[{"title":"Outward Reality","url":"/2026/04/21/reality.html","type":"posts","date":"2026-04-21","excerpt":"How we don't know what's real."},{"title":"A 1.58-Dimensional Object","url":"/2026/04/17/fractal-dimensions.html","type":"posts","date":"2026-04-17","excerpt":"Exploring fractal dimensions from my favorite Numberphile video."},{"title":"Arguments","url":"/2026/01/11/arguments.html","type":"posts","date":"2026-01-11","excerpt":"My thoughts on arguments."},{"title":"The Three Gods Riddle","url":"/2025/12/30/three-gods-riddle.html","type":"posts","date":"2025-12-30","excerpt":"Explaining the solution to the Three Gods Riddle."},{"title":"Hypergraph Theory","url":"/2025/12/23/hypergraphs.html","type":"posts","date":"2025-12-23","excerpt":"An introduction to hypergraph theory and the Erdős–Ko–Rado Theorem."},{"title":"Art Gallery","url":"/2025/12/22/art-gallery.html","type":"posts","date":"2025-12-22","excerpt":"A curated collection of artworks I saw in the Kunsthistorisches Museum in Vienna that have caught my attention and inspired me."},{"title":"Solving PDEs with Neural Networks","url":"/2025/05/12/pinn-attempt1.html","type":"posts","date":"2025-05-12","excerpt":"Physics-Informed Neural Networks approach to solving the 1D heat equation by minimizing PDE residuals and initial condition losses."},{"title":"Face Generator with GANs","url":"/2025/05/09/gan-attempt1.html","type":"posts","date":"2025-05-09","excerpt":"Using Deep Convolutional GANs to generate realistic celebrity face images, trained on 200,000 samples with PyTorch."},{"title":"Investigation of the Genetics of Coronaviruses and the Similarities Between Them","url":"/projects/coronavirus-genetics/","type":"projects","date":"2022-02-01","excerpt":"Applying PCA and diffusion mapping to coronavirus genetic sequences to uncover clustering structure and relationships among coronavirus families."},{"title":"Visualize your Spotify Taste","url":"/projects/spotify-visualizer/","type":"projects","date":"2025-02-10","excerpt":"A web application that integrates with the Spotify API to analyze and visualize your music taste, featuring track analysis and abstract mosaic generation."},{"title":"Differential Privacy in Federated Learning","url":"/projects/differential-privacy/","type":"projects","date":"2025-04-29","excerpt":"Integration of Differential Privacy into a Federated Learning framework using the MIMIC-IV dataset to enhance patient privacy while maintaining model performance."},{"title":"Stargazr","url":"/projects/stargazr/","type":"projects","date":"2025-06-13","excerpt":"A modern stargazing assistant that provides personalized recommendations for the best nights to stargaze, combining astronomy, weather, and light pollution data."},{"title":"The Art of Attention","url":"/projects/art-of-attention/","type":"projects","date":"2025-11-04","excerpt":"Cool plots created from a dynamical system inspired by self-attention mechanisms."},{"title":"Some Structures in Transformer Architectures","url":"/projects/some-structures-in-transformer-architectures/","type":"projects","date":"2025-12-09","excerpt":"Representing decoder-only transformers using Kronecker products to reveal interpretable linear algebraic structure and the introducing the phenomenon of superposition in high-dimensional vector spa..."},{"title":"AI-Powered Project Tracking for Hitachi Energy","url":"/projects/hitachi-energy-capstone/","type":"projects","date":"2026-05-04","excerpt":"An automated BI pipeline built as my NCSU senior capstone project that ingests project tracking data, uses Azure AI to generate persona-tailored insights, and delivers HTML reports and email digest..."},{"title":"On the Metastability of Bipodal States in Transformer Attention Dynamics","url":"/projects/metastability-transformer-attention/","type":"projects","date":"2026-05-22","excerpt":"We study metastability in the transformer attention dynamics, where tokens evolve as interacting particles on the sphere."},{"title":"Deep Learning","url":"/notes/deep-learning/","type":"notes","date":"2026-10-18","excerpt":"These are notes I took while studying deep learning during my semester in Budapest, adapted from lectures given by my delightful instructor Pál Zsámboki. My original, handwritten notes can be found..."