Training an overparameterized neural network can yield minimizers of the same level of training loss and yet different generalization capabilities. With evidence that indicates a correlation between sharpness of minima and their generalization errors, increasing efforts have been made to develop an optimization method to explicitly find flat minima as more generalizable solutions. This sharpness-aware minimization (SAM) strategy, however, has not been studied much yet as to how overparameterization can actually affect its behavior. In this work, we analyze SAM under varying degrees of overparameterization and present both empirical and theoretical results that suggest a critical influence of overparameterization on SAM. Specifically, we first use standard techniques in optimization to prove that SAM can achieve a linear convergence rate under overparameterization in a stochastic setting. We also show that the linearly stable minima found by SAM are indeed flatter and have more uniformly distributed Hessian moments compared to those of SGD. These results are corroborated with our experiments that reveal a consistent trend that the generalization improvement made by SAM continues to increase as the model becomes more overparameterized. We further present that sparsity can open up an avenue for effective overparameterization in practice.
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We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the non-convex training problem as a convex program. We show that the global optima of the convex parameterization are given by a polyhedral set and then extend this characterization to the optimal set of the non-convex training objective. Since all stationary points of the ReLU training problem can be represented as optima of sub-sampled convex programs, our work provides a general expression for all critical points of the non-convex objective. We then leverage our results to provide an optimal pruning algorithm for computing minimal networks, establish conditions for the regularization path of ReLU networks to be continuous, and develop sensitivity results for minimal ReLU networks.
With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.
Neural networks are known to be susceptible to adversarial samples: small variations of natural examples crafted to deliberately mislead the models. While they can be easily generated using gradient-based techniques in digital and physical scenarios, they often differ greatly from the actual data distribution of natural images, resulting in a trade-off between strength and stealthiness. In this paper, we propose a novel framework dubbed Diffusion-Based Projected Gradient Descent (Diff-PGD) for generating realistic adversarial samples. By exploiting a gradient guided by a diffusion model, Diff-PGD ensures that adversarial samples remain close to the original data distribution while maintaining their effectiveness. Moreover, our framework can be easily customized for specific tasks such as digital attacks, physical-world attacks, and style-based attacks. Compared with existing methods for generating natural-style adversarial samples, our framework enables the separation of optimizing adversarial loss from other surrogate losses (e.g., content/smoothness/style loss), making it more stable and controllable. Finally, we demonstrate that the samples generated using Diff-PGD have better transferability and anti-purification power than traditional gradient-based methods. Code will be released in //github.com/xavihart/Diff-PGD
Bi-static sensing is crucial for exploring the potential of networked sensing capabilities in integrated sensing and communications (ISAC). However, it suffers from the challenging clock asynchronism issue. CSI ratio-based sensing is an effective means to address the issue. Its performance bounds, particular for Doppler sensing, have not been fully understood yet. This work endeavors to fill the research gap. Focusing on a single dynamic path in high-SNR scenarios, we derive the closed-form CRB. Then, through analyzing the mutual interference between dynamic and static paths, we simplify the CRB results by deriving close approximations, further unveiling new insights of the impact of numerous physical parameters on Doppler sensing. Moreover, utilizing the new CRB and analyses, we propose novel waveform optimization strategies for noise- and interference-limited sensing scenarios, which are also empowered by closed-form and efficient solutions. Extensive simulation results are provided to validate the preciseness of the derived CRB results and analyses, with the aid of the maximum-likelihood estimator. The results also demonstrate the substantial enhanced Doppler sensing accuracy and the sensing capabilities for low-speed target achieved by the proposed waveform design.
As deep neural networks are more commonly deployed in high-stakes domains, their lack of interpretability makes uncertainty quantification challenging. We investigate the effects of presenting conformal prediction sets$\unicode{x2013}$a method for generating valid confidence sets in distribution-free uncertainty quantification$\unicode{x2013}$to express uncertainty in AI-advised decision-making. Through a large pre-registered experiment, we compare the utility of conformal prediction sets to displays of Top-1 and Top-k predictions for AI-advised image labeling. We find that the utility of prediction sets for accuracy varies with the difficulty of the task: while they result in accuracy on par with or less than Top-1 and Top-k displays for easy images, prediction sets excel at assisting humans in labeling out-of-distribution (OOD) images especially when the set size is small. Our results empirically pinpoint the practical challenges of conformal prediction sets and provide implications on how to incorporate them for real-world decision-making.
The hyperparameters of recommender systems for top-n predictions are typically optimized to enhance the predictive performance of algorithms. Thereby, the optimization algorithm, e.g., grid search or random search, searches for the best hyperparameter configuration according to an optimization-target metric, like nDCG or Precision. In contrast, the optimized algorithm, internally optimizes a different loss function during training, like squared error or cross-entropy. To tackle this discrepancy, recent work focused on generating loss functions better suited for recommender systems. Yet, when evaluating an algorithm using a top-n metric during optimization, another discrepancy between the optimization-target metric and the training loss has so far been ignored. During optimization, the top-n items are selected for computing a top-n metric; ignoring that the top-n items are selected from the recommendations of a model trained with an entirely different loss function. Item recommendations suitable for optimization-target metrics could be outside the top-n recommended items; hiddenly impacting the optimization performance. Therefore, we were motivated to analyze whether the top-n items are optimal for optimization-target top-n metrics. In pursuit of an answer, we exhaustively evaluate the predictive performance of 250 selection strategies besides selecting the top-n. We extensively evaluate each selection strategy over twelve implicit feedback and eight explicit feedback data sets with eleven recommender systems algorithms. Our results show that there exist selection strategies other than top-n that increase predictive performance for various algorithms and recommendation domains. However, the performance of the top ~43% of selection strategies is not significantly different. We discuss the impact of our findings on optimization and re-ranking in recommender systems and feasible solutions.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks, unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. Last, we also identify several challenges, which potentially serve as guidelines for further flourishing the achievements of graph learning in hyperbolic spaces.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.
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