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Raymond Tana

I am a PhD Candidate at Penn State University in Mathematical Logic. Dabble in tech :)

📍 State College PA, San Francisco CA,

Compression and GenAI

💡Theoretical computer science formalizes the equivalence between the ability to compress and the ability to perform induction for generative AI models. In the limit of stronger compression capabilities, one encounters a theoretically perfect learner: AIXI. What can be said about the compression capabilities of current generative models? Main Ideas from

Hyperarithmetical is Effectively (co)-Analytic

The purpose of this blog post is to explain why hyperarithmetic definability exactly agrees with definability at the \(\Delta^1_1\) level of the analytical hierarchy. We follow the steps laid out in Computable Structure Theory: Beyond the arithmetic by Antonio Montalbán (the Draft form from September 23, 2022). This

Designing against Deceit

Only a few months ago in a short manuscript detailing potential issues facing software engineers in the wake of ever-evolving AI systems, researchers Gros, Devanbu, and Yu described an impending reality where most computer code is written by machines [GDY 2023]. In such a reality, how can we guarantee that

The Theory of Representations

I introduce a nuanced discussion on how we represent real numbers in order to get desirable notions of "computability" beyond finitary objects.

MDL, pt 1

We start a series of posts introducing MDL: Minimum Description Length and the MDL Principle; a theory of inductive inference.

Interpretability, pt 1

I summarize some recent results and theories about interpretability in machine learning.

The Natural Number Game

I introduce the online Natural Number Game which uses Lean programming to verify formal proofs of mathematical theorems from Peano's axioms.

Processing.js

We explore the Processing.js library, its use in Khan Academy, and my personal creations in Processing.js.

CoCa Models

Summary of CoCa model based on the preprint by Yu, Wang, et. al.

How to Make a Blog Post

A resource for anyone wishing to build a better workflow when blogging with Ghost. Tips & Tricks and general advice.