Yubei Chen

Shengbang Tong, Yubei Chen, Yi Ma et al.

Recently, self-supervised learning (SSL) has achieved tremendous success in learning image representation. Despite the empirical success, most self-supervised learning methods are rather "inefficient" learners, typically taking hundreds of training epochs to fully converge. In this work, we show that the key towards efficient self-supervised learning is to increase the number of crops from each image instance. Leveraging one of the state-of-the-art SSL method, we introduce a simplistic form of self-supervised learning method called Extreme-Multi-Patch Self-Supervised-Learning (EMP-SSL) that does not rely on many heuristic techniques for SSL such as weight sharing between the branches, feature-wise normalization, output quantization, and stop gradient, etc, and reduces the training epochs by two orders of magnitude. We show that the proposed method is able to converge to 85.1% on CIFAR-10, 58.5% on CIFAR-100, 38.1% on Tiny ImageNet and 58.5% on ImageNet-100 in just one epoch. Furthermore, the proposed method achieves 91.5% on CIFAR-10, 70.1% on CIFAR-100, 51.5% on Tiny ImageNet and 78.9% on ImageNet-100 with linear probing in less than ten training epochs. In addition, we show that EMP-SSL shows significantly better transferability to out-of-domain datasets compared to baseline SSL methods. We will release the code in https://github.com/tsb0601/EMP-SSL.

Shengbang Tong, Xili Dai, Yubei Chen et al.

This paper proposes an unsupervised method for learning a unified representation that serves both discriminative and generative purposes. While most existing unsupervised learning approaches focus on a representation for only one of these two goals, we show that a unified representation can enjoy the mutual benefits of having both. Such a representation is attainable by generalizing the recently proposed \textit{closed-loop transcription} framework, known as CTRL, to the unsupervised setting. This entails solving a constrained maximin game over a rate reduction objective that expands features of all samples while compressing features of augmentations of each sample. Through this process, we see discriminative low-dimensional structures emerge in the resulting representations. Under comparable experimental conditions and network complexities, we demonstrate that these structured representations enable classification performance close to state-of-the-art unsupervised discriminative representations, and conditionally generated image quality significantly higher than that of state-of-the-art unsupervised generative models. Source code can be found at https://github.com/Delay-Xili/uCTRL.

Quentin Garrido, Yubei Chen, Adrien Bardes et al.

Recent approaches in self-supervised learning of image representations can be categorized into different families of methods and, in particular, can be divided into contrastive and non-contrastive approaches. While differences between the two families have been thoroughly discussed to motivate new approaches, we focus more on the theoretical similarities between them. By designing contrastive and covariance based non-contrastive criteria that can be related algebraically and shown to be equivalent under limited assumptions, we show how close those families can be. We further study popular methods and introduce variations of them, allowing us to relate this theoretical result to current practices and show the influence (or lack thereof) of design choices on downstream performance. Motivated by our equivalence result, we investigate the low performance of SimCLR and show how it can match VICReg's with careful hyperparameter tuning, improving significantly over known baselines. We also challenge the popular assumption that non-contrastive methods need large output dimensions. Our theoretical and quantitative results suggest that the numerical gaps between contrastive and non-contrastive methods in certain regimes can be closed given better network design choices and hyperparameter tuning. The evidence shows that unifying different SOTA methods is an important direction to build a better understanding of self-supervised learning.

Bobak T. Kiani, Randall Balestriero, Yubei Chen et al.

The fundamental goal of self-supervised learning (SSL) is to produce useful representations of data without access to any labels for classifying the data. Modern methods in SSL, which form representations based on known or constructed relationships between samples, have been particularly effective at this task. Here, we aim to extend this framework to incorporate algorithms based on kernel methods where embeddings are constructed by linear maps acting on the feature space of a kernel. In this kernel regime, we derive methods to find the optimal form of the output representations for contrastive and non-contrastive loss functions. This procedure produces a new representation space with an inner product denoted as the induced kernel which generally correlates points which are related by an augmentation in kernel space and de-correlates points otherwise. We analyze our kernel model on small datasets to identify common features of self-supervised learning algorithms and gain theoretical insights into their performance on downstream tasks.

