MATHEMATICS
I first met mathematics through competition. Over time, I began to use it to see structure, test assumptions, and work within constraints
— Hoang —
Mathematics and my earliest inquiries
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PIMA · 2025
At PiMA, I followed a mathematical idea from probability and sequences into generative audio models.
AUTOREGRESSIVE MODELS
How can a sequence use its past to predict what comes next?
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WAVENET
Causal and dilated convolutions extend that idea to raw audio.
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THE MATHEMATICS I KEPT RETURNING TO
How much of the past can one neuron actually “see”?
FROM SEQUENCES TO SOUND
That mindset became one of the reasons I chose to attend PiMA…
How far back can a neuron look?
1 → 2 → 4 → 8
Dilated convolutions expand the receptive field without requiring every intermediate point to be processed at every layer.
Rₖ = 2ᵏ
How much of the past can one neuron actually “see”?
A QUESTION INSIDE THE MODEL
However, after the first karaoke session, everyone gradually seemed to understand one another more naturally.
Humor has always been one of the quickest ways I know to make a room feel less guarded.
BEYOND THE MODEL
Humans are — and should be — each other’s companions
How far back can a neuron look?
1 → 2 → 4 → 8
Dilated convolutions expand the receptive field without requiring every intermediate point to be processed at every layer.
Rₖ = 2ᵏ
How much of the past can one neuron actually “see”?
BEYOND THE MODEL
How enchanted is the moment when the last puzzle piece clicks!
Sparse Partial Optimal Transport via Quadratic Regularization.
Acuitas Education · Research Assistant· March–September 2024
Published in the Journal of Computer Science, 2025
I contributed to domain-adaptation experiments comparing QPOT with EPOT in sparsity and classification accuracy. The project showed me how code could test a mathematical idea beyond the page.
01 · APPLIED MATHEMATICS RESEARCH
FROM QUESTIONS TO RESEARCH
VIEW THE RESEARCH →
Classifying Symmetric Avoided Sets of Permutations in S4
Acuitas Education · Research Assistant · June–October 2025
Using Python, I narrowed …… candidate sets to 310, then returned to mathematical arguments to complete the classification.
02 · ALGEBRAIC COMBINATORICS
Mathematics gave me tools to study systems. Economics brought questions about how those systems distribute opportunity.
← THE MINDSET
CONTINUE TO ECONOMICS →