In this paper we introduce a sketching algorithm for constructing a tensor train representation of a probability density from its samples. Our method deviates from the standard recursive SVD-based procedure for constructing a tensor train. Instead we formulate and solve a sequence of small linear systems for the individual tensor train cores. This approach can avoid the curse of dimensionality that threatens both the algorithmic and sample complexities of the recovery problem. Specifically, for Markov models, we prove that the tensor cores can be recovered with a sample complexity that is constant with respect to the dimension. Finally, we illustrate the performance of the method with several numerical experiments.
相關內容
In this paper we prove the efficacy of a simple greedy algorithm for a finite horizon online resource allocation/matching problem, when the corresponding static planning linear program (SPP) exhibits a non-degeneracy condition called the general position gap (GPG). The key intuition that we formalize is that the solution of the reward maximizing SPP is the same as a feasibility Linear Program restricted to the optimal basic activities, and under GPG this solution can be tracked with bounded regret by a greedy algorithm, i.e., without the commonly used technique of periodically resolving the SPP. The goal of the decision maker is to combine resources (from a finite set of resource types) into configurations (from a finite set of feasible configurations) where each configuration is specified by the number of resources consumed of each type and a reward. The resources are further subdivided into three types - offline (whose quantity is known and available at time 0), online-queueable (which arrive online and can be stored in a buffer), and online-nonqueueable (which arrive online and must be matched on arrival or lost). Under GRG we prove that, (i) our greedy algorithm gets bounded any-time regret of $\mathcal{O}(1/\epsilon_0)$ for matching reward ($\epsilon_0$ is a measure of the GPG) when no configuration contains both an online-queueable and an online-nonqueueable resource, and (ii) $\mathcal{O}(\log t)$ expected any-time regret otherwise (we also prove a matching lower bound). By considering the three types of resources, our matching framework encompasses several well-studied problems such as dynamic multi-sided matching, network revenue management, online stochastic packing, and multiclass queueing systems.
With the development of pre-trained language models, remarkable success has been witnessed in dialogue understanding (DU). However, current DU approaches usually employ independent models for each distinct DU task without considering shared knowledge across different DU tasks. In this paper, we propose a unified generative dialogue understanding framework, named {\em UniDU}, to achieve effective information exchange across diverse DU tasks. Here, we reformulate all DU tasks into a unified prompt-based generative model paradigm. More importantly, a novel model-agnostic multi-task training strategy (MATS) is introduced to dynamically adapt the weights of diverse tasks for best knowledge sharing during training, based on the nature and available data of each task. Experiments on ten DU datasets covering five fundamental DU tasks show that the proposed UniDU framework largely outperforms task-specific well-designed methods on all tasks. MATS also reveals the knowledge-sharing structure of these tasks. Finally, UniDU obtains promising performance in the unseen dialogue domain, showing the great potential for generalization.
Spiking Neural Networks (SNNs) are the third generation of artificial neural networks that enable energy-efficient implementation on neuromorphic hardware. However, the discrete transmission of spikes brings significant challenges to the robust and high-performance learning mechanism. Most existing works focus solely on learning between neurons but ignore the influence between synapses, resulting in a loss of robustness and accuracy. To address this problem, we propose a robust and effective learning mechanism by modeling the associative plasticity between synapses (APBS) observed from the physiological phenomenon of associative long-term potentiation (ALTP). With the proposed APBS method, synapses of the same neuron interact through a shared factor when concurrently stimulated by other neurons. In addition, we propose a spatiotemporal cropping and flipping (STCF) method to improve the generalization ability of our network. Extensive experiments demonstrate that our approaches achieve superior performance on static CIFAR-10 datasets and state-of-the-art performance on neuromorphic MNIST-DVS, CIFAR10-DVS datasets by a lightweight convolution network. To our best knowledge, this is the first time to explore a learning method between synapses and an extended approach for neuromorphic data.
Program synthesis or code generation aims to generate a program that satisfies a problem specification. Recent approaches using large-scale pretrained language models (LMs) have shown promising results, yet they have some critical limitations. In particular, they often follow a standard supervised fine-tuning procedure to train a code generation model only from the pairs of natural-language problem descriptions and ground-truth programs. Such paradigm largely ignores some important but potentially useful signals in the problem specification such as unit tests, which thus often results in poor performance when solving complex unseen coding tasks. To address the limitations, we propose "CodeRL", a new framework for program synthesis tasks through pretrained LMs and deep reinforcement learning (RL). Specifically, during training, we treat the code-generating LM as an actor network, and introduce a critic network that is trained to predict the functional correctness of generated programs and provide dense feedback signals to the actor. During inference, we introduce a new generation procedure with a critical sampling strategy that allows a model to automatically regenerate programs based on feedback from example unit tests and critic scores. For the model backbones, we extended the encoder-decoder architecture of CodeT5 with enhanced learning objectives, larger model sizes, and better pretraining data. Our method not only achieves new SOTA results on the challenging APPS benchmark, but also shows strong zero-shot transfer capability with new SOTA results on the simpler MBPP benchmark.
