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Parsimonious Inference Information-Theoretic Foundations for a Complete Theory of Machine Learning (CIS-LDRD Project 218313 Final Technical Report)
This work examines how we may cast machine learning within a complete Bayesian framework to quantify and suppress explanatory complexity from first principles. Our investigation into both the philosophy and mathematics of rational belief leads us to emphasize the critical role of Bayesian inference in learning well-justified predictions within a rigorous and complete extended logic. The Bayesian framework allows us to coherently account for evidence in the learned plausibility of potential explanations. As an extended logic, the Bayesian paradigm regards probability as a notion of degrees of truth. In order to satisfy critical properties of probability as a coherent measure, as well as maintain consistency with binary propositional logic, we arrive at Bayes' Theorem as the only justifiable mechanism to update our beliefs to account for empiracle evidence. Yet, in the machine learning paradigm, where explanations are unconstrained algorithmic abstractions, we arrive at a critical challenge: Bayesian inference requires prior belief. Conventional approaches fail to yield a consistent framework in which we could compare prior plausibility among the infinities of potential choices in learning architectures. The difficulty of articulating well-justified prior belief over abstract models is the provinence of memorization in traditional machine learning training practices. This becomes exceptionally problematic in the context of limited datasets, when we wish to learn justifiable predictions from only a small amount of data.
Unveiling the mechanism of the photocatalytic reduction of CO 2 to formate promoted by porphyrinic Zr-based metal–organic frameworks
A complete picture of the reaction mechanism responsible for the photocatalytic reduction of CO 2 into formate promoted by the Zr-based porphyrinic MOF-545 (PCN-222) in acetonitrile/triethanolamine (CH 3 CN/TEOA) solutions is provided for the first time by combining experimental and computational approaches. Firstly, we combined the metalation of the porphyrin linkers and the synthesis under microwave conditions of nano-sized materials (150–200 nm) to reach one of the highest CO 2 RR activities under visible light irradiation reported so far for a MOF-based catalyst in terms of formate production (identified in all cases as the sole product), i.e., 6000 μmol g –1 after 4 h for the NanoMOF-545(Fe). A thorough mechanistic study of CO 2 RR is provided afterwards, which elucidated the respective roles of TEOA, porphyrin linkers and Zr 6 -nodes. Photophysical measurements of both metalated and unmetalated MOFs excluded the prevailing belief of ligand-to-Zr 6 cluster charge-transfer state formation, while bulk photolysis proved that the porphyrinic linkers of the MOF promote the photooxidation of TEOA under catalytic conditions. DFT calculations allowed characterization with atomistic detail of a novel reaction mechanism whereby TEOA˙ radicals generated photochemically at the porphyrinic linkers play the crucial role of transferring a formal hydride to a CO 2 molecule activated on a Zr IV center, which acts as a Lewis acid. Notably, this mechanism backed by additional experimental assays explains the experimental activity trends observed upon metalation, on the basis of the ability of the materials to accomplish the photo-oxidation of TEOA. Here, while elucidating the reaction pathways at work in Zr 6 -based MOFs with chromophore linkers, the findings reported herein pinpoint new mechanistic features capable of rationalizing other light-driven reactions making use of TEOA (or structurally related donors) and ultimately, inspire the bottom-up design of new catalysts and catalytic routes.