Jiachen Zhu, Katrina Evtimova, Yubei Chen et al.

Transfer learning plays a key role in advancing machine learning models, yet conventional supervised pretraining often undermines feature transferability by prioritizing features that minimize the pretraining loss. In this work, we adapt a self-supervised learning regularization technique from the VICReg method to supervised learning contexts, introducing Variance-Covariance Regularization (VCReg). This adaptation encourages the network to learn high-variance, low-covariance representations, promoting learning more diverse features. We outline best practices for an efficient implementation of our framework, including applying it to the intermediate representations. Through extensive empirical evaluation, we demonstrate that our method significantly enhances transfer learning for images and videos, achieving state-of-the-art performance across numerous tasks and datasets. VCReg also improves performance in scenarios like long-tail learning and hierarchical classification. Additionally, we show its effectiveness may stem from its success in addressing challenges like gradient starvation and neural collapse. In summary, VCReg offers a universally applicable regularization framework that significantly advances transfer learning and highlights the connection between gradient starvation, neural collapse, and feature transferability.

Yubei Chen, Adrien Bardes, Zengyi Li et al.

Self-supervised learning (SSL) has recently achieved tremendous empirical advancements in learning image representation. However, our understanding of the principle behind learning such a representation is still limited. This work shows that joint-embedding SSL approaches primarily learn a representation of image patches, which reflects their co-occurrence. Such a connection to co-occurrence modeling can be established formally, and it supplements the prevailing invariance perspective. We empirically show that learning a representation for fixed-scale patches and aggregating local patch representations as the image representation achieves similar or even better results than the baseline methods. We denote this process as BagSSL. Even with 32x32 patch representation, BagSSL achieves 62% top-1 linear probing accuracy on ImageNet. On the other hand, with a multi-scale pretrained model, we show that the whole image embedding is approximately the average of local patch embeddings. While the SSL representation is relatively invariant at the global scale, we show that locality is preserved when we zoom into local patch-level representation. Further, we show that patch representation aggregation can improve various SOTA baseline methods by a large margin. The patch representation is considerably easier to understand, and this work makes a step to demystify self-supervised representation learning.

Yubei Chen, Zeyu Yun, Yi Ma et al.

We describe a minimalistic and interpretable method for unsupervised learning, without resorting to data augmentation, hyperparameter tuning, or other engineering designs, that achieves performance close to the SOTA SSL methods. Our approach leverages the sparse manifold transform, which unifies sparse coding, manifold learning, and slow feature analysis. With a one-layer deterministic sparse manifold transform, one can achieve 99.3% KNN top-1 accuracy on MNIST, 81.1% KNN top-1 accuracy on CIFAR-10 and 53.2% on CIFAR-100. With a simple gray-scale augmentation, the model gets 83.2% KNN top-1 accuracy on CIFAR-10 and 57% on CIFAR-100. These results significantly close the gap between simplistic "white-box" methods and the SOTA methods. Additionally, we provide visualization to explain how an unsupervised representation transform is formed. The proposed method is closely connected to latent-embedding self-supervised methods and can be treated as the simplest form of VICReg. Though there remains a small performance gap between our simple constructive model and SOTA methods, the evidence points to this as a promising direction for achieving a principled and white-box approach to unsupervised learning.

Zeyu Yun, Juexiao Zhang, Yann LeCun et al.

