What features neural networks learn, and how, remains an open question. In this paper, we introduce Alternating Gradient Flows (AGF), an algorithmic framework that describes the dynamics of feature learning in two-layer networks trained from small initialization. Prior works have shown that gradient flow in this regime exhibits a staircase-like loss curve, alternating between plateaus where neurons slowly align to useful directions and sharp drops where neurons rapidly grow in norm. AGF approximates this behavior as an alternating two-step process: maximizing a utility function over dormant neurons and minimizing a cost function over active ones. AGF begins with all neurons dormant. At each round, a dormant neuron activates, triggering the acquisition of a feature and a drop in the loss. AGF quantifies the order, timing, and magnitude of these drops, matching experiments across architectures. We show that AGF unifies and extends existing saddle-to-saddle analyses in fully connected linear networks and attention-only linear transformers, where the learned features are singular modes and principal components, respectively. In diagonal linear networks, we prove AGF converges to gradient flow in the limit of vanishing initialization. Applying AGF to quadratic networks trained to perform modular addition, we give the first complete characterization of the training dynamics, revealing that networks learn Fourier features in decreasing order of coefficient magnitude. Altogether, AGF offers a promising step towards understanding feature learning in neural networks.

This document provides additional details, analysis, and experimental results. We begin by discussing the detailed experimental setup and implementation of the methods in Section A. Then, we provide additional empirical experiments against several other defense methods in Section B, and a discussion on the stealthiness of the backdoor images in the input space in Section C. Finally, we provide the supporting proofs for the claims in the main paper in Section D. A.1 Datasets As we described in the main paper, we use four datasets, MNIST, CIFAR10, GTSRB, and TinyImagenet, to evaluate our method. Note that MNIST, CIFAR10, and GTSRB have been widely used in the literature of backdoor attacks on DNN. On the other hand, the use of a more complex dataset, TinyImagenet, enables better evaluation for multiple-target backdoor attacks such as all-to-all, thanks to the diversity of images in TinyImagenet and its large number of classes. MNIST [28] is a subset of the larger dataset available from the National Institute of Technology.

Adapting to non-stationary network conditions presents significant challenges for resource adaptation. However, current solutions primarily rely on stationary assumptions. While data-driven reinforcement learning approaches offer promising solutions for handling network dynamics, our systematic investigation reveals a critical limitation: neural networks suffer from plasticity loss, significantly impeding their ability to adapt to evolving network conditions. Through theoretical analysis of neural propagation mechanisms, we demonstrate that existing dormant neuron metrics inadequately characterize neural plasticity loss. To address this limitation, we have developed the Silent Neuron theory, which provides a more comprehensive framework for understanding plasticity degradation. Based on these theoretical insights, we propose the Reset Silent Neuron (ReSiN), which preserves neural plasticity through strategic neuron resets guided by both forward and backward propagation states. In our implementation of an adaptive video streaming system, ReSiN has shown significant improvements over existing solutions, achieving up to 168% higher bitrate and 108% better quality of experience (QoE) while maintaining comparable smoothness. Furthermore, ReSiN consistently outperforms in stationary environments, demonstrating its robust adaptability across different network conditions.

Multi-task reinforcement learning (MTRL) aims to endow a single agent with the ability to perform well on multiple tasks. Recent works have focused on developing novel sophisticated architectures to improve performance, often resulting in larger models; it is unclear, however, whether the performance gains are a consequence of the architecture design itself or the extra parameters. We argue that gains are mostly due to scale by demonstrating that naïvely scaling up a simple MTRL baseline to match parameter counts outperforms the more sophisticated architectures, and these gains benefit most from scaling the critic over the actor. Additionally, we explore the training stability advantages that come with task diversity, demonstrating that increasing the number of tasks can help mitigate plasticity loss. Our findings suggest that MTRL's simultaneous training across multiple tasks provides a natural framework for beneficial parameter scaling in reinforcement learning, challenging the need for complex architectural innovations.

In the realm of neuroscience, it has been observed that biological agents often experience a diminishing ability to adapt over time, analogous to the gradual solidification of neural pathways in the brain (Livingston, 1966). This phenomenon, typically known as the loss of plasticity (Mateos-Aparicio and Rodríguez-Moreno, 2019), significantly affects an agent's capacity to learn continually, especially when agents learn by trial and error in deep reinforcement learning (deep RL) due to the nonstationarity nature. The declining adaptability throughout the learning process can severely hinder the agent's ability to effectively learn and respond to complex or non-stationary scenarios (Abbas et al., 2023). This limitation presents a fundamental obstacle to achieving sustained learning and adaptability in artificial agents, which echoes the plasticity-stability dilemma (Abraham and Robins, 2005) observed in biological neural networks. There have been several recent studies highlighting a significant loss of plasticity in deep RL (Kumar et al., 2020, Lyle et al., 2022), which substantially restricts the agent's ability to learn from subsequent experiences (Lyle et al., 2023, Ma et al., 2023). The identification of primacy bias (Nikishin et al., 2022) further illustrates how agents may become overfitted to early experiences, which inhibits learning from subsequent new data. The consequences of plasticity loss further impede deep RL in continual learning scenarios, where the agent struggles to sequentially learn across a series of different tasks (Dohare et al., 2024). 1

Bridging the gap between diffusion models and human preferences is crucial for their integration into practical generative workflows. While optimizing downstream reward models has emerged as a promising alignment strategy, concerns arise regarding the risk of excessive optimization with learned reward models, which potentially compromises ground-truth performance. In this work, we confront the reward overoptimization problem in diffusion model alignment through the lenses of both inductive and primacy biases. We first identify the divergence of current methods from the temporal inductive bias inherent in the multi-step denoising process of diffusion models as a potential source of overoptimization. Then, we surprisingly discover that dormant neurons in our critic model act as a regularization against overoptimization, while active neurons reflect primacy bias in this setting. Motivated by these observations, we propose Temporal Diffusion Policy Optimization with critic active neuron Reset (TDPO-R), a policy gradient algorithm that exploits the temporal inductive bias of intermediate timesteps, along with a novel reset strategy that targets active neurons to counteract the primacy bias. Empirical results demonstrate the superior efficacy of our algorithms in mitigating reward overoptimization.

In this work we identify the dormant neuron phenomenon in deep reinforcement learning, where an agent's network suffers from an increasing number of inactive neurons, thereby affecting network expressivity. We demonstrate the presence of this phenomenon across a variety of algorithms and environments, and highlight its effect on learning. To address this issue, we propose a simple and effective method (ReDo) that Recycles Dormant neurons throughout training. Our experiments demonstrate that ReDo maintains the expressive power of networks by reducing the number of dormant neurons and results in improved performance.