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Weight decay (WD) is a traditional regularization technique in deep learning, but despite its ubiquity, its behavior is still an area of active research. Golatkar et al. have recently shown that WD only matters at the start of the training in computer vision, upending traditional wisdom. Loshchilov et al. show that for adaptive optimizers, manually decaying weights can outperform adding an l2 penalty to the loss. This technique has become increasingly popular and is referred to as decoupled WD. The goal of this paper is to investigate these two recent empirical observations. We demonstrate that by applying WD only at the start, the network norm stays small throughout training. This has a regularizing effect as the effective gradient updates become larger. However, traditional generalizations metrics fail to capture this effect of WD, and we show how a simple scale-invariant metric can. We also show how the growth of network weights is heavily influenced by the dataset and its generalization properties. For decoupled WD, we perform experiments in NLP and RL where adaptive optimizers are the norm. We demonstrate that the primary issue that decoupled WD alleviates is the mixing of gradients from the objective function and the l2 penalty in the buffers of Adam (which stores the estimates of the first-order moment). Adaptivity itself is not problematic and decoupled WD ensures that the gradients from the l2 term cannot &quot;drown out&quot; the true objective, facilitating easier hyperparameter tuning.

AAAI 2021

Understanding Decoupled and Early Weight Decay

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AMA Research Challenge 2025 

Join the AMA Research Challenge poster symposium and semifinals to explore top research posters and score posters in the semifinals (an AMA member exclusive opportunity).

Weight decay (WD) is a traditional regularization technique in deep learning, but despite its ubiquity, its behavior is still an area of active research. Golatkar et al. have recently shown that WD only matters at the start of the training in computer vision, upending traditional wisdom. Loshchilov et al. show that for adaptive optimizers, manually decaying weights can outperform adding an l2 penalty to the loss. This technique has become increasingly popular and is referred to as decoupled WD. The goal of this paper is to investigate these two recent empirical observations. We demonstrate that by applying WD only at the start, the network norm stays small throughout training. This has a regularizing effect as the effective gradient updates become larger. However, traditional generalizations metrics fail to capture this effect of WD, and we show how a simple scale-invariant metric can. We also show how the growth of network weights is heavily influenced by the dataset and its generalization properties. For decoupled WD, we perform experiments in NLP and RL where adaptive optimizers are the norm. We demonstrate that the primary issue that decoupled WD alleviates is the mixing of gradients from the objective function and the l2 penalty in the buffers of Adam (which stores the estimates of the first-order moment). Adaptivity itself is not problematic and decoupled WD ensures that the gradients from the l2 term cannot "drown out" the true objective, facilitating easier hyperparameter tuning.

technical paper

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

We propose a principled framework that combines adversarial training and provable robustness verification for training certifiably robust neural networks. We formulate the training problem as a joint optimization problem with both empirical and provable robustness objectives and develop a novel gradient-descent technique that can eliminate bias in stochastic multi-gradients. We perform both theoretical analysis on the convergence of the proposed technique and experimental comparison with state-of-the-arts. Results on MNIST and CIFAR-10 show that our method can consistently match or outperform prior approaches for provable lâˆž robustness. Notably, we achieve 6.60% verified test error on MNIST at Îµ = 0.3, and 66.57% on CIFAR-10 with Îµ = 8/255.

Adversarial Training and Provable Robustness: A Tale of Two Objectives

We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an oracle that compares the function values for a given pair of points, and an oracle that outputs a noisy function value for a given point. We show that the sample complexity of optimization using these oracles is polynomial in the relevant parameters. The optimization algorithm that we provide for the comparator oracle is the first algorithm with a known rate of convergence that is polynomial in the number of dimensions. We also give an algorithm for the noisy-value oracle that incurs sublinear regret in the number of queries and polynomial regret in the number of dimensions.

