Gregory Coppola

Gregory Coppola

The most important problem that has emerged after twenty years of popular internet usage is that of fact-checking at scale. This problem is experienced acutely in both of the major internet application platform types, web search and social media. We offer a working definition of what a "platform" is. We critically deconstruct what we call the "PolitiFact" model of fact checking, and show it to be inherently inferior for fact-checking at scale to a platform-b ased solution. Our central contribution is to show how to effectively platformize the problem of fact-checking at scale. We show how a two-dimensional rating system, with dimensions agreement and hotness allows us to create information-seeking queries not possible with the on e-dimensional rating system predominating on existing platforms. And, we show that, underlying our user-friendly user-interface, lies a system that allows the creation of formal proofs in the propositional calculus. Our algorithm is implemented in our open-source DimensionRank software package available at "https://thinkdifferentagain.art".

Gregory Coppola

One of the most expensive parts of maintaining a modern information-sharing platform (e.g., web search, social network) is the task of content-moderation-at-scale. Content moderation is the binary task of determining whether or not a given user-created message meets the editorial team's content guidelines for the site. The challenge is that the number of messages to check scales with the number of users, which is much larger than the number of moderator-employees working for the given platform. We show how content moderation can be achieved significantly more cheaply than before, in the special case where all messages are public, by effectively platformizing the task of content moderation. Our approach is to use a hub-and-spoke model. The hub is the core editorial team delegated by the management of the given platform. The spokes are the individual users. The ratings of the editorial team create the labels for a statistical learning algorithm, while the ratings of the users are used as features. We have implemented a primitive version of this algorithm into our open-source DimensionRank code base, found at "thinkdifferentagain.art".

Gregory Coppola

Transformers are the dominant architecture in AI, yet why they work remains poorly understood. This paper offers a precise answer: a transformer is a Bayesian network. We establish this in five ways. First, we prove that every sigmoid transformer with any weights implements weighted loopy belief propagation on its implicit factor graph. One layer is one round of BP. This holds for any weights -- trained, random, or constructed. Formally verified against standard mathematical axioms. Second, we give a constructive proof that a transformer can implement exact belief propagation on any declared knowledge base. On knowledge bases without circular dependencies this yields provably correct probability estimates at every node. Formally verified against standard mathematical axioms. Third, we prove uniqueness: a sigmoid transformer that produces exact posteriors necessarily has BP weights. There is no other path through the sigmoid architecture to exact posteriors. Formally verified against standard mathematical axioms. Fourth, we delineate the AND/OR boolean structure of the transformer layer: attention is AND, the FFN is OR, and their strict alternation is Pearl's gather/update algorithm exactly. Fifth, we confirm all formal results experimentally, corroborating the Bayesian network characterization in practice. We also establish the practical viability of loopy belief propagation despite the current lack of a theoretical convergence guarantee. We further prove that verifiable inference requires a finite concept space. Any finite verification procedure can distinguish at most finitely many concepts. Without grounding, correctness is not defined. Hallucination is not a bug that scaling can fix. It is the structural consequence of operating without concepts. Formally verified against standard mathematical axioms.

Gregory Coppola

This paper introduces the Quantified Boolean Bayesian Network (QBBN), which provides a unified view of logical and probabilistic reasoning. The QBBN is meant to address a central problem with the Large Language Model (LLM), which has become extremely popular in Information Retrieval, which is that the LLM hallucinates. A Bayesian Network, by construction, cannot hallucinate, because it can only return answers that it can explain. We show how a Bayesian Network over an unbounded number of boolean variables can be configured to represent the logical reasoning underlying human language. We do this by creating a key-value version of the First-Order Calculus, for which we can prove consistency and completeness. We show that the model is trivially trained over fully observed data, but that inference is non-trivial. Exact inference in a Bayesian Network is intractable (i.e. $Ω(2^N)$ for $N$ variables). For inference, we investigate the use of Loopy Belief Propagation (LBP), which is not guaranteed to converge, but which has been shown to often converge in practice. Our experiments show that LBP indeed does converge very reliably, and our analysis shows that a round of LBP takes time $O(N2^n)$, where $N$ bounds the number of variables considered, and $n$ bounds the number of incoming connections to any factor, and further improvements may be possible. Our network is specifically designed to alternate between AND and OR gates in a Boolean Algebra, which connects more closely to logical reasoning, allowing a completeness proof for an expanded version of our network, and also allows inference to follow specific but adequate pathways, that turn out to be fast.

Gregory Coppola

Web Search and Social Media have always been two of the most important applications on the internet. We begin by giving a unified framework, called general search, of which which all search and social media products can be seen as instances. DimensionRank is our main contribution. This is an algorithm for personalized general search, based on neural networks. DimensionRank's bold innovation is to model and represent each user using their own unique personal neural representation vector, a learned representation in a real-valued multidimensional vector space. This is the first internet service we are aware of that to model each user with their own independent representation vector. This is also the first service we are aware of to attempt personalization for general web search. Also, neural representations allows us to present the first Reddit-style algorithm, that is immune to the problem of "brigading". We believe personalized general search will yield a search product orders of magnitude better than Google's one-size-fits-all web search algorithm. Finally, we announce Deep Revelations, a new search and social network internet application based on DimensionRank.