Unsupervised representation learning has seen tremendous progress. However, it is constrained by its reliance on domain specific stationarity and topology, a limitation not found in biological intelligence systems. For instance, unlike computer vision, human vision can process visual signals sampled from highly irregular and non-stationary sensors. We introduce a novel framework that learns from high-dimensional data without prior knowledge of stationarity and topology. Our model, abbreviated as URLOST, combines a learnable self-organizing layer, spectral clustering, and a masked autoencoder (MAE). We evaluate its effectiveness on three diverse data modalities including simulated biological vision data, neural recordings from the primary visual cortex, and gene expressions. Compared to state-of-the-art unsupervised learning methods like SimCLR and MAE, our model excels at learning meaningful representations across diverse modalities without knowing their stationarity or topology. It also outperforms other methods that are not dependent on these factors, setting a new benchmark in the field. We position this work as a step toward unsupervised learning methods capable of generalizing across diverse high-dimensional data modalities.

Pu Hua, Yubei Chen, Huazhe Xu

The low-level sensory and motor signals in deep reinforcement learning, which exist in high-dimensional spaces such as image observations or motor torques, are inherently challenging to understand or utilize directly for downstream tasks. While sensory representations have been extensively studied, the representations of motor actions are still an area of active exploration. Our work reveals that a space containing meaningful action representations emerges when a multi-task policy network takes as inputs both states and task embeddings. Moderate constraints are added to improve its representation ability. Therefore, interpolated or composed embeddings can function as a high-level interface within this space, providing instructions to the agent for executing meaningful action sequences. Empirical results demonstrate that the proposed action representations are effective for intra-action interpolation and inter-action composition with limited or no additional learning. Furthermore, our approach exhibits superior task adaptation ability compared to strong baselines in Mujoco locomotion tasks. Our work sheds light on the promising direction of learning action representations for efficient, adaptable, and composable RL, forming the basis of abstract action planning and the understanding of motor signal space. Project page: https://sites.google.com/view/emergent-action-representation/

Yunhui Guo, Youren Zhang, Yubei Chen et al.

Given an image set without any labels, our goal is to train a model that maps each image to a point in a feature space such that, not only proximity indicates visual similarity, but where it is located directly encodes how prototypical the image is according to the dataset. Our key insight is to perform unsupervised feature learning in hyperbolic instead of Euclidean space, where the distance between points still reflect image similarity, and yet we gain additional capacity for representing prototypicality with the location of the point: The closer it is to the origin, the more prototypical it is. The latter property is simply emergent from optimizing the usual metric learning objective: The image similar to many training instances is best placed at the center of corresponding points in Euclidean space, but closer to the origin in hyperbolic space. We propose an unsupervised feature learning algorithm in Hyperbolic space with sphere pACKing. HACK first generates uniformly packed particles in the Poincaré ball of hyperbolic space and then assigns each image uniquely to each particle. Images after congealing are regarded more typical of the dataset it belongs to. With our feature mapper simply trained to spread out training instances in hyperbolic space, we observe that images move closer to the origin with congealing, validating our idea of unsupervised prototypicality discovery. We demonstrate that our data-driven prototypicality provides an easy and superior unsupervised instance selection to reduce sample complexity, increase model generalization with atypical instances and robustness with typical ones.

Zeyu Yun, Yubei Chen, Bruno A Olshausen et al.

Transformer networks have revolutionized NLP representation learning since they were introduced. Though a great effort has been made to explain the representation in transformers, it is widely recognized that our understanding is not sufficient. One important reason is that there lack enough visualization tools for detailed analysis. In this paper, we propose to use dictionary learning to open up these "black boxes" as linear superpositions of transformer factors. Through visualization, we demonstrate the hierarchical semantic structures captured by the transformer factors, e.g., word-level polysemy disambiguation, sentence-level pattern formation, and long-range dependency. While some of these patterns confirm the conventional prior linguistic knowledge, the rest are relatively unexpected, which may provide new insights. We hope this visualization tool can bring further knowledge and a better understanding of how transformer networks work. The code is available at https://github.com/zeyuyun1/TransformerVis

Jiayun Wang, Jierui Lin, Qian Yu et al.

