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With the goal of improving spectral efficiency, complex rotation-based precoding and power allocation schemes are developed for two multiple-input multiple-output (MIMO) communication systems, namely, simultaneous wireless information and power transfer (SWIPT) and physical layer multicasting. While the state-of-the-art solutions for these problems use very different approaches, the proposed approach treats them similarly using a general tool and works efficiently for any number of antennas at each node. Through modeling the precoder using complex rotation matrices, objective functions (transmission rates) of the above systems can be formulated and solved in a similar structure. Hence, this approach simplifies signaling design for MIMO systems and can reduce the hardware complexity by having one set of parameters to optimize. Extensive numerical results show that the proposed approach outperforms state-of-the-art solutions for both problems. It increases transmission rates for multicasting and achieves higher rate-energy regions in the SWIPT case. In both cases, the improvement is significant (20%-30%) in practically important settings where the users have one or two antennas. Furthermore, the new precoders are less time-consuming than the existing solutions.

We study the problem of approximating edit distance in sublinear time. This is formalized as a promise problem $(k,k^c)$-Gap Edit Distance, where the input is a pair of strings $X,Y$ and parameters $k,c>1$, and the goal is to return YES if $ED(X,Y)\leq k$ and NO if $ED(X,Y)> k^c$. Recent years have witnessed significant interest in designing sublinear-time algorithms for Gap Edit Distance. We resolve the non-adaptive query complexity of Gap Edit Distance, improving over several previous results. Specifically, we design a non-adaptive algorithm with query complexity $\tilde{O}(\frac{n}{k^{c-0.5}})$, and further prove that this bound is optimal up to polylogarithmic factors. Our algorithm also achieves optimal time complexity $\tilde{O}(\frac{n}{k^{c-0.5}})$ whenever $c\geq 1.5$. For $1<c<1.5$, the running time of our algorithm is $\tilde{O}(\frac{n}{k^{2c-1}})$. For the restricted case of $k^c=\Omega(n)$, this matches a known result [Batu, Erg\"un, Kilian, Magen, Raskhodnikova, Rubinfeld, and Sami, STOC 2003], and in all other (nontrivial) cases, our running time is strictly better than all previous algorithms, including the adaptive ones.

Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate notion of multiset-equivariance. We identify that the existing Deep Set Prediction Network (DSPN) can be multiset-equivariant without being hindered by set-equivariance and improve it with approximate implicit differentiation, allowing for better optimization while being faster and saving memory. In a range of toy experiments, we show that the perspective of multiset-equivariance is beneficial and that our changes to DSPN achieve better results in most cases. On CLEVR object property prediction, we substantially improve over the state-of-the-art Slot Attention from 8% to 77% in one of the strictest evaluation metrics because of the benefits made possible by implicit differentiation.

Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.

Distance metric learning based on triplet loss has been applied with success in a wide range of applications such as face recognition, image retrieval, speaker change detection and recently recommendation with the CML model. However, as we show in this article, CML requires large batches to work reasonably well because of a too simplistic uniform negative sampling strategy for selecting triplets. Due to memory limitations, this makes it difficult to scale in high-dimensional scenarios. To alleviate this problem, we propose here a 2-stage negative sampling strategy which finds triplets that are highly informative for learning. Our strategy allows CML to work effectively in terms of accuracy and popularity bias, even when the batch size is an order of magnitude smaller than what would be needed with the default uniform sampling. We demonstrate the suitability of the proposed strategy for recommendation and exhibit consistent positive results across various datasets.

A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific models are learned in the inner-loop, by using only a small amount of data from the current task. A key challenge in scaling these approaches is the need to differentiate through the inner loop learning process, which can impose considerable computational and memory burdens. By drawing upon implicit differentiation, we develop the implicit MAML algorithm, which depends only on the solution to the inner level optimization and not the path taken by the inner loop optimizer. This effectively decouples the meta-gradient computation from the choice of inner loop optimizer. As a result, our approach is agnostic to the choice of inner loop optimizer and can gracefully handle many gradient steps without vanishing gradients or memory constraints. Theoretically, we prove that implicit MAML can compute accurate meta-gradients with a memory footprint that is, up to small constant factors, no more than that which is required to compute a single inner loop gradient and at no overall increase in the total computational cost. Experimentally, we show that these benefits of implicit MAML translate into empirical gains on few-shot image recognition benchmarks.

To mitigate the detection performance drop caused by domain shift, we aim to develop a novel few-shot adaptation approach that requires only a few target domain images with limited bounding box annotations. To this end, we first observe several significant challenges. First, the target domain data is highly insufficient, making most existing domain adaptation methods ineffective. Second, object detection involves simultaneous localization and classification, further complicating the model adaptation process. Third, the model suffers from over-adaptation (similar to overfitting when training with a few data example) and instability risk that may lead to degraded detection performance in the target domain. To address these challenges, we first introduce a pairing mechanism over source and target features to alleviate the issue of insufficient target domain samples. We then propose a bi-level module to adapt the source trained detector to the target domain: 1) the split pooling based image level adaptation module uniformly extracts and aligns paired local patch features over locations, with different scale and aspect ratio; 2) the instance level adaptation module semantically aligns paired object features while avoids inter-class confusion. Meanwhile, a source model feature regularization (SMFR) is applied to stabilize the adaptation process of the two modules. Combining these contributions gives a novel few-shot adaptive Faster-RCNN framework, termed FAFRCNN, which effectively adapts to target domain with a few labeled samples. Experiments with multiple datasets show that our model achieves new state-of-the-art performance under both the interested few-shot domain adaptation(FDA) and unsupervised domain adaptation(UDA) setting.

This paper presents an upgraded, real world application oriented version of gym-gazebo, the Robot Operating System (ROS) and Gazebo based Reinforcement Learning (RL) toolkit, which complies with OpenAI Gym. The content discusses the new ROS 2 based software architecture and summarizes the results obtained using Proximal Policy Optimization (PPO). Ultimately, the output of this work presents a benchmarking system for robotics that allows different techniques and algorithms to be compared using the same virtual conditions. We have evaluated environments with different levels of complexity of the Modular Articulated Robotic Arm (MARA), reaching accuracies in the millimeter scale. The converged results show the feasibility and usefulness of the gym-gazebo 2 toolkit, its potential and applicability in industrial use cases, using modular robots.

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activiation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for a broad family of loss functions, with proper random weight initialization, both gradient descent and stochastic gradient descent can find the global minima of the training loss for an over-parameterized deep ReLU network, under mild assumption on the training data. The key idea of our proof is that Gaussian random initialization followed by (stochastic) gradient descent produces a sequence of iterates that stay inside a small perturbation region centering around the initial weights, in which the empirical loss function of deep ReLU networks enjoys nice local curvature properties that ensure the global convergence of (stochastic) gradient descent. Our theoretical results shed light on understanding the optimization of deep learning, and pave the way to study the optimization dynamics of training modern deep neural networks.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.