Towards free-response paradigm: a theory on decision-making in spiking neural networks

TL;DR

The paper tackles the speed–accuracy trade-off in Spiking Neural Networks (SNNs) by introducing a free-response paradigm inspired by drift–diffusion decision processes. It combines a drift-diffusion-like evidence framework with a fidelity-entropy loss that optimizes both mean discrimination and predictive confidence, enabling adaptive stopping during inference. Empirical results show that fidelity-entropy training preserves accuracy while enhancing confidence expression and speeding convergence, particularly on harder tasks, and that adaptive stopping policies can approach Oracle-level performance while improving efficiency. Overall, the work bridges cognitive decision theory and neuromorphic computing to enable faster, more reliable SNNs for complex decision-making tasks.

Abstract

The energy-efficient and brain-like information processing abilities of Spiking Neural Networks (SNNs) have attracted considerable attention, establishing them as a crucial element of brain-inspired computing. One prevalent challenge encountered by SNNs is the trade-off between inference speed and accuracy, which requires sufficient time to achieve the desired level of performance. Drawing inspiration from animal behavior experiments that demonstrate a connection between decision-making reaction times, task complexity, and confidence levels, this study seeks to apply these insights to SNNs. The focus is on understanding how SNNs make inferences, with a particular emphasis on untangling the interplay between signal and noise in decision-making processes. The proposed theoretical framework introduces a new optimization objective for SNN training, highlighting the importance of not only the accuracy of decisions but also the development of predictive confidence through learning from past experiences. Experimental results demonstrate that SNNs trained according to this framework exhibit improved confidence expression, leading to better decision-making outcomes. In addition, a strategy is introduced for efficient decision-making during inference, which allows SNNs to complete tasks more quickly and can use stopping times as indicators of decision confidence. By integrating neuroscience insights with neuromorphic computing, this study opens up new possibilities to explore the capabilities of SNNs and advance their application in complex decision-making scenarios.

Figures (6)

• Figure 1: The drift-diffusion model framework applied to SNN decision-making. Sensory neurons encode stimulus $\mathbf{x}$ (e.g., an image) into corresponding spike trains via a Poisson process ($\text{Poisson}(\mathbf{x})$). These trains serve as input to a downstream network, which processes the information through successive hidden layers. The final layer of the network employs a linear readout to transform spiking activity $\mathbf{s}(t)$ at time $t$ into evidence $\mathbf{r}(t)$ for decision-making. The decision variable integrates and compares evidence over time ($\sum_{t=1}^{T} (r_1(t) - r_2(t))$), emulating evidence accumulation in the drift-diffusion model, to determine the point of commitment to the decision or the need for additional evidence collection.
• Figure 2: Influence of readout dynamics on model confidence.a, Model confidence, defined as $P(d_i - d_j > 0)$ is quantified by the distance between the readout means ($\mu_i, \mu_j$) and the classification boundary, incorporating variance in the assessment. The analysis, which fixes $\mu_j = \sigma_j = 1, \rho_{ij} =0$, explores the evolution of confidence in readout time $\Delta t$ as $\mu_i$ varies and $\sigma_i$ adjusts according to the coefficient of variation (CV). b, The effect of correlation between readouts on decision confidence is examined under a consistent mean disparity and modified CVs. How confidence $P(d_i - d_j > 0)$ changes under different conditions in a and b is illustrated by color maps.
• Figure 3: Efficacy of fidelity-entropy loss in Training MNNs. a, Training accuracy over epochs for MNNs, comparing models trained with and without fidelity-entropy loss. The shaded regions denote the 95% confidence intervals. b, Case study examples showing the influence of fidelity-entropy loss on model outputs. Correct predictions (red stars) and incorrect predictions (black crosses) are plotted based on the top two readout means, with their covariances represented by ellipses. Solid lines indicate covariances for correct cases, while dashed lines correspond to incorrect ones. The decision boundary is depicted as a dashed line. c, The models' ability to differentiate between correct and incorrect predictions is evaluated by the area under the receiver operating characteristic curve (AUROC), using various output metrics. d, Radial charts illustrating the proportion of samples where the application of fidelity-entropy loss enhances performance across selected metrics.
• Figure 4: Fidelity-entropy loss enhances SNN prediction consistency and efficiency.a, Model performance over readout time, contrasting accuracy (solid line) and consistency entropy (dotted line) between models trained with fidelity (cyan) and without (yellow). b, Probability of correct predictions over readout time, using the samples from Fig. \ref{['fig:3']}b as inputs. Solid and dashed lines indicate right and wrong classifications, respectively, by MNN models, with fidelity (cyan) and without (yellow). c, Pearson correlation coefficients comparing SNN convergence times with MNN confidence metrics. The convergence time of SNNs is defined as the time when the SNN's prediction remains stable after that. d, Violin plots delineating SNN convergence times correlated with correct (red) and incorrect (black) final predictions.
• Figure 5: Efficiency of different stopping policies in SNNs.a, Performance comparison of various stopping policies with adjustable decision thresholds. The Oracle policy (orange star) represents an ideal scenario where inference stops at convergence. The Difference (Diff) policy (circle dot) stops inference when the gap between the top two readouts crosses a threshold. The Maximum (Max) policy halts when the highest readout exceeds its threshold, and the Linear (Lin) policy employs a linear classifier on sorted readouts, stopping when the classifier's score surpasses a predefined threshold. For comparison, the Fixed policy (gray line) represents a uniform stopping time for all samples. b, Minimum readout times required for the Diff, Max, and Lin policies to achieve accuracy within 0.5% of Oracle performance. c, Receiver Operating Characteristic (ROC) curves that evaluate the expression of prediction confidence based on stopping times determined by policies, using thresholds from b.