Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

State space models (SSMs) have shown impressive results on tasks that require modeling long-range dependencies and efficiently scale to long sequences owing to their subquadratic runtime complexity. Originally designed for continuous signals, SSMs have shown superior performance on a plethora of tasks, in vision and audio; however, SSMs still lag Transformer performance in Language Modeling tasks. In this work, we propose a hybrid layer named Block-State Transformer (*BST*), that internally combines an SSM sublayer for long-range contextualization, and a Block Transformer sublayer for short-term representation of sequences. We study three different, and completely *parallelizable*, variants that integrate SSMs and block-wise attention. We show that our model outperforms similar Transformer-based architectures on language modeling perplexity and generalizes to longer sequences. In addition, the Block-State Transformer demonstrates a more than *tenfold* increase in speed at the layer level compared to the Block-Recurrent Transformer when model parallelization is employed.

We investigate the impact of aliasing on generalization in Deep Convolutional Networks and show that data augmentation schemes alone are unable to prevent it due to structural limitations in widely used architectures. Drawing insights from frequency analysis theory, we take a closer look at ResNet and EfficientNet architectures and review the trade-off between aliasing and information loss in each of their major components. We show how to mitigate aliasing by inserting non-trainable low-pass filters at key locations, particularly where networks lack the capacity to learn them. These simple architectural changes lead to substantial improvements in generalization on i.i.d. and even more on out-of-distribution conditions, such as image classification under natural corruptions on ImageNet-C [11] and few-shot learning on Meta-Dataset [26]. State-of-the art results are achieved on both datasets without introducing additional trainable parameters and using the default hyper-parameters of open source codebases.

Recent state-of-the-art performance on human-body pose estimation has been achieved with Deep Convolutional Networks (ConvNets). Traditional ConvNet architectures include pooling and sub-sampling layers which reduce computational requirements, introduce invariance and prevent over-training. These benefits of pooling come at the cost of reduced localization accuracy. We introduce a novel architecture which includes an efficient ‘position refinement’ model that is trained to estimate the joint offset location within a small region of the image. This refinement model is jointly trained in cascade with a state-of-the-art ConvNet model [21] to achieve improved accuracy in human joint location estimation. We show that the variance of our detector approaches the variance of human annotations on the FLIC [20] dataset and outperforms all existing approaches on the MPII-human-pose dataset [1].

Current state-of-the-art classification and detection algorithms train deep convolutional networks using labeled data. In this work we study unsupervised feature learning with convolutional networks in the context of temporally coherent unlabeled data. We focus on feature learning from unlabeled video data, using the assumption that adjacent video frames contain semantically similar information. This assumption is exploited to train a convolutional pooling auto-encoder regularized by slowness and sparsity priors. We establish a connection between slow feature learning and metric learning. Using this connection we define "temporal coherence" -- a criterion which can be used to set hyper-parameters in a principled and automated manner. In a transfer learning experiment, we show that the resulting encoder can be used to define a more semantically coherent metric without the use of labels.

Training deep feature hierarchies to solve supervised learning tasks has achieving state of the art performance on many problems in computer vision. However, a principled way in which to train such hierarchies in the unsupervised setting has remained elusive. In this work we suggest a new architecture and loss for training deep feature hierarchies that linearize the transformations observed in unlabelednatural video sequences. This is done by training a generative model to predict video frames. We also address the problem of inherent uncertainty in prediction by introducing a latent variables that are non-deterministic functions of the input into the network architecture.

The classical paradigm of line and curve detection in images, as prescribed by the Hough transform, breaks down in cluttered and noisy imagery. In this paper we present an "upgraded" and ultimately more robust approach to line detection in images. The classical approach to line detection in imagery is low-pass filtering, followed by edge detection, followed by the application of the Hough transform. Peaks in the Hough transform correspond to straight line segments in the image. In our approach we replace low pass filtering by anisotropic diffusion; we replace edge detection by phase analysis of frequency components; and finally, lines corresponding to peaks in the Hough transform are statistically analyzed to reveal the most prominent and likely line segments (especially if the line thickness is known a priori) in the context of sampling distributions. The technique is demonstrated on real and synthetic aperture sonar (SAS) imagery.