标题： 在函数空间中对句法对象和合并操作进行编码 显示英文标题

标题： Encoding syntactic objects and Merge operations in function spaces

摘要： 我们提供一个数学论证，表明给定词法项在某个函数空间中的表示（例如小波），可以在同一函数空间中构造任意句法对象的忠实表示。这个空间可以赋予一个通过第二Rényi熵构建的交换非结合半环结构。所得的句法对象表示与独异群结构相容。所得的函数集是一个操作符代数，其中操作符中的操作模拟将输入波形转换为编码句法结构的组合输出的电路。Merge在工作区上的作用通过余积和Hopf代数马尔可夫链被忠实实现为这些电路上的作用。这里获得的结果提供了一个构造性论证，表明语法核心计算结构的神经计算实现的理论可能性。我们还给出了这个一般构造的一个特例，在这种情况下，这种Merge的实现方式是在正弦波上进行跨频率相位同步。这也表明Merge可以用半环的后继函数来表示，从而澄清了其与算术后继函数相似性的著名观察。 显示英文摘要

摘要： We provide a mathematical argument showing that, given a representation of lexical items as functions (wavelets, for instance) in some function space, it is possible to construct a faithful representation of arbitrary syntactic objects in the same function space. This space can be endowed with a commutative non-associative semiring structure built using the second Renyi entropy. The resulting representation of syntactic objects is compatible with the magma structure. The resulting set of functions is an algebra over an operad, where the operations in the operad model circuits that transform the input wave forms into a combined output that encodes the syntactic structure. The action of Merge on workspaces is faithfully implemented as action on these circuits, through a coproduct and a Hopf algebra Markov chain. The results obtained here provide a constructive argument showing the theoretical possibility of a neurocomputational realization of the core computational structure of syntax. We also present a particular case of this general construction where this type of realization of Merge is implemented as a cross frequency phase synchronization on sinusoidal waves. This also shows that Merge can be expressed in terms of the successor function of a semiring, thus clarifying the well known observation of its similarities with the successor function of arithmetic.