Signature inversion for monotone paths

The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the signature. We show that these weights on lattice paths satisfy the large deviations principle. In particular, this implies that the probability of picking up a "wrong" path is exponentially small in N. The argument relies on a probabilistic interpretation of the signature for monotone paths

The insertion method to invert the signature of a path

The signature is a representation of a path as an infinite sequence of its iterated integrals. Under certain assumptions, the signature characterizes the path, up to translation and reparameterization. Therefore, a crucial question of interest is the development of efficient algorithms to invert the signature, i.e., to reconstruct the path from the information of its (truncated) signature. In this article, we study the insertion procedure, originally introduced by Chang and Lyons (2019), from both a theoretical and a practical point of view. After describing our version of the method, we give its rate of convergence for piecewise linear paths, accompanied by an implementation in Pytorch. The algorithm is parallelized, meaning that it is very efficient at inverting a batch of signatures simultaneously. Its performance is illustrated with both real-world and simulated examples

Task-Adaptive Negative Class Envision for Few-Shot Open-Set Recognition

Recent works seek to endow recognition systems with the ability to handle the open world. Few shot learning aims for fast learning of new classes from limited examples, while open-set recognition considers unknown negative class from the open world. In this paper, we study the problem of few-shot open-set recognition (FSOR), which learns a recognition system robust to queries from new sources with few examples and from unknown open sources. To achieve that, we mimic human capability of envisioning new concepts from prior knowledge, and propose a novel task-adaptive negative class envision method (TANE) to model the open world. Essentially we use an external memory to estimate a negative class representation. Moreover, we introduce a novel conjugate episode training strategy that strengthens the learning process. Extensive experiments on four public benchmarks show that our approach significantly improves the state-of-the-art performance on few-shot open-set recognition. Besides, we extend our method to generalized few-shot open-set recognition (GFSOR), where we also achieve performance gains on MiniImageNet

Decentralized Non-Convex Learning with Linearly Coupled Constraints

Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns some local information and a local variable for jointly minimizing a cost function, but local variables are coupled by linear constraints. Most of the existing methods for such problems are only applicable for convex problems or problems with specific linear constraints. There still lacks a distributed algorithm for such problems with general linear constraints and under nonconvex setting. In this paper, to tackle this problem, we propose a new algorithm, called "proximal dual consensus" (PDC) algorithm, which combines a proximal technique and a dual consensus method. We build the theoretical convergence conditions and show that the proposed PDC algorithm can converge to an $\epsilon$-Karush-Kuhn-Tucker solution within $\mathcal{O}(1/\epsilon)$ iterations. For computation reduction, the PDC algorithm can choose to perform cheap gradient descent per iteration while preserving the same order of $\mathcal{O}(1/\epsilon)$ iteration complexity. Numerical results are presented to demonstrate the good performance of the proposed algorithms for solving a regression problem and a classification problem over a network where agents have only partial observations of data features

Effective Numerical Simulations of Synchronous Generator System

Synchronous generator system is a complicated dynamical system for energy transmission, which plays an important role in modern industrial production. In this article, we propose some predictor-corrector methods and structure-preserving methods for a generator system based on the first benchmark model of subsynchronous resonance, among which the structure-preserving methods preserve a Dirac structure associated with the so-called port-Hamiltonian descriptor systems. To illustrate this, the simplified generator system in the form of index-1 differential-algebraic equations has been derived. Our analyses provide the global error estimates for a special class of structure-preserving methods called Gauss methods, which guarantee their superior performance over the PSCAD/EMTDC and the predictor-corrector methods in terms of computational stability. Numerical simulations are implemented to verify the effectiveness and advantages of our methods

Few-Shot Object Detection with Fully Cross-Transformer

Few-shot object detection (FSOD), with the aim to detect novel objects using very few training examples, has recently attracted great research interest in the community. Metric-learning based methods have been demonstrated to be effective for this task using a two-branch based siamese network, and calculate the similarity between image regions and few-shot examples for detection. However, in previous works, the interaction between the two branches is only restricted in the detection head, while leaving the remaining hundreds of layers for separate feature extraction. Inspired by the recent work on vision transformers and vision-language transformers, we propose a novel Fully Cross-Transformer based model (FCT) for FSOD by incorporating cross-transformer into both the feature backbone and detection head. The asymmetric-batched cross-attention is proposed to aggregate the key information from the two branches with different batch sizes. Our model can improve the few-shot similarity learning between the two branches by introducing the multi-level interactions. Comprehensive experiments on both PASCAL VOC and MSCOCO FSOD benchmarks demonstrate the effectiveness of our model.Comment: Accepted by CVPR 202