Sketches are the most abstract 2D representations of real-world objects. Although a sketch usually has geometrical distortion and lacks visual cues, humans can effortlessly envision a 3D object from it. This suggests that sketches encode the information necessary for reconstructing 3D shapes. Despite great progress achieved in 3D reconstruction from distortion-free line drawings, such as CAD and edge maps, little effort has been made to reconstruct 3D shapes from free-hand sketches. We study this task and aim to enhance the power of sketches in 3D-related applications such as interactive design and VR/AR games. Unlike previous works, which mostly study distortion-free line drawings, our 3D shape reconstruction is based on free-hand sketches. A major challenge for free-hand sketch 3D reconstruction comes from the insufficient training data and free-hand sketch diversity, e.g. individualized sketching styles. We thus propose data generation and standardization mechanisms. Instead of distortion-free line drawings, synthesized sketches are adopted as input training data. Additionally, we propose a sketch standardization module to handle different sketch distortions and styles. Extensive experiments demonstrate the effectiveness of our model and its strong generalizability to various free-hand sketches. Our code is publicly available at https://github.com/samaonline/3D-Shape-Reconstruction-from-Free-Hand-Sketches.

Jiayun Wang, Yubei Chen, Rudrasis Chakraborty et al.

Deep convolutional neural networks are hindered by training instability and feature redundancy towards further performance improvement. A promising solution is to impose orthogonality on convolutional filters. We develop an efficient approach to impose filter orthogonality on a convolutional layer based on the doubly block-Toeplitz matrix representation of the convolutional kernel instead of using the common kernel orthogonality approach, which we show is only necessary but not sufficient for ensuring orthogonal convolutions. Our proposed orthogonal convolution requires no additional parameters and little computational overhead. This method consistently outperforms the kernel orthogonality alternative on a wide range of tasks such as image classification and inpainting under supervised, semi-supervised and unsupervised settings. Further, it learns more diverse and expressive features with better training stability, robustness, and generalization. Our code is publicly available at https://github.com/samaonline/Orthogonal-Convolutional-Neural-Networks.

Chun-Hsiao Yeh, Ta-Ying Cheng, He-Yen Hsieh et al.

Recent text-to-image diffusion models are able to learn and synthesize images containing novel, personalized concepts (e.g., their own pets or specific items) with just a few examples for training. This paper tackles two interconnected issues within this realm of personalizing text-to-image diffusion models. First, current personalization techniques fail to reliably extend to multiple concepts -- we hypothesize this to be due to the mismatch between complex scenes and simple text descriptions in the pre-training dataset (e.g., LAION). Second, given an image containing multiple personalized concepts, there lacks a holistic metric that evaluates performance on not just the degree of resemblance of personalized concepts, but also whether all concepts are present in the image and whether the image accurately reflects the overall text description. To address these issues, we introduce Gen4Gen, a semi-automated dataset creation pipeline utilizing generative models to combine personalized concepts into complex compositions along with text-descriptions. Using this, we create a dataset called MyCanvas, that can be used to benchmark the task of multi-concept personalization. In addition, we design a comprehensive metric comprising two scores (CP-CLIP and TI-CLIP) for better quantifying the performance of multi-concept, personalized text-to-image diffusion methods. We provide a simple baseline built on top of Custom Diffusion with empirical prompting strategies for future researchers to evaluate on MyCanvas. We show that by improving data quality and prompting strategies, we can significantly increase multi-concept personalized image generation quality, without requiring any modifications to model architecture or training algorithms.

Jiayun Wang, Yubei Chen, Stella X. Yu

Learning visual features from unlabeled images has proven successful for semantic categorization, often by mapping different $views$ of the same object to the same feature to achieve recognition invariance. However, visual recognition involves not only identifying $what$ an object is but also understanding $how$ it is presented. For example, seeing a car from the side versus head-on is crucial for deciding whether to stay put or jump out of the way. While unsupervised feature learning for downstream viewpoint reasoning is important, it remains under-explored, partly due to the lack of a standardized evaluation method and benchmarks. We introduce a new dataset of adjacent image triplets obtained from a viewpoint trajectory, without any semantic or pose labels. We benchmark both semantic classification and pose estimation accuracies on the same visual feature. Additionally, we propose a viewpoint trajectory regularization loss for learning features from unlabeled image triplets. Our experiments demonstrate that this approach helps develop a visual representation that encodes object identity and organizes objects by their poses, retaining semantic classification accuracy while achieving emergent global pose awareness and better generalization to novel objects. Our dataset and code are available at http://pwang.pw/trajSSL/.

