KerCNNs: biologically inspired lateral connections for classification of corrupted images

Abstract

The state of the art in many computer vision tasks is represented by Convolutional Neural Networks (CNNs). Although their hierarchical organization and local feature extraction are inspired by the structure of primate visual systems, the lack of lateral connections in such architectures critically distinguishes their analysis from biological object processing. The idea of enriching CNNs with recurrent lateral connections of convolutional type has been put into practice in recent years, in the form of learned recurrent kernels with no geometrical constraints. In the present work, we introduce biologically plausible lateral kernels encoding a notion of correlation between the feedforward filters of a CNN: at each layer, the associated kernel acts as a transition kernel on the space of activations. The lateral kernels are defined in terms of the filters, thus providing a parameter-free approach to assess the geometry of horizontal connections based on the feedforward structure. We then test this new architecture, which we call KerCNN, on a generalization task related to global shape analysis and pattern completion: once trained for performing basic image classification, the network is evaluated on corrupted testing images. The image perturbations examined are designed to undermine the recognition of the images via local features, thus requiring an integration of context information -which in biological vision is critically linked to lateral connectivity. Our KerCNNs turn out to be far more stable than CNNs and recurrent CNNs to such degradations, thus validating this biologically inspired approach to reinforce object recognition under challenging conditions.

PDE-based Group Equivariant Convolutional Neural Networks

“…The proposed PDE-G-CNNs form a new, unique class of equivariant neural networks, and we show in section 5.4 how regular continuous G-CNNs arise as a special case of our PDE-G-CNNs under a fixed, pre-defined choice of convection parameters KerCNNs An approach to introducing horizontal connectivity in CNNs that does not require a Lie group structure was proposed by Montobbio et al [59,60] in the form of KerCNNs. In this biologically inspired metric model a diffusion process is used to achieve intra-layer connectivity.…”

Reconstructing Group Wavelet Transform From Feature Maps With a Reproducing Kernel Iteration

“…A possible interpretation of the proposed iteration with a kernel defined by the SE(2) group as a neural computation in V1 comes from the modeling of the neural connectivity as a kernel operation (Wilson and Cowan, 1972;Ermentrout and Cowan, 1980;Citti and Sarti, 2015;Montobbio et al, 2018), especially if considered in the framework of a neural system that aims to learn group invariant representations of visual stimuli (Anselmi and Poggio, 2014;Anselmi et al, 2020). A direct comparison of the proposed technique with kernel techniques recently introduced with radically different purposes in Montobbio et al (2018) and Montobbio et al (2019) shows, however, two main differences at the level of the kernel that is used: here, we need the dual wavelet to build the projection kernel, and the iteration kernel effectively contains the feature maps. On the other hand, a possible application is the inclusion of a solvability condition such as Equation ( 14) as iterative steps within learning frameworks such as those of Anselmi et al (2019) and Anselmi et al (2020).…”

“…Moreover, the ideas behind the LNP model have been a main source of inspiration in other disciplines, notably for the design of relevant mathematical and computational theories, such as wavelets and convolutional neural networks (Marr, 1980;LeCun et al, 2010). We also point out that the use of groups and invariances to describe the variability of the neural activity has proved to be a solid idea to build effective models (Citti and Sarti, 2006;Anselmi and Poggio, 2014;Petitot, 2017), whose influence on the design of artificial learning architectures is still very strong (Anselmi et al, 2019(Anselmi et al, , 2020Montobbio et al, 2019;Lafarge et al, 2021).…”

Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration

“…A possible interpretation of this iteration with a kernel defined by the SE(2) group as a neural computation in V1 comes from the modeling of the neural connectivity as a kernel operation [53,29,19,43], especially if considered in the framework of a neural system that aims to learn group invariant representations of visual stimuli [7,6]. A direct comparison of the proposed technique with kernel techniques recently introduced with radically different purposes in [44,43] shows however two main differences at the level of the kernel that is used: here we need the dual wavelet to build the projection kernel, and the iteration kernel effectively contains the feature maps. On the other hand, a possible application is the inclusion of a solvability condition such as (14) as iterative steps within learning frameworks such as those of [5,6].…”

“…Moreover, the ideas behind the LNP model have been a main source of inspiration in other disciplines, notably for the design of relevant mathematical and computational theories, such as wavelets and convolutional neural networks [41,39]. We also point out that the use of groups and invariances to describe the variability of the neural activity has proved to be a solid idea to build effective models [46,18,7], whose influence on the design of artificial learning architectures is still very strong [5,44,6,38],…”