In deep networks with small initialization, training exhibits long plateaus separated by sharp feature-acquisition transitions. Whereas shallow nonlinear networks and deep linear networks are well studied, extending these analyses to deep nonlinear networks remains challenging. We derive an exact identity for the imbalance of Frobenius norms of layer weight matrices that holds for any smooth activation and any differentiable loss and use this to classify activation functions into four universality classes. On the permutation-symmetric submanifold, the identity combines with an approximate balance law to reduce the full matrix flow to a scalar ODE, giving a critical-depth escape time law $τ_\star = Θ(\varepsilon^{-(r-2)})$ governed by the number $r$ of layers at the bottleneck scale rather than the total depth $L$. We find that this same $r-2$ exponent is recovered under He-normal initialization with $r$ bottleneck layers rescaled by $\varepsilon$, where the symmetry manifold is preserved by the flow but not attracting. We find close agreement between our theory and numerical simulations.

Spatio-temporal graphs are widely used in modeling complex dynamic processes such as traffic forecasting, molecular dynamics, and healthcare monitoring. Recently, stringent privacy regulations such as GDPR and CCPA have introduced significant new challenges for existing spatio-temporal graph models, requiring complete unlearning of unauthorized data. Since each node in a spatio-temporal graph diffuses information globally across both spatial and temporal dimensions, existing unlearning methods primarily designed for static graphs and localized data removal cannot efficiently erase a single node without incurring costs nearly equivalent to full model retraining. Therefore, an effective approach for complete spatio-temporal graph unlearning is a pressing need. To address this, we propose CallosumNet, a divide-and-conquer spatio-temporal graph unlearning framework inspired by the corpus callosum structure that facilitates communication between the brain's two hemispheres. CallosumNet incorporates two novel techniques: (1) Enhanced Subgraph Construction (ESC), which adaptively constructs multiple localized subgraphs based on several factors, including biologically-inspired virtual ganglions; and (2) Global Ganglion Bridging (GGB), which reconstructs global spatio-temporal dependencies from these localized subgraphs, effectively restoring the full graph representation. Empirical results on four diverse real-world datasets show that CallosumNet achieves complete unlearning with only 1%-2% relative MAE loss compared to the gold model, significantly outperforming state-of-the-art baselines. Ablation studies verify the effectiveness of both proposed techniques.

Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants, Adaptive self-consistency (ASC) and Early-stopping self-consistency (ESC), dynamically adjust the number of samples based on the posterior distribution of a set of pre-samples, reducing the cost of SC with minimal impact on performance. Both methods, however, do not exploit the prior information about question difficulty. It often results in unnecessary repeated sampling for easy questions that could be accurately answered with just one attempt, wasting resources. To tackle this problem, we propose Difficulty-Adaptive Self-Consistency (DSC), which leverages the difficulty information from both prior and posterior perspectives to adaptively allocate inference resources, further reducing the cost of SC. To demonstrate the effectiveness of DSC, we conduct extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning on six benchmarks. The empirical results show that DSC consistently surpasses the strong baseline ASC and ESC in terms of costs by a significant margin, while attaining comparable performances.

To develop robust manipulation policies, quantifying robustness is essential. Evaluating robustness in general dexterous manipulation, nonetheless, poses significant challenges due to complex hybrid dynamics, combinatorial explosion of possible contact interactions, global geometry, etc. This paper introduces ``caging in motion'', an approach for analyzing manipulation robustness through energy margins and caging-based analysis. Our method assesses manipulation robustness by measuring the energy margin to failure and extends traditional caging concepts for a global analysis of dynamic manipulation. This global analysis is facilitated by a kinodynamic planning framework that naturally integrates global geometry, contact changes, and robot compliance. We validate the effectiveness of our approach in the simulation and real-world experiments of multiple dynamic manipulation scenarios, highlighting its potential to predict manipulation success and robustness.

