Neural Comput - A no-go theorem for one-layer feedforward networks.

Tópicos

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Resumo

It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain the set of possible response patterns, thereby shaping the neural code. This implies the existence of neural codes that cannot arise solely from feedforward processing. We set out to find such codes in the context of one-layer feedforward networks and identified a large class of combinatorial codes that indeed cannot be shaped by the feedforward architecture alone. However, these codes are difficult to distinguish from codes that share the same sets of maximal activity patterns in the presence of subtractive noise. When we coarsened the notion of combinatorial neural code to keep track of only maximal patterns, we found the surprising result that all such codes can in fact be realized by one-layer feedforward networks. This suggests that recurrent or many-layer feedforward architectures are not necessary for shaping the (coarse) combinatorial features of neural codes. In particular, it is not possible to infer a computational role for recurrent connections from the combinatorics of neural response patterns alone. Our proofs use mathematical tools from classical combinatorial topology, such as the nerve lemma and the existence of an inverse nerve. An unexpected corollary of our main result is that any prescribed (finite) homotopy type can be realized by a subset of the form [Formula: see text], where is a polyhedron.

Resumo Limpo

often hypothes crucial role recurr connect brain constrain set possibl respons pattern therebi shape neural code impli exist neural code aris sole feedforward process set find code context onelay feedforward network identifi larg class combinatori code inde shape feedforward architectur alon howev code difficult distinguish code share set maxim activ pattern presenc subtract nois coarsen notion combinatori neural code keep track maxim pattern found surpris result code can fact realiz onelay feedforward network suggest recurr manylay feedforward architectur necessari shape coars combinatori featur neural code particular possibl infer comput role recurr connect combinator neural respons pattern alon proof use mathemat tool classic combinatori topolog nerv lemma exist invers nerv unexpect corollari main result prescrib finit homotopi type can realiz subset form formula see text polyhedron

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