About Me
Hi — I’m Yuta Agawa, an independent researcher working at the intersection of Mathematical Physics (non-equilibrium quantum dynamics), Computational Neuroscience, and Foundational Machine Learning.
Across these areas, I take a structural approach: I look for exact mechanisms and invariants that explain how complex systems behave, whether the system is a synapse, a learning algorithm, or a many-body Hamiltonian. I’m also applying the same mindset to the design of a next-generation differentiable programming language for high-performance mathematical modelling.
Although my tools are mathematical, my motivations are human. My reinforcement learning work grew out of living with OCD: I wanted a precise way to describe how delayed, stochastic feedback can lock behaviour into harmful loops. When I couldn’t find the right formalism, I adapted analysis techniques from mathematical physics to a minimal, inspectable setting and proved the resulting phenomenon. My work on integrability began similarly — by noticing a clean geometric pattern in flow-equation notes and following it to an exact result. In both cases, the goal is the same: turn intuition into verifiable structure.
I try to treat uncertainty as part of the problem statement: make it explicit, quantify it where possible, and design around it.
A Note on My Research Portfolio (ORCID)
As an independent researcher, I maintain two complementary streams of work. To make the status of each item clear on ORCID, I use the following title conventions:
- Formal Research (Standard): Peer-review–oriented research and engineering outputs (AI safety, reinforcement learning, mathematical physics), written to standard academic conventions and intended for review, reuse, and standardisation.
- Personal Exploration (Prefix: [Theoretical Hypothesis]): Private exploratory work in quantum field theory and unification. These are unofficial preprints: they may contain rigorous first-principles derivations, but they are presented as hypotheses and invitations for discussion rather than established scientific consensus.
I. Formal Research & Engineering
My formal research and engineering focus on deriving exact conditions for system behaviour and translating those results into practical tools, evaluation protocols, and standards.
1. Foundations of Reinforcement Learning & AI Safety
I study the stability of learning dynamics in agents with biologically inspired memory architectures. In my work on Sign-Gated Dual-Trace Temporal-Difference (TD) Learning, I proved a phenomenon I call “Pathological Reinforcement,” where an agent can systematically reinforce behaviour with negative expected return.
Key Theoretical Result: I derived gamma-invariant necessary and sufficient conditions for this hazard. Under single-spike conditions, the sign of the expected parameter update \(\mathbb{E}[\Delta\theta]\) is independent of the discount factor \(\gamma\). The hazard manifests if and only if:
where \(n_{+}\) and \(n_{-}\) are the asymmetric trace decay rates, and \(L\) is the outcome delay. The proof also yields a closed-form critical delay threshold \(L^{\dagger}\), giving a concrete bound that can be used in safety analysis for autonomous systems.
This work is meant to be useful beyond theory: I contributed public comments and concrete templates so that architectural hazards can be stress-tested and documented in a standardised way.
2. Mathematical Physics: Emergent Integrability
In non-equilibrium quantum dynamics, I study the mathematical structure of flow equations (continuous unitary transformations). My work focuses on the Wegner-type flow equation, which diagonalises Hamiltonians by continuously decoupling off-diagonal interaction terms.
Key Theoretical Result: I proved that the high-dimensional diagonalisation flow can collapse into a simpler, exactly integrable dynamical system. Under specific conditions, the flow of the interaction parameters \(x(s)\) is governed by a second-order gradient system:
This finding, which I call “Emergent Integrability,” shows that the diagonalisation trajectory follows the gradient of a potential landscape, revealing hidden structure in the unitary transformation itself.
3. Engineering: Differentiable Programming Language
(Coming Soon) I am currently architecting a new differentiable programming language for high-performance mathematical modelling. The goal is to bridge symbolic mathematics and numerical optimisation by treating differentiation as a first-class concept in the language’s type system, making it easier to build physics-informed machine learning models and other optimisation-driven simulators.
II. Personal Exploration: QFT & Unification
Beyond my formal research, I spend personal time studying the geometry of gauge theories — especially the Yang-Mills mass gap problem and unification ideas.
I think of these topics as “mathematical strength training” — a way to keep my reasoning sharp. The notes and papers I write in this category may include rigorous first-principles derivations, but I’m also mindful of how deep and unresolved these problems remain.
Accordingly, I mark these items with [Theoretical Hypothesis] in my publication list. I share them not as definitive solutions, but as invitations to careful theoretical discussion — and I welcome thoughtful critique and collaboration.
Selected References
- Agawa, Y. (2025). Pathological Reinforcement in Sign-Gated Dual-Trace Temporal-Difference Learning: Gamma-Invariant Necessary and Sufficient Conditions and Robust Bounds. Zenodo. DOI: 10.5281/zenodo.16889669
- Agawa, Y. (2025). Emergent Integrability in a Wegner-type Flow Equation. Zenodo. DOI: 10.5281/zenodo.14359669
- Agawa, Y. (2025). Technical Brief and Expanded Public Comment: A Concrete Proposal for a Result Descriptor for Architectural Hazards. Submitted to NIST. Zenodo. DOI: 10.5281/zenodo.16887999
- Agawa, Y. (2025). Technical Brief and Public Comment Submitted in Response to the NIST AI Standards "Zero Drafts" Pilot Project. Submitted to NIST. Zenodo. DOI: 10.5281/zenodo.16888077
