In this section, we provide proofs for Proposition 2.1.B. Inthe proof, we inherit the notations that weuseforprovingTheorem2.1. The instance normalization that we incorporate into the DGM is not the same as the instance normalization that is typically used in image stylization [35]. CNN-F-5 significantly improves the robustness of CNN. CNN-F achieves higher accuracy on MNIST than CNN for under both standard training and adversarial training.

A.1 Generative model We choose the deconvolutional generative model (DGM) [25] as the generative feedback in CNN-F. The graphical model of the DGM is shown in Figure 2 (middle). In this section, we provide proofs for Theorem 2.1. Without loss of generality, we consider a DGM that has the following architecture. Lemma A.1 shows that logits output from the corresponding CNN of the DGM is proportional to the inner product of generated image and input image plus Lemma A.1 to show that CNN performs Bayesian inference in the DGM.

We thank the reviewers for their thoughtful feedback. Due to space limit, we address the main concerns here. R4 How do losses affect performance? We included the ablation study in Appendix (line 522). Empirically, we find that 5 iterations lead to a stable solution.

We investigate the design of pooling methods used to summarize the outputs of transformer embedding models, primarily motivated by reinforcement learning and vision applications. This work considers problems where a subset of the input vectors contains requisite information for a downstream task (signal) while the rest are distractors (noise). By framing pooling as vector quantization with the goal of minimizing signal loss, we demonstrate that the standard methods used to aggregate transformer outputs, AvgPool, MaxPool, and ClsToken, are vulnerable to performance collapse as the signal-to-noise ratio (SNR) of inputs fluctuates. We then show that an attention-based adaptive pooling method can approximate the signal-optimal vector quantizer within derived error bounds for any SNR. Our theoretical results are first validated by supervised experiments on a synthetic dataset designed to isolate the SNR problem, then generalized to standard relational reasoning, multi-agent reinforcement learning, and vision benchmarks with noisy observations, where transformers with adaptive pooling display superior robustness across tasks.

This paper introduces an adaptive model-free deep reinforcement approach that can recognize and adapt to the diurnal patterns in the ride-sharing environment with car-pooling. Deep Reinforcement Learning (RL) suffers from catastrophic forgetting due to being agnostic to the timescale of changes in the distribution of experiences. Although RL algorithms are guaranteed to converge to optimal policies in Markov decision processes (MDPs), this only holds in the presence of static environments. However, this assumption is very restrictive. In many real-world problems like ride-sharing, traffic control, etc., we are dealing with highly dynamic environments, where RL methods yield only sub-optimal decisions. To mitigate this problem in highly dynamic environments, we (1) adopt an online Dirichlet change point detection (ODCP) algorithm to detect the changes in the distribution of experiences, (2) develop a Deep Q Network (DQN) agent that is capable of recognizing diurnal patterns and making informed dispatching decisions according to the changes in the underlying environment. Rather than fixing patterns by time of week, the proposed approach automatically detects that the MDP has changed, and uses the results of the new model. In addition to the adaptation logic in dispatching, this paper also proposes a dynamic, demand-aware vehicle-passenger matching and route planning framework that dynamically generates optimal routes for each vehicle based on online demand, vehicle capacities, and locations. Evaluation on New York City Taxi public dataset shows the effectiveness of our approach in improving the fleet utilization, where less than 50% of the fleet are utilized to serve the demand of up to 90% of the requests, while maximizing profits and minimizing idle times.

Neural networks are vulnerable to input perturbations such as additive noise and adversarial attacks. In contrast, human perception is much more robust to such perturbations. The Bayesian brain hypothesis states that human brains use an internal generative model to update the posterior beliefs of the sensory input. This mechanism can be interpreted as a form of self-consistency between the maximum a posteriori (MAP) estimation of an internal generative model and the external environment. Inspired by such hypothesis, we enforce self-consistency in neural networks by incorporating generative recurrent feedback. We instantiate this design on convolutional neural networks (CNNs). The proposed framework, termed Convolutional Neural Networks with Feedback (CNN-F), introduces a generative feedback with latent variables to existing CNN architectures, where consistent predictions are made through alternating MAP inference under a Bayesian framework. In the experiments, CNN-F shows considerably improved adversarial robustness over conventional feedforward CNNs on standard benchmarks.