Reza Shamji

Research Associate @ Zitnik Lab (Harvard Medical School) Applying to PhDs in mathematics, Fall 2026 — chasing whether free will and consciousness can be mathematically modeled.

New essay → How AI Actually Works — AI from the ground up through the math, no buzzwords. Walks Vision Transformers from pixels → attention → vision-language models, and ends on the bigger question I’m chasing.


Research Vision

The question I want to spend my life on: can free will and consciousness be mathematically modeled — or are humans, in some formal sense, beyond mathematics? That is the single thing I want to know before I die, and the reason I am applying to PhDs in mathematics this fall.

Why I’m starting in AI: because it is the closest thing to mathematically-defined human reasoning I have seen in my lifetime, which makes it the right place to begin — even though it isn’t the destination. Even “superintelligence,” as it’s usually defined, lives in the language of productivity and economic value, not the language of agency, free will, or consciousness. AI gets me near the math. The math is what I will need to take the bigger question further.

Within AI, the bet I’m making: backpropagation — the chain rule we use to update every weight in a network — does not look like how brains actually learn. Real neurons appear to update locally: each connection adjusts based on the activity of the two cells it sits between, sometimes gated by a chemical signal like dopamine. Backprop, by contrast, needs a global error signal that travels backwards across the entire network through carefully matched weights — something brains do not appear to implement. Whether the brain nonetheless approximates something gradient-like through some other mechanism is genuinely open. And backprop has its own problems even in silico — vanishing gradients, credit assignment, an implicit-bias story still unsettled. The honest position is that the function-update rule is the open frontier; if we want intelligences different from the ones gradient descent produces, that is where I want to look first.

And this is where the small question meets the large one. The bet on alternatives to backprop holds in both directions AI could be heading. If the goal is to reach the human brain — the highest intelligence we have evidence of — backprop is the wrong tool, for the reasons above. If the goal is to surpass it (which I find more honest — humans have placed ourselves at the center of the world, and assuming the brain is the ceiling of possible intelligence is the same instinct), backprop has scaled impressively and may keep doing so, but empirically, scaled backprop today has not even reached human-level intelligence. In either case, I think an alternative function-update rule is required — to close that gap, and to push past it.

That is what connects this work to the bigger question. I’m not claiming the math of free will and consciousness lives literally inside an alternative to backprop — that would be a leap. What I am claiming is that chasing such an alternative is the closest grounded AI problem to the question I actually care about: close enough to give me a real taste of the mathematical foundations, and concrete enough that I can do real work on it now — instead of waving hands about consciousness from the outside.

Before my PhD, I want to work on:


Looking for Collaborations

I’m looking for collaborators before I submit math PhD applications this fall. If you work on alternatives to backpropagation, the mathematics of why current architectures work, or formal approaches to consciousness, agency, or free will (however speculative) — I’d love to connect. Early feedback and shared projects would help me ground my direction before applications.


Writing


Preprints & Manuscripts


Research & Engineering

Zitnik Lab — Research Associate (Sept 2025 – Present)

KG-Router — Knowledge-Graph–Grounded Routing for High-Stakes QA

External Stakeholder Collaboration

Infrastructure & ToolUniverse Integration


Kempner Institute — ML Research Engineer Intern (Multimodal AI) (Jun – Sept 2025)

Advised by Yilun Du & Sham Kakade.

Large-Scale Ablation Study & Key Findings

Infrastructure & Benchmarking

Findings underpin the VLM architecture design space preprint (ICML 2026 submission under review, manuscript and code available upon request).


Selected Projects

ChainEnv RL Benchmarks (JAX)

A compact sandbox to probe exploration under sparse rewards in a tunable 1-D chain (pure, vectorized JAX; laptop-friendly).
Repo: github.com/rezashamji/jax-chainenv-benchmarks


Technical Skills


Education

Harvard University — A.B. in Computer Science (Secondary in Economics) May 2025

Relevant Coursework: Algorithms & Limitations, Distributed Systems & Machine Organization, Semantics of Programming Languages, Probability, Linear Algebra


Languages

English (native) · Mandarin (fluent)