Traffic speed prediction is the key to many valuable applications, and it is also a challenging task because of its various influencing factors. Recent work attempts to obtain more information through various hybrid models, thereby improving the prediction accuracy. However, the spatial information acquisition schemes of these methods have two-level differentiation problems. Either the modeling is simple but contains little spatial information, or the modeling is complete but lacks flexibility. In order to introduce more spatial information on the basis of ensuring flexibility, this paper proposes IRNet (Transferable Intersection Reconstruction Network). First, this paper reconstructs the intersection into a virtual intersection with the same structure, which simplifies the topology of the road network. Then, the spatial information is subdivided into intersection information and sequence information of traffic flow direction, and spatiotemporal features are obtained through various models. Third, a self-attention mechanism is used to fuse spatiotemporal features for prediction. In the comparison experiment with the baseline, not only the prediction effect, but also the transfer performance has obvious advantages.
This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single deletion are limited to have information rate at most $1/2$ (achieved by the trivial 2-fold repetition code). Previously, it was (erroneously) reported that more generally no non-trivial linear codes correcting $k$ deletions exist, i.e., that the $(k+1)$-fold repetition codes and its rate of $1/(k+1)$ are basically optimal for any $k$. We disprove this and show the existence of binary linear codes of length $n$ and rate just below $1/2$ capable of correcting $\Omega(n)$ insertions and deletions. This identifies rate $1/2$ as a sharp threshold for recovery from deletions for linear codes, and reopens the quest for a better understanding of the capabilities of linear codes for correcting insertions/deletions. We prove novel outer bounds and existential inner bounds for the rate vs. (edit) distance trade-off of linear insdel codes. We complement our existential results with an efficient synchronization-string-based transformation that converts any asymptotically-good linear code for Hamming errors into an asymptotically-good linear code for insdel errors. Lastly, we show that the $\frac{1}{2}$-rate limitation does not hold for affine codes by giving an explicit affine code of rate $1-\epsilon$ which can efficiently correct a constant fraction of insdel errors.
Policy learning in multi-agent reinforcement learning (MARL) is challenging due to the exponential growth of joint state-action space with respect to the number of agents. To achieve higher scalability, the paradigm of centralized training with decentralized execution (CTDE) is broadly adopted with factorized structure in MARL. However, we observe that existing CTDE algorithms in cooperative MARL cannot achieve optimality even in simple matrix games. To understand this phenomenon, we introduce a framework of Generalized Multi-Agent Actor-Critic with Policy Factorization (GPF-MAC), which characterizes the learning of factorized joint policies, i.e., each agent's policy only depends on its own observation-action history. We show that most popular CTDE MARL algorithms are special instances of GPF-MAC and may be stuck in a suboptimal joint policy. To address this issue, we present a novel transformation framework that reformulates a multi-agent MDP as a special "single-agent" MDP with a sequential structure and can allow employing off-the-shelf single-agent reinforcement learning (SARL) algorithms to efficiently learn corresponding multi-agent tasks. This transformation retains the optimality guarantee of SARL algorithms into cooperative MARL. To instantiate this transformation framework, we propose a Transformed PPO, called T-PPO, which can theoretically perform optimal policy learning in the finite multi-agent MDPs and shows significant outperformance on a large set of cooperative multi-agent tasks.
In the domain generalization literature, a common objective is to learn representations independent of the domain after conditioning on the class label. We show that this objective is not sufficient: there exist counter-examples where a model fails to generalize to unseen domains even after satisfying class-conditional domain invariance. We formalize this observation through a structural causal model and show the importance of modeling within-class variations for generalization. Specifically, classes contain objects that characterize specific causal features, and domains can be interpreted as interventions on these objects that change non-causal features. We highlight an alternative condition: inputs across domains should have the same representation if they are derived from the same object. Based on this objective, we propose matching-based algorithms when base objects are observed (e.g., through data augmentation) and approximate the objective when objects are not observed (MatchDG). Our simple matching-based algorithms are competitive to prior work on out-of-domain accuracy for rotated MNIST, Fashion-MNIST, PACS, and Chest-Xray datasets. Our method MatchDG also recovers ground-truth object matches: on MNIST and Fashion-MNIST, top-10 matches from MatchDG have over 50% overlap with ground-truth matches.
Generative models are now capable of producing highly realistic images that look nearly indistinguishable from the data on which they are trained. This raises the question: if we have good enough generative models, do we still need datasets? We investigate this question in the setting of learning general-purpose visual representations from a black-box generative model rather than directly from data. Given an off-the-shelf image generator without any access to its training data, we train representations from the samples output by this generator. We compare several representation learning methods that can be applied to this setting, using the latent space of the generator to generate multiple "views" of the same semantic content. We show that for contrastive methods, this multiview data can naturally be used to identify positive pairs (nearby in latent space) and negative pairs (far apart in latent space). We find that the resulting representations rival those learned directly from real data, but that good performance requires care in the sampling strategy applied and the training method. Generative models can be viewed as a compressed and organized copy of a dataset, and we envision a future where more and more "model zoos" proliferate while datasets become increasingly unwieldy, missing, or private. This paper suggests several techniques for dealing with visual representation learning in such a future. Code is released on our project page: //ali-design.github.io/GenRep/
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191