},{"title":"Introduction","url":"/notes/deep-learning/intro/","type":"notes","date":"2026-06-12","excerpt":"In this course, I will assume that you already have some basic knowledge about what machine learning is, and roughly what deep learning is. I will also assume that you are aware of the differences ..."},{"title":"Linear Regression","url":"/notes/deep-learning/linear-regression/","type":"notes","date":"2026-07-28","excerpt":"We’ll start off where we left off last time. Recall that we have the following two objects:  The (input) feature space: $\\mathscr X\\subseteq\\mathbb{R}^d$. This is the set of outcomes for the input ..."},{"title":"Classification and Logistic Regression","url":"/notes/deep-learning/logistic-regression/","type":"notes","date":"2026-07-28","excerpt":"We shall now consider the case where the target space $\\mathscr Y$ is finite. Recall from the introduction that this is a classification problem. Unless stated otherwise, we let $\\mathscr Y = {0, \\..."},{"title":"Negative Log Likelihood","url":"/notes/deep-learning/negative-log-likelihood/","type":"notes","date":"2026-07-29","excerpt":"Now that we’ve built multinomial logistic regression (a model that outputs a predicted class distribution $p_\\theta(\\mathbf x) \\in \\Delta^{c-1}$), we’ll now answer question of which loss function t..."},{"title":"Binary Logistic Regression","url":"/notes/deep-learning/binary-logistic-regression/","type":"notes","date":"2026-07-31","excerpt":"We now turn to the special case $c = 2$: binary classification. The two classes are $\\mathscr Y = {0, 1}$, typically called the negative and positive class. Rather than a whole new model, binary lo..."},{"title":"Gradient Descent","url":"/notes/deep-learning/gradient-descent/","type":"notes","date":"2026-08-01","excerpt":"So far, we’ve discussed different kinds of models and loss functions. We also mentioned that we need to tune the parameters $\\theta$ of the model in some way that minimizes the loss function. Recal..."},{"title":"Confidence Intervals and Ensembles","url":"/notes/deep-learning/confidence-intervals-and-ensembles/","type":"notes","date":"2026-08-05","excerpt":"Last time, we introduced Stochastic Gradient Descent (SGD), which requires choosing samples at random. Recall from the linear regression note that random number generators in computers depend on th..."},{"title":"Hyperparameter Search and Early Stopping","url":"/notes/deep-learning/hyperparameter-search-early-stopping/","type":"notes","date":"2026-08-06","excerpt":"In the last note, we introduced ensembles: training $n$ independently-seeded copies of a model at once, both to get confidence intervals on performance and, typically, better predictions from aggre..."},{"title":"Naive Set Theory","url":"/notes/naive-set-theory/","type":"notes","date":"2026-10-18","excerpt":"These notes follow Paul Halmos’s Naive Set Theory."},{"title":"N-BEATS","url":"/notes/nbeats/","type":"notes","date":"1111-11-11","excerpt":"I was part of a research lab as during the summer after my freshman year in college. I was apparently going to be studying time series techniques, and so the PI assigned me my first task: read and ..."},{"title":"About","url":"/about.html","type":"page","excerpt":"About page."},{"title":"Activity","url":"/activity.html","type":"page","excerpt":"Activity feed Vasu Menon across GitHub, Letterboxd, and more."},{"title":"Contact","url":"/contact.html","type":"page","excerpt":"Get in touch."},{"title":"Watching","url":"/films.html","type":"page","excerpt":"Films and movies."},{"title":"Graph","url":"/graph/","type":"page","excerpt":"Every post, project, and note on this site, drawn as a map of what relates to what."},{"title":"Listening","url":"/listening.html","type":"page","excerpt":"Music and artists."},{"title":"Making","url":"/making.html","type":"page","excerpt":"Music."},{"title":"Now","url":"/now.html","type":"page","excerpt":"What I'm up to right now."},{"title":"Reading","url":"/reading.html","type":"page","excerpt":"Books I'm reading and have read."},{"title":"Urbex","url":"/urbex.html","type":"page","excerpt":"Urban exploration photos and locations."},{"title":"Coding Time","url":"/wakatime.html","type":"page","excerpt":"My coding time statistics via WakaTime."}]