The first large-scale deployment of private federated learning uses differentially private counting in the continual release model as a subroutine (Google AI blog titled "Federated Learning with Formal Differential Privacy Guarantees"). In this case, a concrete bound on the error is very relevant to reduce the privacy parameter. The standard mechanism for continual counting is the binary mechanism. We present a novel mechanism and show that its mean squared error is both asymptotically optimal and a factor 10 smaller than the error of the binary mechanism. We also show that the constants in our analysis are almost tight by giving non-asymptotic lower and upper bounds that differ only in the constants of lower-order terms. Our algorithm is a matrix mechanism for the counting matrix and takes constant time per release. We also use our explicit factorization of the counting matrix to give an upper bound on the excess risk of the private learning algorithm of Denisov et al. (NeurIPS 2022). Our lower bound for any continual counting mechanism is the first tight lower bound on continual counting under approximate differential privacy. It is achieved using a new lower bound on a certain factorization norm, denoted by $\gamma_F(\cdot)$, in terms of the singular values of the matrix. In particular, we show that for any complex matrix, $A \in \mathbb{C}^{m \times n}$, \[ \gamma_F(A) \geq \frac{1}{\sqrt{m}}\|A\|_1, \] where $\|\cdot \|$ denotes the Schatten-1 norm. We believe this technique will be useful in proving lower bounds for a larger class of linear queries. To illustrate the power of this technique, we show the first lower bound on the mean squared error for answering parity queries.

We study fine-grained error bounds for differentially private algorithms for counting under continual observation. Our main insight is that the matrix mechanism when using lower-triangular matrices can be used in the continual observation model. More specifically, we give an explicit factorization for the counting matrix $M_\mathsf{count}$ and upper bound the error explicitly. We also give a fine-grained analysis, specifying the exact constant in the upper bound. Our analysis is based on upper and lower bounds of the {\em completely bounded norm} (cb-norm) of $M_\mathsf{count}$. Along the way, we improve the best-known bound of 28 years by Mathias (SIAM Journal on Matrix Analysis and Applications, 1993) on the cb-norm of $M_\mathsf{count}$ for a large range of the dimension of $M_\mathsf{count}$. Furthermore, we are the first to give concrete error bounds for various problems under continual observation such as binary counting, maintaining a histogram, releasing an approximately cut-preserving synthetic graph, many graph-based statistics, and substring and episode counting. Finally, we note that our result can be used to get a fine-grained error bound for non-interactive local learning {and the first lower bounds on the additive error for $(\epsilon,\delta)$-differentially-private counting under continual observation.} Subsequent to this work, Henzinger et al. (SODA2023) showed that our factorization also achieves fine-grained mean-squared error.

Recent advances in visual representation learning allowed to build an abundance of powerful off-the-shelf features that are ready-to-use for numerous downstream tasks. This work aims to assess how well these features preserve information about the objects, such as their spatial location, their visual properties and their relative relationships. We propose to do so by evaluating them in the context of visual reasoning, where multiple objects with complex relationships and different attributes are at play. More specifically, we introduce a protocol to evaluate visual representations for the task of Visual Question Answering. In order to decouple visual feature extraction from reasoning, we design a specific attention-based reasoning module which is trained on the frozen visual representations to be evaluated, in a spirit similar to standard feature evaluations relying on shallow networks. We compare two types of visual representations, densely extracted local features and object-centric ones, against the performances of a perfect image representation using ground truth. Our main findings are two-fold. First, despite excellent performances on classical proxy tasks, such representations fall short for solving complex reasoning problem. Second, object-centric features better preserve the critical information necessary to perform visual reasoning. In our proposed framework we show how to methodologically approach this evaluation.

Mapping with uncertainty representation is required in many research domains, such as localization and sensor fusion. Although there are many uncertainty explorations in pose estimation of an ego-robot with map information, the quality of the reference maps is often neglected. To avoid the potential problems caused by the errors of maps and a lack of the uncertainty quantification, an adequate uncertainty measure for the maps is required. In this paper, uncertain building models with abstract map surface using Gaussian Process (GP) is proposed to measure the map uncertainty in a probabilistic way. To reduce the redundant computation for simple planar objects, extracted facets from a Gaussian Mixture Model (GMM) are combined with the implicit GP map while local GP-block techniques are used as well. The proposed method is evaluated on LiDAR point clouds of city buildings collected by a mobile mapping system. Compared to the performances of other methods such like Octomap, Gaussian Process Occupancy Map (GPOM) and Bayersian Generalized Kernel Inference (BGKOctomap), our method has achieved higher Precision-Recall AUC for evaluated buildings.