Chenjie Hao, Weyl Lu, Yifan Xu et al.

An embodied system must not only model the patterns of the external world but also understand its own motion dynamics. A motion dynamic model is essential for efficient skill acquisition and effective planning. In this work, we introduce the neural motion simulator (MoSim), a world model that predicts the future physical state of an embodied system based on current observations and actions. MoSim achieves state-of-the-art performance in physical state prediction and provides competitive performance across a range of downstream tasks. This works shows that when a world model is accurate enough and performs precise long-horizon predictions, it can facilitate efficient skill acquisition in imagined worlds and even enable zero-shot reinforcement learning. Furthermore, MoSim can transform any model-free reinforcement learning (RL) algorithm into a model-based approach, effectively decoupling physical environment modeling from RL algorithm development. This separation allows for independent advancements in RL algorithms and world modeling, significantly improving sample efficiency and enhancing generalization capabilities. Our findings highlight that world models for motion dynamics is a promising direction for developing more versatile and capable embodied systems.

Zengyi Li, Yubei Chen, Yann LeCun et al.

Given a union of non-linear manifolds, non-linear subspace clustering or manifold clustering aims to cluster data points based on manifold structures and also learn to parameterize each manifold as a linear subspace in a feature space. Deep neural networks have the potential to achieve this goal under highly non-linear settings given their large capacity and flexibility. We argue that achieving manifold clustering with neural networks requires two essential ingredients: a domain-specific constraint that ensures the identification of the manifolds, and a learning algorithm for embedding each manifold to a linear subspace in the feature space. This work shows that many constraints can be implemented by data augmentation. For subspace feature learning, Maximum Coding Rate Reduction (MCR$^2$) objective can be used. Putting them together yields {\em Neural Manifold Clustering and Embedding} (NMCE), a novel method for general purpose manifold clustering, which significantly outperforms autoencoder-based deep subspace clustering. Further, on more challenging natural image datasets, NMCE can also outperform other algorithms specifically designed for clustering. Qualitatively, we demonstrate that NMCE learns a meaningful and interpretable feature space. As the formulation of NMCE is closely related to several important Self-supervised learning (SSL) methods, we believe this work can help us build a deeper understanding on SSL representation learning.

Chun-Hsiao Yeh, Cheng-Yao Hong, Yen-Chi Hsu et al.

Contrastive learning (CL) is one of the most successful paradigms for self-supervised learning (SSL). In a principled way, it considers two augmented "views" of the same image as positive to be pulled closer, and all other images as negative to be pushed further apart. However, behind the impressive success of CL-based techniques, their formulation often relies on heavy-computation settings, including large sample batches, extensive training epochs, etc. We are thus motivated to tackle these issues and establish a simple, efficient, yet competitive baseline of contrastive learning. Specifically, we identify, from theoretical and empirical studies, a noticeable negative-positive-coupling (NPC) effect in the widely used InfoNCE loss, leading to unsuitable learning efficiency concerning the batch size. By removing the NPC effect, we propose decoupled contrastive learning (DCL) loss, which removes the positive term from the denominator and significantly improves the learning efficiency. DCL achieves competitive performance with less sensitivity to sub-optimal hyperparameters, requiring neither large batches in SimCLR, momentum encoding in MoCo, or large epochs. We demonstrate with various benchmarks while manifesting robustness as much less sensitive to suboptimal hyperparameters. Notably, SimCLR with DCL achieves 68.2% ImageNet-1K top-1 accuracy using batch size 256 within 200 epochs pre-training, outperforming its SimCLR baseline by 6.4%. Further, DCL can be combined with the SOTA contrastive learning method, NNCLR, to achieve 72.3% ImageNet-1K top-1 accuracy with 512 batch size in 400 epochs, which represents a new SOTA in contrastive learning. We believe DCL provides a valuable baseline for future contrastive SSL studies.

