Can we build neural networks that do not merely happen to realize all Boolean functions with their associated computational structure, but do so in a certifiable way for every parameter choice? This talk introduces stochastic Boolean circuits, a neural architecture for reasoning with built-in circuit structure. The starting point is a simple but important observation: although ordinary neural networks can represent Boolean gates such as NOT and AND, these exact configurations occupy thin, nongeneric regions of parameter space, making such reasoning fragile and unlikely to arise in a certifiable way through standard training. In response, we construct a model whose parameters define distributions over Boolean circuits directly. We show three main results: (i) for every parameter choice, the model samples a valid Boolean circuit almost surely (certifiable reasoning); (ii) with suitable parameters, it can compute any Boolean function with arbitrarily high probability (universality); and (iii) for sparse Boolean functions, the required size scales efficiently with dimension. We also present experiments showing that the model remains competitive on Boolean truth-table tasks while preserving neuronwise Boolean structure, unlike matched ReLU MLP baselines. The talk connects ideas from neural network expressivity, circuit complexity, and interpretability to propose a route toward more reliable neural reasoning systems.

Bio: Hrad Ghoukasian is a Research Assistant at McMaster University, where he is currently working with Anastasis Kratsios on AI reasoning. He previously completed his M.Sc. in Computer Science at McMaster University under the supervision of Shahab Asoodeh, with research focused on trustworthy machine learning, primarily from a theoretical perspective. Earlier, he was a Research Intern at the Vector Institute, where he worked under the supervision of Xiaoxiao Li.

Bio: Wenhao Li is a PhD student at the University of Toronto working on reasoning and neural program synthesis. He previously earned his Computer Science degree from the University of Waterloo and has over a decade of industry experience in AI, software architecture, data systems, and streaming platforms. His work bridges research and practice, with experience leading R&D teams and developing AI-driven systems in facial recognition, recommendation, and large-scale media technology.