Threshold Adaptation in Spiking Networks Enables Shortest Path Finding and Place Disambiguation

TL;DR

The paper tackles back-tracing and ambiguity handling in uni-directional spiking networks for navigation. It introduces spike timing-dependent threshold adaptation (STDTA) to enable replay-based back-tracing and shortest-path planning, and ambiguity-dependent threshold adaptation (ADTA) to identify less ambiguous places for improved localization. Through simulations in a spiking HTM variant (S-HTM) with population-coded locations, the authors demonstrate efficient path finding with few replays and successful place disambiguation across similar environments. This work advances practical neuromorphic localization and navigation by providing biologically inspired yet hardware-friendly mechanisms for sequential planning and context-aware placement.

Abstract

Efficient spatial navigation is a hallmark of the mammalian brain, inspiring the development of neuromorphic systems that mimic biological principles. Despite progress, implementing key operations like back-tracing and handling ambiguity in bio-inspired spiking neural networks remains an open challenge. This work proposes a mechanism for activity back-tracing in arbitrary, uni-directional spiking neuron graphs. We extend the existing replay mechanism of the spiking hierarchical temporal memory (S-HTM) by our spike timing-dependent threshold adaptation (STDTA), which enables us to perform path planning in networks of spiking neurons. We further present an ambiguity dependent threshold adaptation (ADTA) for identifying places in an environment with less ambiguity, enhancing the localization estimate of an agent. Combined, these methods enable efficient identification of the shortest path to an unambiguous target. Our experiments show that a network trained on sequences reliably computes shortest paths with fewer replays than the steps required to reach the target. We further show that we can identify places with reduced ambiguity in multiple, similar environments. These contributions advance the practical application of biologically inspired sequential learning algorithms like the S-HTM towards neuromorphic localization and navigation.

Figures (6)

• Figure 1: (Left) The uni-directionally connected network graph during replay, initiated at A and with two paths to the target G. Shown are a replay without back-tracing and two replays with back-tracing, i.e. with neuronal activity traced backwards from target to start. (Right) The activity of the neuronal populations visualized with timing, demonstrating that threshold adaptation in combination with activity back-tracing enables path planning in snn.
• Figure 2: The network structure of our version of the shtm after learning two sequences (brown, turquoise) from the environment shown in Fig. \ref{['fig:problem']}. Akin to the original shtm bouhadjar_sequence_2022, our version consists of excitatory subpopulations $\mathcal{M}_{l}$, one for each location $l$. Each of these subpopulations is equipped with an inhibitory neuron $\mathcal{I}_l$, which is active during prediction and replay. The newly introduced global inhibitory neuron $\bar{\mathcal{I}}$ receives excitatory input from all local inhibitory neurons and maintains inhibitory connections to the excitatory subpopulations. It is only active during replay, to enable path selection by inhibiting alternative, slower paths. Adapted from bouhadjar_coherent_2023.
• Figure 3: (a) Two example environments alongside the target path. (b) An overview of 3 replay phases for a path planning or place disambiguation problem. The ovals represent an active (orange) or inactive (grey) subset of a subpopulation, representing a context. The first replay is only necessary for place disambiguation, where a target location with reduced ambiguity (less active neurons) is identified and its threshold is adapted (pink). During path planning, however, the target is manually set before Replay 2. Due to the reduced threshold, the neurons in subpopulation $\mathcal{M}_{G}$ spike earlier than the neurons in $\mathcal{M}_{E}$, which are consequently inhibited by $\bar{I}$. After Replay 2, the information of the earlier spike time is propagated to the neurons in $\mathcal{M}_{C}$ by a spike timing dependent rule, resulting in a threshold adaptation for $\mathcal{M}_{C}$. During the final replay, this leads to an inhibition of the competing subpopulation (path) $\mathcal{M}_{D}$, resulting in neuronal activity representing the final shortest path.
• Figure 4: (a) (Top) A graphical representation of active connections between locations before and (bottom) after replay with the shortest path (turquoise), an alternative path (brown), and the target (red). (b) An overview of the corner stones of the back-tracing and threshold adaptation process, showing events from populations $\mathcal{M}_{J}$, $\mathcal{M}_{G}$, and $\mathcal{M}_{H}$. (c) (top) The results of the path planning replay process for a target path from A to J with the events for all neuronal populations, the final path of active neuronal populations (right), (bottom) and the thresholds throughout the replay phases. The neuronal events include a somatic spike (orange), triggered by a dendritic plateau potential (blue), or the initial, external input (grey), together with local (green) and global inhibition (red). The steps of the back-tracing are highlighted for each phase, including the current target (solid red), the inhibited alternative population (dashed red), and the populations performing an STDTA update (purple).
• Figure 5: (a) A graphical representation of the environments used for the place disambiguation experiments, environments 1 and 2 are used for the first experiment and all three for the second. (b) The results of the first place disambiguation experiment for environments 1 and 2, with the events for all neuronal populations (top), the final path of active neuronal populations (right), and the thresholds throughout the replay phases (bottom). The neuronal events are depicted as in Fig. \ref{['fig:eval_path_c']}, except for the newly introduced adta updates due to reduced ambiguity (pink).