Reinforcement learning for control over continuous spaces typically uses high-entropy stochastic policies, such as Gaussian distributions, for local exploration and estimating policy gradient to optimize performance. Many robotic control problems deal with complex unstable dynamics, where applying actions that are off the feasible control manifolds can quickly lead to undesirable divergence. In such cases, most samples taken from the ambient action space generate low-value trajectories that hardly contribute to policy improvement, resulting in slow or failed learning. We propose to improve action selection in this model-free RL setting by introducing additional adaptive control steps based on Extremum-Seeking Control (ESC). On each action sampled from stochastic policies, we apply sinusoidal perturbations and query for estimated Q-values as the response signal. Based on ESC, we then dynamically improve the sampled actions to be closer to nearby optima before applying them to the environment. Our methods can be easily added in standard policy optimization to improve learning efficiency, which we demonstrate in various control learning environments.

Self-consistency (SC) has been a widely used decoding strategy for chain-of-thought reasoning. Despite bringing significant performance improvements across a variety of multi-step reasoning tasks, it is a high-cost method that requires multiple sampling with the preset size. In this paper, we propose a simple and scalable sampling process, \textbf{E}arly-Stopping \textbf{S}elf-\textbf{C}onsistency (ESC), to greatly reduce the cost of SC without sacrificing performance. On this basis, one control scheme for ESC is further derivated to dynamically choose the performance-cost balance for different tasks and models. To demonstrate ESC's effectiveness, we conducted extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning over language models with varying scales. The empirical results show that ESC reduces the average number of sampling of chain-of-thought reasoning by a significant margin on six benchmarks, including MATH (-33.8%), GSM8K (-80.1%), StrategyQA (-76.8%), CommonsenseQA (-78.5%), Coin Flip (-84.2%) and Last Letters (-67.4%), while attaining comparable performances.

The ability to accurately locate and navigate to a specific object is a crucial capability for embodied agents that operate in the real world and interact with objects to complete tasks. Such object navigation tasks usually require large-scale training in visual environments with labeled objects, which generalizes poorly to novel objects in unknown environments. In this work, we present a novel zero-shot object navigation method, Exploration with Soft Commonsense constraints (ESC), that transfers commonsense knowledge in pre-trained models to open-world object navigation without any navigation experience nor any other training on the visual environments. First, ESC leverages a pre-trained vision and language model for open-world prompt-based grounding and a pre-trained commonsense language model for room and object reasoning. Then ESC converts commonsense knowledge into navigation actions by modeling it as soft logic predicates for efficient exploration. Extensive experiments on MP3D, HM3D, and RoboTHOR benchmarks show that our ESC method improves significantly over baselines, and achieves new state-of-the-art results for zero-shot object navigation (e.g., 288% relative Success Rate improvement than CoW on MP3D).

Social insect colonies routinely face large vertebrate predators, against which they need to mount a collective defense. To do so, honeybees use an alarm pheromone that recruits nearby bees into mass stinging of the perceived threat. This alarm pheromone is carried directly on the stinger, hence its concentration builds up during the course of the attack. Here, we investigate how individual bees react to different alarm pheromone concentrations, and how this evolved response-pattern leads to better coordination at the group level. We first present an individual dose-response curve to the alarm pheromone, obtained experimentally. Second, we apply Projective Simulation to model each bee as an artificial learning agent that relies on the pheromone concentration to decide whether to sting or not. If the emergent collective performance benefits the colony, the individual reactions that led to it are enhanced via reinforcement learning, thus emulating natural selection. Predators are modeled in a realistic way so that the effect of factors such as their resistance, their killing rate or their frequency of attacks can be studied. We are able to reproduce the experimentally measured response-pattern of real bees, and to identify the main selection pressures that shaped it. Finally, we apply the model to a case study: by tuning the parameters to represent the environmental conditions of European or African bees, we can predict the difference in aggressiveness observed between these two subspecies.