Independent research · mathematics · machine learning
I study structural questions in nonlinear systems and machine learning. Analytic arguments carry the general results; exact or certified computation enters where a finite witness or quantitative bound bears proof weight.
Recent papers ask when local or finite structure determines global behavior: exactness for signed supports, injectivity mechanisms for ridge networks, and kernels of geometric representations.
Characterizes when an interior signed support is SONC-exact through nonseparability. The universal theorem is analytic; exact elimination, interval arithmetic, and certificate replay support the explicit three-negative witness and quantitative benchmark.
Constructs an explicit sigmoid ridge network with an everywhere-positive Jacobian determinant and a segment-averaged Jacobian with negative determinant. The example separates pointwise positivity from the averaged-Jacobian mechanism at planar width four; the global behavior of its canonical witness is resolved in the follow-up below.
Develops a global inversion theorem for planar saturating ridge networks and resolves the certified separation witness as an injective global diffeomorphism onto an explicit nonconvex octagon. Exact and validated parameter certificates show that the mechanism persists on an explicit open neighborhood.
Identifies the Ptolemy identity behind complex orthogonality, proves essential rigidity of the sign rule, and determines the rational kernel on the inner pure braid groups at n = 3 and n = 4 along certified Delaunay flip sequences.
Interactive teaching tools and compact engineering studies make the same ideas inspectable at a different scale.
Twelve bilingual, single-file applets for search, logic, Bayesian reasoning, supervised and unsupervised learning, neural networks, vision, and reinforcement learning. Each runs in the browser without a build step.
A CPU-scale reproduction of a qualitative DeepSeekMath ranking, paired with a compact operator zoo for comparing regularized policy-improvement updates under one notation and one training interface.
Projects across AI evaluation, retrieval, agents, machine learning, data systems, Rust protocols, infrastructure, and security. Each project states its implemented scope and includes tests or executable checks where appropriate.
I am an independent researcher and computer-science educator with a background spanning computer science, mathematics, physics, and secondary STEM education.
I am interested in problems where a structural argument can replace brute force, or where computation can be made exact enough to carry a proof obligation. Current work crosses nonlinear optimization, neural networks, algebraic computation, and AI post-training.
I teach computer science and AI. That work shapes the research presentation: definitions arrive before machinery, claims remain scoped to their evidence, and an implementation should reveal the idea rather than conceal it.
For research collaboration, technical review, or roles in mathematical AI, machine learning, and research engineering.