Sphere Neural-Network for Higher-level Cognition

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• Tiansi Dong
• Tuesday 18 July 2023, 17:00-18:00
• Lecture Theatre 2, Computer Laboratory, William Gates Building.

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To simulate higher-level cognition of our mind, deep-learning needs to go beyond the statistic learning framework, and reason with out-of distribution data. Here, we present a qualitative extension by promoting vectors into spheres as the input-output signals, and come up to the Sphere Neural-Network (SphNN). We show that the sphere has the representation power to introduce the methodology of reasoning by model construction into the neural computing. This enables SphNN to determine, without training data (therefore, robust to out-of-distribution data), the validity of long-chained syllogistic reasoning, the microcosm of higher-level cognition, by constructing Euler diagrams in the vector space, with the worst computational complexity of O(N^2) (where N is the length of the chain). A high-level process for model construction plans the neighbourhood transition towards the target model, by using a deterministic neurosymbolic causal schema and habitual neural operations that gradually transform the current relation towards the neighbourhood relation. SphNN is the first neural model that carries out explainable and deterministic syllogistic reasoning (Experiment 1), with theoretical proof; Compared with ChatGPT in long-chained syllogistic reasoning, SphNN achieves 100% for all 1200 tasks, while ChatGPT achieved an average accuracy of 62.8% (Experiment 2). In our experiments, ChatGPT may also give a correct answer with a false explanation, suggesting that ChatGPT may not truly construct the human-like models used in its answers. SphNN is able to evaluate the answer of ChatGPT by constructing models, and give feedback through prompts. This improves the accuracy of ChatGPT from 80.86% to 93.75% in deciding the satisfiability of atomic syllogistic reasoning (shown in Experiment 3). By fixing centre orientations of spheres to pre-trained embeddings from LLMs, e.g. ChatGPT, Experiment 4 shows that pre-trained vector embeddings, such as GLOVE , BERT, ChatGPT, can very well approximate orientations of the sphere centres. Experiment 5 shows rigorous logic deduction cannot be achieved through supervised learning. SphNN demonstrates a new way of realising logic deduction through explicit model construction in the vector space, and significantly narrows the gap between higher-level cognition and deep-learning, and will enhance collaborations among neural computing, classic AI, and cognitive science to develop novel neural models that reach the explainability and determinacy of higher-level cognition.

————— Tiansi Dong leads the new neurosymbolic research at Fraunhofer Institute IAIS

https://www.iais.fraunhofer.de/en/research/artificial-intelligence/neurosymbolic-representation-learning.html

https://cl-cam-ac-uk.zoom.us/j/93040206714?pwd=aFVNeExndzFWSk50b0dSWldSaXFndz09

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