Yunhui Guo, Xudong Wang, Yubei Chen et al.

Hyperbolic space can naturally embed hierarchies, unlike Euclidean space. Hyperbolic Neural Networks (HNNs) exploit such representational power by lifting Euclidean features into hyperbolic space for classification, outperforming Euclidean neural networks (ENNs) on datasets with known semantic hierarchies. However, HNNs underperform ENNs on standard benchmarks without clear hierarchies, greatly restricting HNNs' applicability in practice. Our key insight is that HNNs' poorer general classification performance results from vanishing gradients during backpropagation, caused by their hybrid architecture connecting Euclidean features to a hyperbolic classifier. We propose an effective solution by simply clipping the Euclidean feature magnitude while training HNNs. Our experiments demonstrate that clipped HNNs become super-hyperbolic classifiers: They are not only consistently better than HNNs which already outperform ENNs on hierarchical data, but also on-par with ENNs on MNIST, CIFAR10, CIFAR100 and ImageNet benchmarks, with better adversarial robustness and out-of-distribution detection.

Jiayun Wang, Yubei Chen, Stella X. Yu et al.

Deep learning has achieved tremendous success by training increasingly large models, which are then compressed for practical deployment. We propose a drastically different approach to compact and optimal deep learning: We decouple the Degrees of freedom (DoF) and the actual number of parameters of a model, optimize a small DoF with predefined random linear constraints for a large model of arbitrary architecture, in one-stage end-to-end learning. Specifically, we create a recurrent parameter generator (RPG), which repeatedly fetches parameters from a ring and unpacks them onto a large model with random permutation and sign flipping to promote parameter decorrelation. We show that gradient descent can automatically find the best model under constraints with faster convergence. Our extensive experimentation reveals a log-linear relationship between model DoF and accuracy. Our RPG demonstrates remarkable DoF reduction and can be further pruned and quantized for additional run-time performance gain. For example, in terms of top-1 accuracy on ImageNet, RPG achieves $96\%$ of ResNet18's performance with only $18\%$ DoF (the equivalent of one convolutional layer) and $52\%$ of ResNet34's performance with only $0.25\%$ DoF! Our work shows a significant potential of constrained neural optimization in compact and optimal deep learning.

Ho Yin Chau, Frank Qiu, Yubei Chen et al.

Discrete spatial patterns and their continuous transformations are two important regularities contained in natural signals. Lie groups and representation theory are mathematical tools that have been used in previous works to model continuous image transformations. On the other hand, sparse coding is an important tool for learning dictionaries of patterns in natural signals. In this paper, we combine these ideas in a Bayesian generative model that learns to disentangle spatial patterns and their continuous transformations in a completely unsupervised manner. Images are modeled as a sparse superposition of shape components followed by a transformation that is parameterized by n continuous variables. The shape components and transformations are not predefined, but are instead adapted to learn the symmetries in the data, with the constraint that the transformations form a representation of an n-dimensional torus. Training the model on a dataset consisting of controlled geometric transformations of specific MNIST digits shows that it can recover these transformations along with the digits. Training on the full MNIST dataset shows that it can learn both the basic digit shapes and the natural transformations such as shearing and stretching that are contained in this data.

