A Hebbian Approach to Non-Spatial Prelinguistic Reasoning

Abstract

This research integrates key concepts of Computational Neuroscience, including the Bienestock-CooperMunro (BCM) rule, Spike Timing-Dependent Plasticity Rules (STDP), and the Temporal Difference Learning algorithm, with an important structure of Deep Learning (Convolutional Networks) to create an architecture with the potential of replicating observations of some cognitive experiments (particularly, those that provided some basis for sequential reasoning) while sharing the advantages already achieved by the previous proposals. In particular, we present Ring Model B, which is capable of associating visual with auditory stimulus, performing sequential predictions, and predicting reward from experience. Despite its simplicity, we considered such abilities to be a first step towards the formulation of more general models of prelinguistic reasoning.

Keywords: BCM theory; Convolutional Neural Networks; Hebbian learning; Spike Timing-Dependent Plasticity; Temporal Difference Learning.

Figure 1

Percentual change in the amplitude of the Excitatory Postsynaptic Potential (EPSC) measured with the differente $t_{post}-t_{pre}$ (ms), according to the results of [9] (based on [4], redrawn using $H\left(\tau \right)=\frac{140}{\tau }$).

Figure 2

Simulated behavior of the simplified model with a recurrent self-connection $w_r=0.5$ and $\mathbf{h}=(1,-1)$.

Figure 3

Architecture for TDL based on [54].

Figure 4

Schematic representation of Ring Model A. For visual simplicity, some connections are not presented, such as the recurrent self-connections of $\mathbf{r}$. The feature vector $\mathbf{u}$ is fully connected with the Hebbian layer $\mathbf{v}$, but the diagram is focused on the second recognized item. Each entry of $\mathbf{v}$ is connected with one entry of $\mathbf{r}$, as well. Additionally, $K=6$ in this particular case.

Figure 5

Schematic representation of Ring Model B. For visual simplicity, some connections are not drawn (see the caption of Figure 4). In addition, ${\mathbf{x}}_i$ por $i=1,\dots ,5$ are not visible.

Figure 6

Plot of the neural activity of the neuron $v_1$ with the Oja learning rule. Local maxima (upper peaks) appeared when the pattern was presented, whereas the local minima appeared in absence of the pattern. Abrupt increments in the neural activity were due to the enhancement of the weights via audio.

Figure 7

Plot of the neural activity of the neuron $v_1$ with BCM learning rule. Local maxima (upper peaks) appeared when the pattern was presented, whereas the local minima appeared in absence of the pattern. Abrupt increments on the neural activity were due to the enhancement of the weights via audio.

Figure 8

Neural activity of $v_A$ (blue), $v_B$ (red), $v_C$ (green), and $v_D$ (yellow) using Model A. Stimulus B was presented in the time interval $[21,33]$.

Figure 9

Neural activity of $r_A$ (blue), $r_B$ (red) and z (green).

Figure 10

Neural activity of $v_A$ (blue), $v_B$ (red), $v_C$ (green), and $v_D$ (yellow) using Model B. Stimulus A was presented in the interval $[28,40]$.