Kelvin Peng · svah-x

Kelvin Peng彭从楷

I am an undergraduate in Combinatorics & Optimization at the University of Waterloo. I do research in machine learning, with a focus on mathematical reasoning and latent-space reasoning.

status

bmath '27 · combinatorics & optimization · uwaterloo

interests

reasoning · interpretability · graph theory

contact

[email protected]

Research interests.

a proper 3-edge-coloring of the pentagonal prism; each color class is a perfect matching.

interest 01

Graph theory & combinatorics

Edge colorings, matchings, and the structure of graphs. I am particularly interested in problems whose solutions can be verified mechanically.

information moving between layer states.

interest 02

Model internals

A transformer computes by carrying a single hidden state through a stack of layers, each of which reads from it and writes back. I study how information moves through that stack, and how that movement can be measured in trained models.

h ← f(h, x), iterated until the state converges.

interest 03

Recurrent reasoning

Reasoning need not be written out as text. A family of models instead applies the same network repeatedly, refining a latent state until it converges. I study these recurrent reasoners on structured tasks whose difficulty can be controlled precisely.

manuscripts

2026 Probing the Emergent Global Workspace of Reasoning Models on Structured Reasoning Tasks First author (with Taoli Cheng). Short version accepted at the NeurIPS 2026 MATH-AI workshop; full version under review at ICLR 2027. Intervenes on the internal states of recursive and autoregressive reasoners on verifiable multi-solution tasks.

2026 When Wrong Answers Remain Unsettled: Failure Dynamics in Recurrent Reasoners Co-first author with Jiucheng Zang, Yankai Wei and Peng Cheng; all four authors contributed equally. Under review at ICLR 2027. Studies failure dynamics under continued recurrent computation.

Selected projects.

Research prototypes, training infrastructure, and one hackathon entry. Source code is on GitHub.

PRTS — menu bar companion

A macOS menu bar and Windows tray application. Priestess, a character from Arknights, sits in the tray as a small icon; clicking it opens a popover with her character art and a chat interface backed by the Claude Code or Codex CLI already installed on the machine. Her expression follows the tone of each reply, she remains on the desktop as a companion while idle, and she can run a fixed allowlist of local actions: play music, open an application or URL, set a reminder. Prebuilt releases for macOS and Windows.

electron · node · claude code · codexgithub ↗

2026

TopoAdamW

An AdamW variant that adjusts its step size using topological summaries of the local loss surface, computed with GUDHI. A guard limits the adjustment when the geometry estimate is unreliable. Benchmarked against standard AdamW on CIFAR-10.

pytorch · gudhi · tdagithub ↗

2025

Geometry Dash agent

A DreamerV3-style agent that learns to play Geometry Dash from pixels. Most of the effort went into infrastructure: a custom Gymnasium environment and a Windows-to-WSL bridge that keeps observations, actions, and logs aligned at 60 frames per second.

jax · gymnasium · model-based rlgithub ↗

2025

Efficient LLM fine-tuning

Fine-tuning pipelines for Dream-7B and GPT-OSS-20B on mathematical text, using 4-bit QLoRA, gradient checkpointing, and DeepSpeed. On the benchmarks used, mathematical accuracy improved by about 20% while VRAM use fell by more than half, so the full pipeline runs on a single 16 GB GPU.

pytorch · deepspeed · qlora

2025

AlterEgo

A hackathon entry from LA Hacks. It asks seven questions, then generates a version of the user twenty years older: an aged portrait, a narrated life story, and a conversation with that person.

claude · fastapi · react · elevenlabsdevpost ↗

2026

Virtual wind tunnel

A real-time CFD laboratory in the browser: a lattice-Boltzmann (D2Q9) solver with momentum-exchange force measurement, validated against the canonical cylinder benchmark. Place a standard dummy, a car, a rocket, or any drawn or uploaded shape in the test section; set wind speed, air temperature and surface friction; read the drag coefficient from the balance and observe the Kármán vortex street.

cfd · lattice-boltzmann · canvaslive demo ↗

2026

Background.

I began with competition mathematics (Euclid, first place in British Columbia) and came to machine learning from the mathematical side.

At Waterloo I study Combinatorics & Optimization. Much of machine learning reduces to graph and optimization problems, so the degree and the research complement each other.

My earlier work was in reinforcement learning and training efficiency; several of the projects above date from that period.

education & awards

2023 — 2027 University of Waterloo BMath, Combinatorics & Optimization. Graph theory, nonlinear optimization, number theory, computational mathematics; neural networks (in progress); quantum information processing (Winter 2027).

2021 — 22 Euclid Mathematics Contest First in British Columbia · school champion, twice · honour roll.

2022 Canadian Senior Math Contest School champion · honour roll.

toolkit

languages: python · c/c++ · racket · sql · latex
frameworks: pytorch · jax · deepspeed · huggingface
mathematics: graph theory · combinatorial opt · tda · cryptography
infra: linux · cuda · docker · wandb · runpod

Contact.

I am open to research collaborations and internships. Email is the most reliable way to reach me.

[email protected]

click to copy

Kelvin Peng彭从楷

Research interests.

Graph theory & combinatorics

Model internals

Recurrent reasoning

Selected projects.

PRTS — menu bar companion

TopoAdamW

Geometry Dash agent

Efficient LLM fine-tuning

AlterEgo

Virtual wind tunnel

Open-source courses.

Background.

Contact.