Allostatic Control of Persistent States in Spiking Neural Networks for perception and computation

TL;DR

Problem: controlling the position of persistent bumps in a ring attractor to align internal representations with changing environments. Approach: AlloNet couples a Hammel allostatic controller with a ring attractor, using a two-stage tuning and gain-modulation to move the bump and a readout to generate a reference signal, enabling subitizing as an allostatic process. Findings: the model generates numerosity representations with reaction-time and error dynamics that qualitatively resemble human subitizing under certain synaptic time constants; neural-dynamics analyses reveal how bump speed and stability depend on excitatory time constants and show gain-field-like responses in cortical areas. Significance: provides a neuromorphic, allostatic framework for controlling persistent representations in perception and computation, extendable to other abstract-symbolic mappings beyond numerosity; future work includes incorporating learning and validating against empirical neural data.

Abstract

We introduce a novel model for updating perceptual beliefs about the environment by extending the concept of Allostasis to the control of internal representations. Allostasis is a fundamental regulatory mechanism observed in animal physiology that orchestrates responses to maintain a dynamic equilibrium in bodily needs and internal states. In this paper, we focus on an application in numerical cognition, where a bump of activity in an attractor network is used as a spatial numerical representation. While existing neural networks can maintain persistent states, to date, there is no unified framework for dynamically controlling spatial changes in neuronal activity in response to environmental changes. To address this, we couple a well known allostatic microcircuit, the Hammel model, with a ring attractor, resulting in a Spiking Neural Network architecture that can modulate the location of the bump as a function of some reference input. This localized activity in turn is used as a perceptual belief in a simulated subitization task a quick enumeration process without counting. We provide a general procedure to fine-tune the model and demonstrate the successful control of the bump location. We also study the response time in the model with respect to changes in parameters and compare it with biological data. Finally, we analyze the dynamics of the network to understand the selectivity and specificity of different neurons to distinct categories present in the input. The results of this paper, particularly the mechanism for moving persistent states, are not limited to numerical cognition but can be applied to a wide range of tasks involving similar representations.

Figures (5)

• Figure 1: AlloNet model definition. A. Overview of model architecture. Two inputs are associated to homeostasis model: Environmental input (S1) and Ring attractor feedback (S2). B. Representation of how Hammel model is used in the architecture. Higher and lower neurons are associated to one-to-all connection onto high gain modulation (HGM) and low gain modulation (LGM) respectively. C. Synaptic connection management between the ring attractor and gain modulation neurons (LGM and HGM). D. Representation of S1 and S2. These define how information, both external input (bottom figure) and feedback input (top figure), is being represented into the network.
• Figure 2: Overview the fine-tuning stages for the model. Each time-step used by the simulator is equivalent to an interval of 1ms. A. Heat map for the firing rate in ratio to the two inputs to the Hammel model, simulated by a Poisson generator. Left. Activity (Firing rate) in lower neuron for different input frequencies. Right. Activity of higher neuron. The model is simulated for 10000 time-steps for each combination of input frequencies. B. Setup for the fine-tuning process of the gain modulation neurons as described in the text. A similar setup from diagram A. Poisson generators are then used for simulating the bump of the ring attractor and the Hammel model effector output. The colors represent firing rates in response to different combinations of firing. C. Response of the bump for two different frequencies of the external input (50000 time-steps). Left. Raster plot. Right. Average firing rate of the readout neurons. The colors represent the ranges for different numbers (see below).
• Figure 3: Simulated behavioral responses for a subitizing task. A. We use the AlloNet model to define a homeostatic match between the internal representation of numbers and stimuli in the environment (dots). B. Reaction times in association to number representation defined as the time of first spike in the correct representation. Responses in S2 neurons are used for determining reaction time. The experiments are repeated for different synaptic time constants of the HGM and LGM. C. Error percentage based on the responses at different stopping time-steps in 20 trials (see text) D. Bar plot to define quality score for different excitatory synaptic time constants and different numbers. The different bar represents the number being represented (color-coded) and the groupings of these bars are reported based on their synaptic time constants.
• Figure 4: Heat-map to plot the network persistent state over time. The y-axis of the plot is the number representation index, and the y-axis of the sub-plot is the neuron index of the ring attractor network. The x-axis of the plot is the column for different synaptic time constant runs and the x-axis of the sub-plot is the time of the run iteration. The white lines in the sub-plots define the different numerosities, i.e., [starting point,1,2,3,4] from bottom to top.
• Figure 5: Neural dynamics and dynamics of the bump. The color is encoded to the location of the bump activity (shown by the number represented on the left of the plots in figure 5A) A. Responses of a single neuron of the ring attractor (63) sensitive to number 3. Top. Raster plot for 20 trials of each numerosity. Bottom. Corresponding firing rates. Right. Responses of the gain field in the vicinity of the ring ($\pm 10$ neurons). B. Centroid of the bump computed as the expected value of position (neuron) with respect to the normalized firing rate. The spike trains are also plotted in the background for each numerosity. C. Speed of the bump smoothed with 5 samples sliding window for each numerosity. Dotted line is the corresponding step for lower synaptic time constant ($\tau_{ex} = 900ms$).