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We prove that training neural networks on 1-D data is equivalent to solving a convex Lasso problem with a fixed, explicitly defined dictionary matrix of features. The specific dictionary depends on the activation and depth. We consider 2-layer networks with piecewise linear activations, deep narrow ReLU networks with up to 4 layers, and rectangular and tree networks with sign activation and arbitrary depth. Interestingly in ReLU networks, a fourth layer creates features that represent reflections of training data about themselves. The Lasso representation sheds insight to globally optimal networks and the solution landscape.

We introduce CyberDemo, a novel approach to robotic imitation learning that leverages simulated human demonstrations for real-world tasks. By incorporating extensive data augmentation in a simulated environment, CyberDemo outperforms traditional in-domain real-world demonstrations when transferred to the real world, handling diverse physical and visual conditions. Regardless of its affordability and convenience in data collection, CyberDemo outperforms baseline methods in terms of success rates across various tasks and exhibits generalizability with previously unseen objects. For example, it can rotate novel tetra-valve and penta-valve, despite human demonstrations only involving tri-valves. Our research demonstrates the significant potential of simulated human demonstrations for real-world dexterous manipulation tasks. More details can be found at //cyber-demo.github.io

Imitation learning has shown great potential for enabling robots to acquire complex manipulation behaviors. However, these algorithms suffer from high sample complexity in long-horizon tasks, where compounding errors accumulate over the task horizons. We present PRIME (PRimitive-based IMitation with data Efficiency), a behavior primitive-based framework designed for improving the data efficiency of imitation learning. PRIME scaffolds robot tasks by decomposing task demonstrations into primitive sequences, followed by learning a high-level control policy to sequence primitives through imitation learning. Our experiments demonstrate that PRIME achieves a significant performance improvement in multi-stage manipulation tasks, with 10-34% higher success rates in simulation over state-of-the-art baselines and 20-48% on physical hardware.

We address the problem of accurately interpolating measured anechoic steering vectors with a deep learning framework called the neural field. This task plays a pivotal role in reducing the resource-intensive measurements required for precise sound source separation and localization, essential as the front-end of speech recognition. Classical approaches to interpolation rely on linear weighting of nearby measurements in space on a fixed, discrete set of frequencies. Drawing inspiration from the success of neural fields for novel view synthesis in computer vision, we introduce the neural steerer, a continuous complex-valued function that takes both frequency and direction as input and produces the corresponding steering vector. Importantly, it incorporates inter-channel phase difference information and a regularization term enforcing filter causality, essential for accurate steering vector modeling. Our experiments, conducted using a dataset of real measured steering vectors, demonstrate the effectiveness of our resolution-free model in interpolating such measurements.

Unsupervised sentence representation learning aims to transform input sentences into fixed-length vectors enriched with intricate semantic information while obviating the reliance on labeled data. Recent progress within this field, propelled by contrastive learning and prompt engineering, has significantly bridged the gap between unsupervised and supervised strategies. Nonetheless, the potential utilization of Chain-of-Thought, remains largely untapped in this trajectory. To unlock the latent capabilities of pre-trained models, such as BERT, we propose a two-stage approach for sentence representation: comprehension and summarization. Subsequently, the output of the latter phase is harnessed as the embedding of the input sentence. For further performance enhancement, we introduce an extended InfoNCE Loss by incorporating the contrast between positive and negative instances. Additionally, we also refine the existing template denoising technique to better mitigate the perturbing influence of prompts on input sentences. Rigorous experimentation substantiates our method, CoT-BERT, transcending a suite of robust baselines without necessitating other text representation models or external databases.

