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  1. Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N,D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field. 
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  2. Recent years have witnessed significant progress in understanding the relationship between the connectivity of a deep network's architecture as a graph, and the network's performance. A few prior arts connected deep architectures to expander graphs or Ramanujan graphs, and particularly,[7] demonstrated the use of such graph connectivity measures with ranking and relative performance of various obtained sparse sub-networks (i.e. models with prune masks) without the need for training. However, no prior work explicitly explores the role of parameters in the graph's connectivity, making the graph-based understanding of prune masks and the magnitude/gradient-based pruning practice isolated from one another. This paper strives to fill in this gap, by analyzing the Weighted Spectral Gap of Ramanujan structures in sparse neural networks and investigates its correlation with final performance. We specifically examine the evolution of sparse structures under a popular dynamic sparse-to-sparse network training scheme, and intriguingly find that the generated random topologies inherently maximize Ramanujan graphs. We also identify a strong correlation between masks, performance, and the weighted spectral gap. Leveraging this observation, we propose to construct a new "full-spectrum coordinate'' aiming to comprehensively characterize a sparse neural network's promise. Concretely, it consists of the classical Ramanujan's gap (structure), our proposed weighted spectral gap (parameters), and the constituent nested regular graphs within. In this new coordinate system, a sparse subnetwork's L2-distance from its original initialization is found to have nearly linear correlated with its performance. Eventually, we apply this unified perspective to develop a new actionable pruning method, by sampling sparse masks to maximize the L2-coordinate distance. Our method can be augmented with the "pruning at initialization" (PaI) method, and significantly outperforms existing PaI methods. With only a few iterations of training (e.g 500 iterations), we can get LTH-comparable performance as that yielded via "pruning after training", significantly saving pre-training costs. Codes can be found at: 
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    Free, publicly-accessible full text available December 10, 2024
  3. The prosperity of deep learning and automated machine learning (AutoML) is largely rooted in the development of novel neural networks -- but what defines and controls the "goodness" of networks in an architecture space? Test accuracy, a golden standard in AutoML, is closely related to three aspects: (1) expressivity (how complicated functions a network can approximate over the training data); (2) convergence (how fast the network can reach low training error under gradient descent); (3) generalization (whether a trained network can be generalized from the training data to unseen samples with low test error). However, most previous theory papers focus on fixed model structures, largely ignoring sophisticated networks used in practice. To facilitate the interpretation and understanding of the architecture design by AutoML, we target connecting a bigger picture: how does the architecture jointly impact its expressivity, convergence, and generalization? We demonstrate the "no free lunch" behavior in networks from an architecture space: given a fixed budget on the number of parameters, there does not exist a single architecture that is optimal in all three aspects. In other words, separately optimizing expressivity, convergence, and generalization will achieve different networks in the architecture space. Our analysis can explain a wide range of observations in AutoML. Experiments on popular benchmarks confirm our theoretical analysis. Our codes are attached in the supplement. 
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    Free, publicly-accessible full text available September 15, 2024
  4. Free, publicly-accessible full text available October 1, 2024
  5. Abstract

    Deep learning has become a popular tool for computer-aided diagnosis using medical images, sometimes matching or exceeding the performance of clinicians. However, these models can also reflect and amplify human bias, potentially resulting inaccurate missed diagnoses. Despite this concern, the problem of improving model fairness in medical image classification by deep learning has yet to be fully studied. To address this issue, we propose an algorithm that leverages the marginal pairwise equal opportunity to reduce bias in medical image classification. Our evaluations across four tasks using four independent large-scale cohorts demonstrate that our proposed algorithm not only improves fairness in individual and intersectional subgroups but also maintains overall performance. Specifically, the relative change in pairwise fairness difference between our proposed model and the baseline model was reduced by over 35%, while the relative change in AUC value was typically within 1%. By reducing the bias generated by deep learning models, our proposed approach can potentially alleviate concerns about the fairness and reliability of image-based computer-aided diagnosis.

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    Free, publicly-accessible full text available December 1, 2024
  6. Free, publicly-accessible full text available July 23, 2024
  7. Many machine learning problems can be abstracted in solving game theory formulations and boil down to optimizing nested objectives, such as generative adversarial networks (GANs) and multi-agent reinforcement learning. Solving these games requires finding their stable fixed points or Nash equilibrium. However, existing algorithms for solving games suffer from empirical instability, hence demanding heavy ad-hoc tuning in practice. To tackle these challenges, we resort to the emerging scheme of Learning to Optimize (L2O), which discovers problem-specific efficient optimization algorithms through data-driven training. Our customized L2O framework for differentiable game theory problems, dubbed “Learning to Play Games" (L2PG), seeks a stable fixed point solution, by predicting the fast update direction from the past trajectory, with a novel gradient stability-aware, sign-based loss function. We further incorporate curriculum learning and self-learning to strengthen the empirical training stability and generalization of L2PG. On test problems including quadratic games and GANs, L2PG can substantially accelerate the convergence, and demonstrates a remarkably more stable trajectory. Codes are available at 
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    Free, publicly-accessible full text available July 1, 2024
  8. Federated learning (FL) emerges as a popular distributed learning schema that learns a model from a set of participating users without sharing raw data. One major challenge of FL comes with heterogeneous users, who may have distributionally different (or non-iid) data and varying computation resources. As federated users would use the model for prediction, they often demand the trained model to be robust against malicious attackers at test time. Whereas adversarial training (AT) provides a sound solution for centralized learning, extending its usage for federated users has imposed significant challenges, as many users may have very limited training data and tight computational budgets, to afford the data-hungry and costly AT. In this paper, we study a novel FL strategy: propagating adversarial robustness from rich-resource users that can afford AT, to those with poor resources that cannot afford it, during federated learning. We show that existing FL techniques cannot be effectively integrated with the strategy to propagate robustness among non-iid users and propose an efficient propagation approach by the proper use of batch-normalization. We demonstrate the rationality and effectiveness of our method through extensive experiments. Especially, the proposed method is shown to grant federated models remarkable robustness even when only a small portion of users afford AT during learning. Source code can be accessed at 
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    Free, publicly-accessible full text available June 27, 2024
  9. Free, publicly-accessible full text available September 17, 2024