7 / papers

Mathematical Foundations

Category theory, sheaves, and formal structure applied to systems that were built empirically. 7 open-access papers by Pranay Mahendrakar, each with a permanent DOI.

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Spend the Budget on the Known or the Unknown? Open-Set Active Learning Scores Two Opposed Objectives Under One Name, Its Filtering Side's Own Results Do Not Treat Unknowns as Waste, and the Winner Is Set by a Relevance Label and a Query Price the Benchmarks Fix in Advance

Active learning chooses which unlabelled examples a human should label. When the unlabelled pool contains classes the model has never been shown, two lines of work give opposite instructions under the same name. One, usually called…

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How Many Classes Are Out There? In Category Discovery the Class Count Is Granularity Carried Over From the Labelled Set, Supplying It Can Supply the Taxonomy, and Without It the Count Is Set by a Hyperparameter

Category discovery asks a model to sort an unlabelled image collection into classes, some of which it has never been shown, using a labelled subset of other classes as its guide. Almost every method needs one number before it can produce…

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The Allowance Is Doing the Work: Constructed Premises in Chain-of-Thought Step Verification, What Formal Validity Still Certifies Once They Are Permitted, and the Dependence Test Argumentation Runs and Step Verification Does Not

A verifier that checks the steps of a chain of thought cannot demand that each step state everything it relies on, because no real step does. Every published step verifier therefore permits a class of premises that the text does not…

DOI

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What has Pranay Mahendrakar published on Mathematical Foundations?

Pranay Mahendrakar has published 7 open-access papers on Mathematical Foundations: "Spend the Budget on the Known or the Unknown? Open-Set Active Learning Scores Two Opposed Objectives Under One Name, Its Filtering Side's Own Results Do Not Treat Unknowns as Waste, and the Winner Is Set by a Relevance Label and a Query Price the Benchmarks Fix in Advance", "How Many Classes Are Out There? In Category Discovery the Class Count Is Granularity Carried Over From the Labelled Set, Supplying It Can Supply the Taxonomy, and Without It the Count Is Set by a Hyperparameter", "The Allowance Is Doing the Work", "Formal Verification of Neural Network Safety Beyond Toy Examples", "Energy-Based Models for Reasoning", "Sheaf-Theoretic Semantics and Quantum Contextuality in Large Language Models" and "Quantum Mirrors of the Mind". Each is deposited on Zenodo with a permanent DOI and is free to read.

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