Spatiotemporal predictive learning, which predicts future frames through historical prior knowledge with the aid of deep learning, is widely used in many fields. Previous work essentially improves the model performance by widening or deepening the network, but it also brings surging memory overhead, which seriously hinders the development and application of this technology. In order to improve the performance without increasing memory consumption, we focus on scale, which is another dimension to improve model performance but with low memory requirement. The effectiveness has been widely demonstrated in many CNN-based tasks such as image classification and semantic segmentation, but it has not been fully explored in recent RNN models. In this paper, learning from the benefit of multi-scale, we propose a general framework named Multi-Scale RNN (MS-RNN) to boost recent RNN models for spatiotemporal predictive learning. We verify the MS-RNN framework by thorough theoretical analyses and exhaustive experiments, where the theory focuses on memory reduction and performance improvement while the experiments employ eight RNN models (ConvLSTM, TrajGRU, PredRNN, PredRNN++, MIM, MotionRNN, PredRNN-V2, and PrecipLSTM) and four datasets (Moving MNIST, TaxiBJ, KTH, and Germany). The results show the efficiency that RNN models incorporating our framework have much lower memory cost but better performance than before. Our code is released at \url{//github.com/mazhf/MS-RNN}.

Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids (in Lagrangian descriptions). Existing approaches, however, require the supervision of consecutive particle properties, including positions and velocities. In this paper, we consider a partially observable scenario known as fluid dynamics grounding, that is, inferring the state transitions and interactions within the fluid particle systems from sequential visual observations of the fluid surface. We propose a differentiable two-stage network named NeuroFluid. Our approach consists of (i) a particle-driven neural renderer, which involves fluid physical properties into the volume rendering function, and (ii) a particle transition model optimized to reduce the differences between the rendered and the observed images. NeuroFluid provides the first solution to unsupervised learning of particle-based fluid dynamics by training these two models jointly. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities. It is a potential alternative approach to understanding complex fluid mechanics, such as turbulence, that are difficult to model using traditional methods of mathematical physics.

There recently has been a surge of interest in developing a new class of deep learning (DL) architectures that integrate an explicit time dimension as a fundamental building block of learning and representation mechanisms. In turn, many recent results show that topological descriptors of the observed data, encoding information on the shape of the dataset in a topological space at different scales, that is, persistent homology of the data, may contain important complementary information, improving both performance and robustness of DL. As convergence of these two emerging ideas, we propose to enhance DL architectures with the most salient time-conditioned topological information of the data and introduce the concept of zigzag persistence into time-aware graph convolutional networks (GCNs). Zigzag persistence provides a systematic and mathematically rigorous framework to track the most important topological features of the observed data that tend to manifest themselves over time. To integrate the extracted time-conditioned topological descriptors into DL, we develop a new topological summary, zigzag persistence image, and derive its theoretical stability guarantees. We validate the new GCNs with a time-aware zigzag topological layer (Z-GCNETs), in application to traffic forecasting and Ethereum blockchain price prediction. Our results indicate that Z-GCNET outperforms 13 state-of-the-art methods on 4 time series datasets.

State-of-the-art Convolutional Neural Network (CNN) benefits a lot from multi-task learning (MTL), which learns multiple related tasks simultaneously to obtain shared or mutually related representations for different tasks. The most widely-used MTL CNN structure is based on an empirical or heuristic split on a specific layer (e.g., the last convolutional layer) to minimize different task-specific losses. However, this heuristic sharing/splitting strategy may be harmful to the final performance of one or multiple tasks. In this paper, we propose a novel CNN structure for MTL, which enables automatic feature fusing at every layer. Specifically, we first concatenate features from different tasks according to their channel dimension, and then formulate the feature fusing problem as discriminative dimensionality reduction. We show that this discriminative dimensionality reduction can be done by 1x1 Convolution, Batch Normalization, and Weight Decay in one CNN, which we refer to as Neural Discriminative Dimensionality Reduction (NDDR). We perform ablation analysis in details for different configurations in training the network. The experiments carried out on different network structures and different task sets demonstrate the promising performance and desirable generalizability of our proposed method.

We study the problem of learning to reason in large scale knowledge graphs (KGs). More specifically, we describe a novel reinforcement learning framework for learning multi-hop relational paths: we use a policy-based agent with continuous states based on knowledge graph embeddings, which reasons in a KG vector space by sampling the most promising relation to extend its path. In contrast to prior work, our approach includes a reward function that takes the accuracy, diversity, and efficiency into consideration. Experimentally, we show that our proposed method outperforms a path-ranking based algorithm and knowledge graph embedding methods on Freebase and Never-Ending Language Learning datasets.