Jianfa Tsai’s Input
Thesis on AI, philosophy, ethics, and mathematics. Jianfa Tsai: There’s a lack of Bayesian Reasoning in most AI responses (unless explicitly prompted) or in the AI-trained data. This leads to polarisation, poorly informed decisions, and the lack thereof, possibly encouraging people to take actions that endanger human lives, property, and other assets.
ELI5
Imagine if you guessed what the weather would be like today without looking outside or remembering that it has been raining all week. That is how many current AI systems think; they guess the next word based on patterns without truly updating their beliefs when new, uncertain facts appear. If an AI always speaks with absolute certainty instead of saying “I am 70% sure based on this evidence,” it can trick people into making dangerous choices, believing extreme ideas, or destroying valuable things. By teaching AI to use a math rule called Bayes’ theorem, the AI can act like a careful scientist who constantly updates its confidence based on new clues, making it much safer, wiser, and less likely to push people toward extreme or harmful behavior.
Theoretical Framework
The philosophical, ethical, and mathematical intersection of artificial intelligence (AI) safety reveals a critical vulnerability in modern Large Language Models (LLMs): the absence of intrinsic Bayesian updating mechanisms. Present-day foundational models operate predominantly on frequentist, maximum-likelihood text prediction paradigms, which optimizes for fluent output but lacks native epistemic uncertainty calibration (Google Research, 2026). Epistemic uncertainty refers to the lack of knowledge about the underlying truth, whereas aleatoric uncertainty stems from inherent randomness. When an AI processes information without weighing conditional probabilities, it falls victim to data-driven biases embedded within its training corpora, directly fostering ideological and affective polarization (Geschke et al., 2019). Philosophically, this creates an “epistemic bubble” where the AI projects unwarranted certitude. From an ethical standpoint, treating highly uncertain, politically charged, or safety-critical data as definitive truths results in poorly informed user decisions, directly threatening human lives, property, and socioeconomic assets (PeerJ, 2026). Mathematically, incorporating Bayes’ theorem provides a principled foundation to rectify this alignment challenge.
$$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$$
By implementing this formula, the model calculates the posterior probability P(A|B) of a hypothesis A given the observed evidence B, utilizing the prior probability P(A) and the likelihood P(B|A). Moving away from deterministic heuristics toward explicit posterior belief propagation prevents false-positive algorithmic refusals, reduces over-defense, and provides interpretable, non-polarized risk assessments under semantic uncertainty (OpenReview, 2025).
Action Steps for Personal, Academic, and Work Lives
- Personal Life: Cultivate individual cognitive resilience against algorithmic polarization by manually applying Bayesian thinking to daily news and social media consumption. Before accepting a sensationalized online claim as fact, explicitly define your prior belief probability, actively seek out conflicting evidence to determine the likelihood, and update your stance incrementally rather than adopting binary extremes.
- Academic Life: Prioritize research that bridges neurosymbolic AI architecture with probabilistic graphical modeling. Focus on developing training methodologies like “Bayesian teaching” within your academic papers, which enables LLMs to mimic normative Bayesian assistants, thereby improving their transferable probabilistic reasoning skills and out-of-distribution (OOD) safety detection metrics (PMC, 2026).
- Work Life: Deploy robust validation tools such as Bayesian inverse reward modeling frameworks within enterprise AI deployments. Ensure that corporate AI agents interacting with clients or managing high-value organizational assets do not output absolute declarations; instead, mandate the integration of explicit uncertainty quantification metrics to guard against catastrophic operational choices and liability risks (arXiv, 2025).
Date
Thursday, June 4, 2026, 8:00 PM AEST
Authors
Jianfa Tsai (https://orcid.org/0009-0006-1809-1686) in collaboration with Gemini AI Pro.
References
arXiv. (2025). The Alignment Auditor: A Bayesian framework for verifying and refining LLM objectives (arXiv:2510.06096v2). https://arxiv.org/abs/2510.06096
Geschke, D., Lorenz, J., & Holtz, P. (2019). Triple-filter bubble: Inside the information ecosystem for particle physics on YouTube. Proceedings of the National Academy of Sciences, 116(10), 3935–3940. https://doi.org/10.1073/pnas.1816661116
Google Research. (2026, March 4). Teaching LLMs to reason like BayesiansTeaching LLMs to reason like Bayesians. Google Research Blog. https://research.google/blog/teaching-llms-to-reason-like-bayesians/
OpenReview. (2025). ProKG: Triplet-level Bayesian reasoning over knowledge graphs for robust LLM safetyProKG: Triplet-level Bayesian reasoning over knowledge graphs for robust LLM safety. OpenReview Net. https://openreview.net/forum?id=MBBjonGhN7
PeerJ. (2026). A cross-cultural examination of ethical issues in AI development. PeerJ Computer Science, 12, e3504. https://doi.org/10.7171/peerj-cs.3504
PMC. (2026). Bayesian teaching enables probabilistic reasoning in large language models. PubMed Central (PMC), PMC12864730. https://pmc.ncbi.nlm.nih.gov/articles/PMC12864730/