Underwater navigation presents several challenges, including unstructured unknown environments, lack of reliable localization systems (e.g., GPS), and poor visibility. Furthermore, good-quality obstacle detection sensors for underwater robots are scant and costly; and many sensors like RGB-D cameras and LiDAR only work in-air. To enable reliable mapless underwater navigation despite these challenges, we propose a low-cost end-to-end navigation system, based on a monocular camera and a fixed single-beam echo-sounder, that efficiently navigates an underwater robot to waypoints while avoiding nearby obstacles. Our proposed method is based on Proximal Policy Optimization (PPO), which takes as input current relative goal information, estimated depth images, echo-sounder readings, and previous executed actions, and outputs 3D robot actions in a normalized scale. End-to-end training was done in simulation, where we adopted domain randomization (varying underwater conditions and visibility) to learn a robust policy against noise and changes in visibility conditions. The experiments in simulation and real-world demonstrated that our proposed method is successful and resilient in navigating a low-cost underwater robot in unknown underwater environments. The implementation is made publicly available at https://github.com/dartmouthrobotics/deeprl-uw-robot-navigation.

We study the problem of training and certifying adversarially robust quantized neural networks (QNNs). Quantization is a technique for making neural networks more efficient by running them using low-bit integer arithmetic and is therefore commonly adopted in industry. Recent work has shown that floating-point neural networks that have been verified to be robust can become vulnerable to adversarial attacks after quantization, and certification of the quantized representation is necessary to guarantee robustness. In this work, we present quantization-aware interval bound propagation (QA-IBP), a novel method for training robust QNNs. Inspired by advances in robust learning of non-quantized networks, our training algorithm computes the gradient of an abstract representation of the actual network. Unlike existing approaches, our method can handle the discrete semantics of QNNs. Based on QA-IBP, we also develop a complete verification procedure for verifying the adversarial robustness of QNNs, which is guaranteed to terminate and produce a correct answer. Compared to existing approaches, the key advantage of our verification procedure is that it runs entirely on GPU or other accelerator devices. We demonstrate experimentally that our approach significantly outperforms existing methods and establish the new state-of-the-art for training and certifying the robustness of QNNs.

Traffic state prediction in a transportation network is paramount for effective traffic operations and management, as well as informed user and system-level decision-making. However, long-term traffic prediction (beyond 30 minutes into the future) remains challenging in current research. In this work, we integrate the spatio-temporal dependencies in the transportation network from network modeling, together with the graph convolutional network (GCN) and graph attention network (GAT). To further tackle the dramatic computation and memory cost caused by the giant model size (i.e., number of weights) caused by multiple cascaded layers, we propose sparse training to mitigate the training cost, while preserving the prediction accuracy. It is a process of training using a fixed number of nonzero weights in each layer in each iteration. We consider the problem of long-term traffic speed forecasting for a real large-scale transportation network data from the California Department of Transportation (Caltrans) Performance Measurement System (PeMS). Experimental results show that the proposed GCN-STGT and GAT-STGT models achieve low prediction errors on short-, mid- and long-term prediction horizons, of 15, 30 and 45 minutes in duration, respectively. Using our sparse training, we could train from scratch with high sparsity (e.g., up to 90%), equivalent to 10 times floating point operations per second (FLOPs) reduction on computational cost using the same epochs as dense training, and arrive at a model with very small accuracy loss compared with the original dense training

We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold $p\in[0,1]$ over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on $3$ stochastic non-linear reinforcement learning tasks.

神经网络作为快速物理模拟器具有许多工程设计任务的潜力。广泛应用程序的先决条件是易于使用的工作流程，用于在合理的时间内生成培训数据集，并且网络可以推广到看不见的系统的能力。与大多数以前的培训系统类似于评估数据集的工作相反，我们建议将培训系统的类型调整到网络体系结构中。具体而言，我们应用一个完全卷积的网络，因此设计了具有随机分配的物理属性的随机体素的3D系统。该想法已测试电子系统中的瞬时热扩散。仅在随机的“ Minecraft”系统上进行训练，我们获得了对电子系统的良好概括，这是训练系统的四倍（一步预测误差为0.07％，比0.8％）。

在智能系统（例如自动驾驶和机器人导航）中，轨迹预测一直是一个长期存在的问题。最近在大规模基准测试的最新模型一直在迅速推动性能的极限，主要集中于提高预测准确性。但是，这些模型对效率的强调较少，这对于实时应用至关重要。本文提出了一个名为Gatraj的基于注意力的图形模型，其预测速度要高得多。代理的时空动力学，例如行人或车辆，是通过注意机制建模的。代理之间的相互作用是通过图卷积网络建模的。我们还实施了拉普拉斯混合物解码器，以减轻模式崩溃，并为每个代理生成多种模式预测。我们的模型以在多个开放数据集上测试的更高预测速度与最先进的模型相同的性能。