Smooth Convex Optimization Using Sub-Zeroth-Order Oracles

Adversarial attack can misguide the deep neural networks (DNNs) with adding small-magnitude perturbations to normal examples, which is mainly determined by the gradient of the loss function with respect to inputs. Previously, various strategies have been proposed to enhance the performance of adversarial attacks. However, all these methods only  utilize the gradients in the present and past to generate adversarial examples. Until now, the trend of gradient change in the future (i.e., the derivative of gradient) has not been considered yet. Inspired by the classic proportional-integral-derivative (PID) controller in the field of automatic control, we propose a new PID-based approach for generating adversarial examples. The gradients in the present and past, and the derivative of gradient are considered in our method, which correspond to the components of P, I and D in the PID controller, respectively.  Extensive experiments consistently demonstrate that our method can achieve higher attack success rates and exhibit better transferability compared with the state-of-the-art gradient-based adversarial attacks. Furthermore, our method possesses good extensibility and can be applied to almost all available gradient-based adversarial attacks.

PID-Based Approach to Adversarial Attacks

Humans possess an inherent ability to chunk sequences into their constituent parts. In fact, this ability is thought to bootstrap language skills and learning of image patterns which might be a key to a more animal-like type of intelligence. Here, we propose a continual generalization of the chunking problem (an unsupervised problem), encompassing fixed and probabilistic chunks, discovery of temporal and causal structures and their continual variations. Additionally, we propose an algorithm called SyncMap that can learn and adapt to changes in the problem by creating a dynamic map which preserves the correlation between variables. Results of SyncMap  suggest that the proposed algorithm learn near optimal solutions, despite the presence of many types of structures and their continual variation. When compared to Word2vec, PARSER and MRIL, SyncMap surpasses or ties with the best algorithm on 66% of the scenarios while being the second best in the remaining 34%. SyncMap's model-free simple dynamics and the absence of loss functions reveal that, perhaps surprisingly, much can be done with self-organization alone.

Continual General Chunking Problem and SyncMap

Kalman Filter (KF) is widely used in various domains to perform sequential learning or variable estimation. In the context of autonomous vehicles, KF constitutes the core component of many Advanced Driver Assistance Systems (ADAS), such as Forward Collision Warning (FCW). It tracks the states (distance, velocity etc.) of relevant traffic objects based on sensor measurements. The tracking output of KF is often fed into downstream logic to produce alerts, which will then be used by human drivers to make driving decisions in near-collision scenarios. In this paper, we study adversarial attacks on KF as part of the more complex machine-human hybrid system of Forward Collision Warning. Our attack goal is to negatively affect human braking decisions by causing KF to output incorrect state estimations that lead to false or delayed alerts. We accomplish this by sequentially manipulating measure ments fed into the KF, and propose a novel Model Predictive Control (MPC) approach to compute the optimal manipulation. Via experiments conducted in a simulated driving environment, we show that the attacker is able to successfully change FCW alert signals through planned manipulation over measurements prior to the desired target time. These results demonstrate that our attack can stealthily mislead a distracted human driver and cause vehicle collisions.

Sequential Attacks on Kalman Filter-Based Forward Collision Warning Systems

Time series forecasting and spatiotemporal kriging are the two most important tasks in spatiotemporal data analysis. Recent research on graph neural networks has made substantial progress in time series forecasting, while little attention has been paid to the kriging problem---recovering signals for unsampled locations/sensors. Most existing scalable kriging methods (e.g., matrix/tensor completion) are transductive, and thus full retraining is required when we have a new sensor to interpolate. In this paper, we develop an Inductive Graph Neural Network Kriging (IGNNK) model to recover data for unsampled sensors on a network/graph structure. To generalize the effect of distance and reachability, we generate random subgraphs as samples and the corresponding adjacency matrix for each sample. By reconstructing all signals on each sample subgraph, IGNNK can effectively learn the spatial message passing mechanism. Empirical results on several real-world spatiotemporal datasets demonstrate the effectiveness of our model. In addition, we also find that the learned model can be successfully transferred to the same type of kriging tasks on an unseen dataset. Our results show that: 1) GNN is an efficient and effective tool for spatial kriging; 2) inductive GNNs can be trained using dynamic adjacency matrices; 3) a trained model can be transferred to new graph structures and 4) IGNNK can be used to generate virtual sensors.

