From dendritic computation to symbolic operation.
Pascal Nieters
Institute of Cognitive Science, Osnabrück University

Summary. Neuromorphic computing aims to provide new technologies and substrates for artificial
neural networks to implement cognitive computations otherwise implemented by brains. However, it is
not clear how symbolic manipulations our minds carry out routinely are implemented in subsymbolic
neural computation. Therefore, we ask what neuromorphic theories are missing. Our hypothesisis that neural dendrites are substrates for logical operations and that single neurons embedded inlarger networks are already capable structured representations of knowledge. We discuss how newneuromorphic computers can benefit from implementing local, structured computers with memory as
part of larger networks to unlock a new category of computations.

Traditional von-Neumann computers are well-formalized and understood systems that do however
become more and more difficult to scale. Newly developed approaches to computation, for example neuromorphic computing inspired by brain circuits, promise to break through this apparent glass-ceiling but
do not offer a clear-cut formalisation of computation and often end up as black-box approaches to computation. This tension between understanding computation and scaling new computational paradigms is
also reflected in the debate between connectionists and proponents of traditional cognitive architecturesin neural network research [1, 2]. Proposed solutions usually entail implementing reasoning on top of aconnectionist implementation. For example, conceptors have recently been introduced as a method toassign transient dynamics characterized by regions in the phase space of recurrent networks to symbols
that can be combined with logical connectives [3]. In all cases, models fundamentally agree on the basic
notion of what a neural network is: A network of single, atomic nodes following the point-neuron model
established early pioneers of neural computation.
However, we now know that the picture is incomplete. Cellular recordings and observational studies
during animal behavior have now convincingly shown that the dendritic trees of neurons are heavily
involved in neural processing [4, 5]. In response to significant coincident spiking input, segments of thedendritic tree actively respond by actively generating a local plateau potential significantly longer thanthe effect individual spikes have on the membrane potential. The significant difference in time scale andthe all-or-non nature of the plateau response imply that the picture of individual neurons implementing
a linear non-linear mapping of the rate of a spike train onto the rate of its own spike train cannot holdfor neurons in which plateau potentials play an important role for computation. Instead, the distributed
representations underlying the spiking input to a neuron turns into a localized representation of a coincidence detection which is kept in memory within a dendrite segment and accessible to its neighbours forcomputational purposes.
We have shown in previous work how this simple mechanism is ideally suited to recognizing sequenceswith significant timing invariance, a necessary feature for any circuit processing inputs from a real, dynamic environment [6]. Here, we go beyond simple sequences and describe computation in branching
dendritic trees as structured, logical sentences over symbols rank-ordered in time.
The underlying model is simple enough (Fig. 1 b.): Dendrite segments are organized in a tree, eachsegments output is input to its parent. For each segment to generate a plateau, a certain number ofdendritic inputs from child segments are required in addition to excitatory synaptic input that crosses
a threshold and implements coincidence detection. Inhibitory inputs interrupt the plateau process andeither prevent it entirely if they occur just before excitatory inputs or cancel the plateau outright if theyoccur during plateau generation.
Each detection represents a coinciding combination of input spikes as predicate symbol and inhibition
as the negation of it. Because inhibition only interacts only with plateau processes, this is not a true
negation but a veto – similar to McCulloch and Pitts circuits [7]. Dendritic input from child segments
must always occur before the detection of a symbol at a parent segment, so the dendritic tree naturallyoperates on symbolic expressions that are rank-ordered in time. Depending on the dendritic threshold of
the parent segment, different logical connections between sibling segments can be implemented. Startingat the root of the tree, the recursive definition of the computation of a single neuron with segmented
dendritic tree is (see Fig. 1 c. for an example):XYSt =st∧ ¬st ∧S[j]t−1|{z}|{z}π∈κ j∈π
excitation inhibition |{z}dendritic gating

Figure 1: Neuron to logical circuit. (a.) Segments of a pyramidal neuron map onto a (b.) segmented
dendritic tree driven by dendritic inputs on top of synaptic excitation and inhibition. (c.) The computational function of these neurons can be formalized as predicate sentences over symbols rank-ordered intime when connected to input populations.
We do not argue that symbolic thought is a higher level process implemented on top of a subsymbolic
substrate. Instead, we argue, structured and symbolic representations are inherently integrated in neuralnetworks in the “subatomic” structures of dendritic trees of single neurons. Representations are distributed among many different neurons on the network level, but local to individual dendrite segments
and part of constituent structures on the neuron level.
Our work provides a fundamentally new approach to computation in neural network with direct implications for neuromorphic hardware: Dendritic structures and longer time scales are decidedly importantfor computational function in our model. But all other new computational architectures that follow
the parallel and distributed computation paradigm exemplified by neural networks can also learn fromthe biological phenomenon of plateau potentials in dendritic trees. Generally, local memory traces intiny, symbolic computers embedded in larger, dynamic networks may are a promising path to implement
cognitive functions in new computing systems.

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