Neurally plausible mechanisms for learning selective and invariant representations

Abstract

Coding for visual stimuli in the ventral stream is known to be invariant to object identity preserving nuisance transformations. Indeed, much recent theoretical and experimental work suggests that the main challenge for the visual cortex is to build up such nuisance invariant representations. Recently, artificial convolutional networks have succeeded in both learning such invariant properties and, surprisingly, predicting cortical responses in macaque and mouse visual cortex with unprecedented accuracy. However, some of the key ingredients that enable such success—supervised learning and the backpropagation algorithm—are neurally implausible. This makes it difficult to relate advances in understanding convolutional networks to the brain. In contrast, many of the existing neurally plausible theories of invariant representations in the brain involve unsupervised learning, and have been strongly tied to specific plasticity rules. To close this gap, we study an instantiation of simple-complex cell model and show, for a broad class of unsupervised learning rules (including Hebbian learning), that we can learn object representations that are invariant to nuisance transformations belonging to a finite orthogonal group. These findings may have implications for developing neurally plausible theories and models of how the visual cortex or artificial neural networks build selectivity for discriminating objects and invariance to real-world nuisance transformations.

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

“…To prove (ii), one needs to show that the elements of W ψ (H R ) are continuous functions, that W ψ (H R ) W ψ W * γ is selfadjoint and idempotent, and that (12). The continuity can be obtained as a consequence of the continuity of the unitary representation (5) and, by the same arguments used to prove (i) we can easily see that 12) can be obtained directly by (6) and the definition of W ψ .…”

“…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.…”

“…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],…”

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.…”