Zengyi Li, Yubei Chen, Friedrich T. Sommer

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the efficiency of MCMC methods. Augmenting samplers with neural networks can potentially improve their efficiency. Previous neural network based samplers were trained with objectives that either did not explicitly encourage exploration, or used a L2 jump objective which could only be applied to well structured distributions. Thus it seems promising to instead maximize the proposal entropy for adapting the proposal to distributions of any shape. To allow direct optimization of the proposal entropy, we propose a neural network MCMC sampler that has a flexible and tractable proposal distribution. Specifically, our network architecture utilizes the gradient of the target distribution for generating proposals. Our model achieves significantly higher efficiency than previous neural network MCMC techniques in a variety of sampling tasks. Further, the sampler is applied on training of a convergent energy-based model of natural images. The adaptive sampler achieves unbiased sampling with significantly higher proposal entropy than Langevin dynamics sampler.

Hong-Ye Hu, Dian Wu, Yi-Zhuang You et al.

Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, RG-Flow, which can separate information at different scales of images and extract disentangled representations at each scale. We demonstrate our method on synthetic multi-scale image datasets and the CelebA dataset, showing that the disentangled representations enable semantic manipulation and style mixing of the images at different scales. To visualize the latent representations, we introduce receptive fields for flow-based models and show that the receptive fields of RG-Flow are similar to those of convolutional neural networks. In addition, we replace the widely adopted isotropic Gaussian prior distribution by the sparse Laplacian distribution to further enhance the disentanglement of representations. From a theoretical perspective, our proposed method has $O(\log L)$ complexity for inpainting of an image with edge length $L$, compared to previous generative models with $O(L^2)$ complexity.

Zengyi Li, Yubei Chen, Friedrich T. Sommer

Energy-Based Models (EBMs) assign unnormalized log-probability to data samples. This functionality has a variety of applications, such as sample synthesis, data denoising, sample restoration, outlier detection, Bayesian reasoning, and many more. But training of EBMs using standard maximum likelihood is extremely slow because it requires sampling from the model distribution. Score matching potentially alleviates this problem. In particular, denoising score matching \citep{vincent2011connection} has been successfully used to train EBMs. Using noisy data samples with one fixed noise level, these models learn fast and yield good results in data denoising \citep{saremi2019neural}. However, demonstrations of such models in high quality sample synthesis of high dimensional data were lacking. Recently, \citet{song2019generative} have shown that a generative model trained by denoising score matching accomplishes excellent sample synthesis, when trained with data samples corrupted with multiple levels of noise. Here we provide analysis and empirical evidence showing that training with multiple noise levels is necessary when the data dimension is high. Leveraging this insight, we propose a novel EBM trained with multi-scale denoising score matching. Our model exhibits data generation performance comparable to state-of-the-art techniques such as GANs, and sets a new baseline for EBMs. The proposed model also provides density information and performs well in an image inpainting task.

Juexiao Zhang, Yubei Chen, Brian Cheung et al.

Co-occurrence statistics based word embedding techniques have proved to be very useful in extracting the semantic and syntactic representation of words as low dimensional continuous vectors. In this work, we discovered that dictionary learning can open up these word vectors as a linear combination of more elementary word factors. We demonstrate many of the learned factors have surprisingly strong semantic or syntactic meaning corresponding to the factors previously identified manually by human inspection. Thus dictionary learning provides a powerful visualization tool for understanding word embedding representations. Furthermore, we show that the word factors can help in identifying key semantic and syntactic differences in word analogy tasks and improve upon the state-of-the-art word embedding techniques in these tasks by a large margin.

Brian Cheung, Alex Terekhov, Yubei Chen et al.

We present a method for storing multiple models within a single set of parameters. Models can coexist in superposition and still be retrieved individually. In experiments with neural networks, we show that a surprisingly large number of models can be effectively stored within a single parameter instance. Furthermore, each of these models can undergo thousands of training steps without significantly interfering with other models within the superposition. This approach may be viewed as the online complement of compression: rather than reducing the size of a network after training, we make use of the unrealized capacity of a network during training.

Yubei Chen, Dylan M. Paiton, Bruno A. Olshausen

We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility. The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes. When stacked, it also models hierarchical composition. We provide a theoretical description of the transform and demonstrate properties of the learned representation on both synthetic data and natural videos.