First, the gating mechanism is ubiquitous in RNNs, and usually thought of as a heuristic forsmoothingoptimization[28].

We introduce a simple sequence model inspired by control systems thatgeneralizes these approaches while addressing their shortcomings.

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence $u \mapsto y$ by simply simulating a linear continuous-time state-space representation $\dot{x} = Ax + Bu, y = Cx + Du$. Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation. We then incorporate and generalize recent theory on continuous-time memorization to introduce a trainable subset of structured matrices $A$ that endow LSSLs with long-range memory.

A comparison is summarized in Table 6.

We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings.

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence u \mapsto y by simply simulating a linear continuous-time state-space representation \dot{x} Ax Bu, y Cx Du . Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation.

Longitudinal analysis in medical imaging is crucial to investigate the progressive changes in anatomical structures or disease progression over time. In recent years, a novel class of algorithms has emerged with the goal of learning disease progression in a self-supervised manner, using either pairs of consecutive images or time series of images. By capturing temporal patterns without external labels or supervision, longitudinal self-supervised learning (LSSL) has become a promising avenue. To better understand this core method, we explore in this paper the LSSL algorithm under different scenarios. The original LSSL is embedded in an auto-encoder (AE) structure. However, conventional self-supervised strategies are usually implemented in a Siamese-like manner. Therefore, (as a first novelty) in this study, we explore the use of Siamese-like LSSL. Another new core framework named neural ordinary differential equation (NODE). NODE is a neural network architecture that learns the dynamics of ordinary differential equations (ODE) through the use of neural networks. Many temporal systems can be described by ODE, including modeling disease progression. We believe that there is an interesting connection to make between LSSL and NODE. This paper aims at providing a better understanding of those core algorithms for learning the disease progression with the mentioned change. In our different experiments, we employ a longitudinal dataset, named OPHDIAT, targeting diabetic retinopathy (DR) follow-up. Our results demonstrate the application of LSSL without including a reconstruction term, as well as the potential of incorporating NODE in conjunction with LSSL.

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence $u \mapsto y$ by simply simulating a linear continuous-time state-space representation $\dot{x} = Ax + Bu, y = Cx + Du$. Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation. We then incorporate and generalize recent theory on continuous-time memorization to introduce a trainable subset of structured matrices $A$ that endow LSSLs with long-range memory. Empirically, stacking LSSL layers into a simple deep neural network obtains state-of-the-art results across time series benchmarks for long dependencies in sequential image classification, real-world healthcare regression tasks, and speech. On a difficult speech classification task with length-16000 sequences, LSSL outperforms prior approaches by 24 accuracy points, and even outperforms baselines that use hand-crafted features on 100x shorter sequences.

Longitudinal neuroimaging or biomedical studies often acquire multiple observations from each individual over time, which entails repeated measures with highly interdependent variables. In this paper, we discuss the implication of repeated measures design on unsupervised learning by showing its tight conceptual connection to self-supervised learning and factor disentanglement. Leveraging the ability for `self-comparison' through repeated measures, we explicitly separate the definition of the factor space and the representation space enabling an exact disentanglement of time-related factors from the representations of the images. By formulating deterministic multivariate mapping functions between the two spaces, our model, named Longitudinal Self-Supervised Learning (LSSL), uses a standard autoencoding structure with a cosine loss to estimate the direction linked to the disentangled factor. We apply LSSL to two longitudinal neuroimaging studies to show its unique advantage in extracting the `brain-age' information from the data and in revealing informative characteristics associated with neurodegenerative and neuropsychological disorders. For a downstream task of supervised diagnosis classification, the representations learned by LSSL permit faster convergence and higher (or similar) prediction accuracy compared to several other representation learning techniques.

In this paper, we propose a novel similarity measure and then introduce an efficient strategy to learn it by using only similar pairs for person verification. Unlike existing metric learning methods, we consider both the difference and commonness of an image pair to increase its discriminativeness. Under a pairconstrained Gaussian assumption, we show how to obtain the Gaussian priors (i.e., corresponding covariance matrices) of dissimilar pairs from those of similar pairs. The application of a log likelihood ratio makes the learning process simple and fast and thus scalable to large datasets. Additionally, our method is able to handle heterogeneous data well. Results on the challenging datasets of face verification (LFW and Pub-Fig) and person re-identification (VIPeR) show that our algorithm outperforms the state-of-the-art methods.