Both neurophysiological and psychophysical experiments have pointed out the crucial role of recurrent and feedback connections to process context-dependent information in the early visual cortex. While numerous models have accounted for feedback effects at either neural or representational level, none of them were able to bind those two levels of analysis. Is it possible to describe feedback effects at both levels using the same model? We answer this question by combining Predictive Coding (PC) and Sparse Coding (SC) into a hierarchical and convolutional framework applied to realistic problems. In the Sparse Deep Predictive Coding (SDPC) model, the SC component models the internal recurrent processing within each layer, and the PC component describes the interactions between layers using feedforward and feedback connections. Here, we train a 2-layered SDPC on two different databases of images, and we interpret it as a model of the early visual system (V1 & V2). We first demonstrate that once the training has converged, SDPC exhibits oriented and localized receptive fields in V1 and more complex features in V2. Second, we analyze the effects of feedback on the neural organization beyond the classical receptive field of V1 neurons using interaction maps. These maps are similar to association fields and reflect the Gestalt principle of good continuation. We demonstrate that feedback signals reorganize interaction maps and modulate neural activity to promote contour integration. Third, we demonstrate at the representational level that the SDPC feedback connections are able to overcome noise in input images. Therefore, the SDPC captures the association field principle at the neural level which results in a better reconstruction of blurred images at the representational level.

Rationale and objectivesNon-invasive quantification of the severity of pharyngeal airflow obstruction would enable recognition of obstructive versus central manifestation of sleep apnoea, and identification of symptomatic individuals with severe airflow obstruction despite a low apnoea–hypopnoea index (AHI). Here we provide a novel method that uses simple airflow-versus-time (“shape”) features from individual breaths on an overnight sleep study to automatically and non-invasively quantify the severity of airflow obstruction without oesophageal catheterisation.Methods41 individuals with suspected/diagnosed obstructive sleep apnoea (AHI range 0–91 events·h−1) underwent overnight polysomnography with gold-standard measures of airflow (oronasal pneumotach: “flow”) and ventilatory drive (calibrated intraoesophageal diaphragm electromyogram: “drive”). Obstruction severity was defined as a continuous variable (flow:drive ratio). Multivariable regression used airflow shape features (inspiratory/expiratory timing, flatness, scooping, fluttering) to estimate flow:drive ratio in 136 264 breaths (performance based on leave-one-patient-out cross-validation). Analysis was repeated using simultaneous nasal pressure recordings in a subset (n=17).ResultsGold-standard obstruction severity (flow:drive ratio) varied widely across individuals independently of AHI. A multivariable model (25 features) estimated obstruction severity breath-by-breath (R2=0.58 versus gold-standard, p<0.00001; mean absolute error 22%) and the median obstruction severity across individual patients (R2=0.69, p<0.00001; error 10%). Similar performance was achieved using nasal pressure.ConclusionsThe severity of pharyngeal obstruction can be quantified non-invasively using readily available airflow shape information. Our work overcomes a major hurdle necessary for the recognition and phenotyping of patients with obstructive sleep disordered breathing.

Hierarchical sparse coding (HSC) is a powerful model to efficiently represent multidimensional, structured data such as images. The simplest solution to solve this computationally hard problem is to decompose it into independent layer-wise subproblems. However, neuroscientific evidence would suggest interconnecting these subproblems as in predictive coding (PC) theory, which adds top-down connections between consecutive layers. In this study, we introduce a new model, 2-layer sparse predictive coding, to assess the impact of this interlayer feedback connection. In particular, the 2L-SPC is compared with a hierarchical Lasso (Hi-La) network made out of a sequence of independent Lasso layers. The 2L-SPC and a 2-layer Hi-La net- works are trained on four different databases and with different sparsity parameters on each layer. First, we show that the overall prediction error generated by 2L-SPC is lower thanks to the feedback mechanism as it transfers prediction error between layers. Second, we demonstrate that the inference stage of the 2L-SPC is faster to converge and generates a refined representation in the second layer compared to the Hi-La model. Third, we show that the 2L-SPC top-down connection accelerates the learning process of the HSC problem. Finally, the analysis of the emerging dictionaries shows that the 2L-SPC features are more generic and present a larger spatial extension.