of AutoBalance over state-of-the-art approaches. Our experimental findings are complemented with theoretical insights on loss function design and the benefits of train-validation split. All code is available open-source.

Post-hoc Models for Performance Estimation of Machine Learning Inference

Estimating how well a machine learning model performs during inference is critical in a variety of scenarios (for example, to quantify uncertainty, or to choose from a library of available models). However, the standard accuracy estimate of softmax confidence is not versatile and cannot reliably predict different performance metrics (e.g., F1-score, recall) or the performance in different application scenarios or input domains. In this work, we systematically generalize performance estimation to a diverse set of metrics and scenarios and discuss generalized notions of uncertainty calibration. We propose the use of post-hoc models to accomplish this goal and investigate design parameters, including the model type, feature engineering, and performance metric, to achieve the best estimation quality. Emphasis is given to object detection problems and, unlike prior work, our approach enables the estimation of per-image metrics such as recall and F1-score. Through extensive experiments with computer vision models and datasets in three use cases -- mobile edge offloading, model selection, and dataset shift -- we find that proposed post-hoc models consistently outperform the standard calibrated confidence baselines. To the best of our knowledge, this is the first work to develop a unified framework to address different performance estimation problems for machine learning inference.

Noise-Sampling Cross Entropy Loss: Improving Disparity Regression Via Cost Volume Aware Regularizer

Recent end-to-end deep neural networks for disparity regression have achieved the state-of-the-art performance. However, many well-acknowledged specific properties of disparity estimation are omitted in these deep learning algorithms. Especially, matching cost volume, one of the most important procedure, is treated as a normal intermediate feature for the following softargmin regression, lacking explicit constraints compared with those traditional algorithms. In this paper, inspired by previous canonical definition of cost volume, we propose the noise-sampling cross entropy loss function to regularize the cost volume produced by deep neural networks to be unimodal and coherent. Extensive experiments validate that the proposed noise-sampling cross entropy loss can not only help neural networks learn more informative cost volume, but also lead to better stereo matching performance compared with several representative algorithms.

Niose-Sampling Cross Entropy Loss: Improving Disparity Regression Via Cost Volume Aware Regularizer

Recent end-to-end deep neural networks for disparity regression have achieved the state-of-the-art performance. However, many well-acknowledged specific properties of disparity estimation are omitted in these deep learning algorithms. Especially, matching cost volume, one of the most important procedure, is treated as a normal intermediate feature for the following softargmin regression, lacking explicit constraints compared with those traditional algorithms. In this paper, inspired by previous canonical definition of cost volume, we propose the noise-sampling cross entropy loss function to regularize the cost volume produced by deep neural networks to be unimodal and coherent. Extensive experiments validate that the proposed noise-sampling cross entropy loss can not only help neural networks learn more informative cost volume, but also lead to better stereo matching performance compared with several representative algorithms.

LCSCNet: Linear Compressing Based Skip-Connecting Network for Image Super-Resolution

In this paper, we develop a concise but efficient network architecture called linear compressing based skip-connecting network (LCSCNet) for image super-resolution. Compared with two representative network architectures with skip connections, ResNet and DenseNet, a linear compressing layer is designed in LCSCNet for skip connection, which connects former feature maps and distinguishes them from newly-explored feature maps. In this way, the proposed LCSCNet enjoys the merits of the distinguish feature treatment of DenseNet and the parameter-economic form of ResNet. Moreover, to better exploit hierarchical information from both low and high levels of various receptive fields in deep models, inspired by gate units in LSTM, we also propose an adaptive element-wise fusion strategy with multi-supervised training. Experimental results in comparison with state-of-the-art algorithms validate the effectiveness of LCSCNet.