Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate differential privacy by training their models with (differentially) private SGD .

We thank the reviewers for their positive and constructive feedback. We address several points in the review below. The bias reduction technique in Section 5 is designed for DP-SGD with clipping. When it is applied to DP-SGD, the update rule is shown below. Typos: Thank you for pointing them out, we will correct the typos.

In the arbitrary pattern formation problem, $n$ autonomous, mobile robots must form an arbitrary pattern $P \subseteq \mathbb{R}^2$. The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to communicate. An important distinction is whether robots have memory and/or a limited viewing range. Previous work managed to form $P$ under a natural symmetry condition if robots have no memory but an unlimited viewing range [22] or if robots have a limited viewing range but memory [25]. In the latter case, $P$ is only formed in a shrunk version that has constant diameter. Without memory and with limited viewing range, forming arbitrary patterns remains an open problem. We provide a partial solution by showing that $P$ can be formed under the same symmetry condition if the robots' initial diameter is $\leq 1$. Our protocol partitions $P$ into rotation-symmetric components and exploits the initial mutual visibility to form one cluster per component. Using a careful placement of the clusters and their robots, we show that a cluster can move in a coordinated way through its component while drawing $P$ by dropping one robot per pattern coordinate.

Symmetry is a fundamental aspect of many real-world robotic tasks. However, current deep reinforcement learning (DRL) approaches can seldom harness and exploit symmetry effectively. Often, the learned behaviors fail to achieve the desired transformation invariances and suffer from motion artifacts. For instance, a quadruped may exhibit different gaits when commanded to move forward or backward, even though it is symmetrical about its torso. This issue becomes further pronounced in high-dimensional or complex environments, where DRL methods are prone to local optima and fail to explore regions of the state space equally. Past methods on encouraging symmetry for robotic tasks have studied this topic mainly in a single-task setting, where symmetry usually refers to symmetry in the motion, such as the gait patterns. In this paper, we revisit this topic for goal-conditioned tasks in robotics, where symmetry lies mainly in task execution and not necessarily in the learned motions themselves. In particular, we investigate two approaches to incorporate symmetry invariance into DRL -- data augmentation and mirror loss function. We provide a theoretical foundation for using augmented samples in an on-policy setting. Based on this, we show that the corresponding approach achieves faster convergence and improves the learned behaviors in various challenging robotic tasks, from climbing boxes with a quadruped to dexterous manipulation.

In this paper, we present DevFormer, a novel transformer-based architecture for addressing the complex and computationally demanding problem of hardware design optimization. Despite the demonstrated efficacy of transformers in domains including natural language processing and computer vision, their use in hardware design has been limited by the scarcity of offline data. Our approach addresses this limitation by introducing strong inductive biases such as relative positional embeddings and action-permutation symmetricity that effectively capture the hardware context and enable efficient design optimization with limited offline data. We apply DevFoemer to the problem of decoupling capacitor placement and show that it outperforms state-of-the-art methods in both simulated and real hardware, leading to improved performances while reducing the number of components by more than $30\%$. Finally, we show that our approach achieves promising results in other offline contextual learning-based combinatorial optimization tasks.

Many real world complex systems can be analyzed through a graph/ network prospective. There are two classical and well-known classes of complex networks, scale-fr ee networks and small world networks, which play a significant role in many domains such as social networks, b iology, cognitive science and signal processing [1, 4, 27, 44]. The human genome is a beautiful example of complex dynamic graph. The genome-wide chromosomal conformation (Hi-C) map represents the spatia l proximity of different parts of genome capturing the genome structure over time [40, 42]. When studying s uch dynamic graphs, one is often required to identify the pattern/couple changes including degree distributio n, path lengths, clustering coefficients, etc, in the graph topology in order to capture the dynamics [25, 33, 41]. The von Neumann entropy of a graph, first introduced by Braunst ein et al. [8], is a spectral measure used in structural pattern recognition. The intuition behind this me asure is linking the graph Laplacian to density matrices from quantum mechanics, and measuring the comp lexity of the graphs in terms of the von Neumman entropy of the corresponding density matrices [32]. In ad dition, the measure can be viewed as the information theoretic Shannon entropy, i.e., S null