Inductive Graph Neural Networks for Spatiotemporal Kriging

In continuing tasks, average-reward reinforcement learning may be a more appropriate problem formulation than the more common discounted reward formulation. As usual, learning an optimal policy in this setting typically requires a large amount of training experiences. Reward shaping is a common approach for incorporating domain knowledge into reinforcement learning in order to speed up convergence to an optimal policy. However, to the best of our knowledge, the theoretical properties of reward shaping have thus far only been established in the discounted setting. This paper presents the first reward shaping framework for average-reward learning and proves that, under standard assumptions, the optimal policy under the original reward function can be recovered. In order to avoid the need for manual construction of the shaping function, we introduce a method for utilizing domain knowledge expressed as a temporal logic formula. The formula is automatically translated to a shaping function that provides additional reward throughout the learning process. We evaluate the proposed method on three continuing tasks. In all cases, shaping speeds up the average-reward learning rate without any reduction in the performance of the learned policy compared to relevant baselines.

Temporal-Logic-Based Reward Shaping for Continuing Reinforcement Learning Tasks

AI practitioners typically strive to develop the most  accurate systems,  making an implicit assumption that the AI system will function autonomously. However, in practice, AI systems often are used to provide advice to people in domains ranging from criminal justice and finance to healthcare. In such AI-advised decision making, humans and machines form a team, where the human is responsible for making final decisions.   But is the most accurate AI the best teammate? We argue "not necessarily" --- predictable performance may be worth a slight sacrifice in AI accuracy. Instead, we argue that AI systems should be trained in a human-centered manner, directly optimized for team performance. We study this proposal for a specific type of human-AI teaming, where the human overseer chooses to either accept the AI recommendation or solve the task themselves. To optimize the team performance for this setting we maximize the team's expected utility, expressed in terms of the quality of the final decision, cost of verifying, and individual accuracies of people and machines. Our experiments with linear and non-linear models on real-world, high-stakes datasets show that the most accuracy AI may not lead to highest team performance and show the benefit of modeling teamwork during training through improvements in expected team utility across datasets, considering parameters such as human skill and the cost of mistakes. We discuss the shortcoming of current optimization approaches beyond well-studied loss functions such as log-loss, and encourage future work on AI optimization problems motivated by human-AI collaboration.

Is the Most Accurate AI the Best Teammate? Optimizing AI for Teamwork

We study a variant of stochastic bandits where the feedback model is specified by a graph. In this setting, after playing an arm, one can observe rewards of not only the played arm but also other arms that are adjacent to the played arm in the graph. Most of the existing work assumes the reward distributions are stationary over time, which, however, is often violated in common scenarios such as recommendation systems and online advertising. To address this limitation, we study stochastic bandits with graph feedback in non-stationary environments and propose algorithms with graph-dependent dynamic regret bounds. When the number of reward distribution changes L is known in advance, one of our algorithms achieves an Ã•(âˆš(Î±LT)) dynamic regret bound. We also develop an adaptive algorithm that can adapt to unknown L and attain an Ã•(âˆš(Î¸LT)) dynamic regret. Here, Î± and Î¸ are some graph-dependent quantities and T is the time horizon.

Stochastic Bandits with Graph Feedback in Non-Stationary Environments

We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. 
Based on the weak regularity lemma from the theory of graphons, we leverage a step function to approximate a graphon. 
We show that the cut distance of graphons can be relaxed to the Gromov-Wasserstein distance of their step functions. 
Accordingly, given a set of graphs generated by an underlying graphon, we learn the corresponding step function as the Gromov-Wasserstein barycenter of the given graphs.
Furthermore, we develop several enhancements and extensions of the basic algorithm, e.g., the smoothed Gromov-Wasserstein barycenter for guaranteeing the continuity of the learned graphons and the mixed Gromov-Wasserstein barycenters for learning multiple structured graphons. 
The proposed approach overcomes drawbacks of prior state-of-the-art methods, and outperforms them on both synthetic and real-world data. 
The code is available at https://github.com/HongtengXu/SGWB-Graphon.

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