Relational and Analogical Reasoning with Spiking Neural Networks

Abstract

Relational reasoning---the ability to abstract structural patterns independently of surface details---is a defining feature of human intelligence and a core challenge for artificial systems. In this thesis, we investigate whether bio-inspired spiking neural networks (SNNs), trained with minimal supervision and minimal embedded domain knowledge, can develop relational abstraction capabilities on Raven's Progressive Matrices (RPMs), a canonical benchmark for cognitive reasoning.

A guiding principle throughout this work is a systematic minimisation of domain knowledge. Rather than embedding handcrafted rules, symbolic representations, or modular decompositions, we explore whether relational reasoning can emerge from general-purpose neural dynamics alone. Domain knowledge is not merely an engineering detail but a conceptual axis shaping model interpretability, generalisation, and flexibility. In many real-world scenarios, the absence of such prior knowledge is precisely what makes learning necessary---since the relevant structures must be discovered, not pre-specified.

We begin with baseline evaluations on the RAVEN and I-RAVEN datasets, assessing the performance of three spiking architectures---the SNN, the Spiking Self-Organising Map (SSOM), and the Liquid State Machine (LSM)---each using leaky integrate-and-fire neurons with adaptive thresholds. Our results show that the LSM consistently outperforms the other spiking models, achieving robust relational generalisation despite minimal supervision. Notably, all spiking networks exhibit a remarkable capacity to learn relational structures under extremely small data regimes, matching or exceeding previous supervised baselines when trained on limited samples. This suggests that bio-inspired learning dynamics, such as spike-timing-dependent plasticity (STDP) and competitive inhibition, confer unique advantages in low-data, weak-supervision settings.

Subsequent experiments explore the role of data stratification. Contrary to common assumptions, we find that stratification offers only modest improvements overall. However, its benefits are more pronounced in extremely small training regimes, where coverage of structural patterns becomes a limiting factor. As the training set size increases, these advantages diminish, suggesting that the core difficulty lies not in class frequency imbalance but in the structural complexity of abstract reasoning tasks. Spiking models, particularly the LSM, show surprising resilience to unbalanced datasets, further emphasising their capacity to discover structure without heavy supervision or domain scaffolding.

Finally, we introduce curriculum learning paradigms, showing that structured, incremental exposure to reasoning tasks significantly enhances abstraction capabilities across all spiking models. Curriculum learning smooths learning dynamics, reduces overfitting, and fosters better relational generalisation. The LSM, again, proves particularly well-suited to these strategies, demonstrating scalable, stable improvements with increasing training complexity.

Across all chapters, a consistent message emerges: relational abstraction can develop in spiking systems without explicit symbolic bias when learning dynamics, data structuring, and architectural design are carefully aligned. Minimising domain knowledge does not cripple learning; rather, it clarifies where current models fall short and where biological principles like competition, temporal dynamics, and recurrence offer promising routes forward.

In conclusion, this thesis presents biologically plausible pathways for achieving abstract, flexible reasoning under conditions of limited supervision and minimal prior knowledge. Our findings challenge the notion that deep abstraction requires heavy engineering and suggest that self-organising, minimally guided systems can form the foundation for the next generation of interpretable, robust, and cognitively inspired artificial intelligence. Show more