A No-Go Theorem for One-Layer Feedforward Networks
A No-Go Theorem for One-Layer Feedforward Networks
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DOI：
10.1162/neco_a_00657
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发表时间：
2013-10
影响因子：
2.9
通讯作者：
Chad Giusti;V. Itskov
中科院分区：
文献类型：
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作者：
Chad Giusti;V. Itskov
摘要人们经常假设，大脑中反复出现的连接的一个关键作用是限制可能的反应模式，从而塑造神经代码。这意味着神经代码的存在，不能仅仅产生于前馈处理。我们开始在单层前馈网络的背景下寻找这样的代码，并确定了一大类组合代码，这些代码确实不能单独由前馈架构来塑造。然而，这些代码是难以区分的代码，共享相同的最大活动模式的减法噪声的存在。当我们粗化组合神经代码的概念以仅跟踪最大模式时，我们发现了令人惊讶的结果，即所有此类代码实际上都可以通过单层前馈网络实现。这表明，递归或多层前馈架构对于塑造神经代码的（粗糙）组合特征是不必要的。特别是，它是不可能的，以推断一个计算的作用，经常性的连接，从神经反应模式的组合。我们的证明使用经典组合拓扑学的数学工具，如神经引理和逆神经的存在性。我们的主要结果的一个意想不到的推论是，任何规定的（有限）同伦类型可以实现的形式的子集，其中是一个多面体。
Abstract 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 , where is a polyhedron.