Stochastic Gradient in Hilbert Spaces
I wrote a free, proof-complete monograph on stochastic gradient methods in infinite-dimensional Hilbert spaces. It starts from the functional-analysis foundations (Riesz, Radon–Nikodym), gives five equivalent definitions of stochastic gradients, proves existence/uniqueness of the dynamics, connects the continuum limit to gradient-flow PDEs, and derives explicit convergence rates under multiple assumption sets (convex, strongly convex, PL/KL, heavy-tailed noise, proximal). It also covers special cases (Gaussian/RKHS), extends to Hilbert manifolds/Banach spaces, analyzes…
What it does
In the maker’s words, at launch
I wrote a free, proof-complete monograph on stochastic gradient methods in infinite-dimensional Hilbert spaces. It starts from the functional-analysis foundations (Riesz, Radon–Nikodym), gives five equivalent definitions of stochastic gradients, proves existence/uniqueness of the dynamics, connects the continuum limit to gradient-flow PDEs, and derives explicit convergence rates under multiple assumption sets (convex, strongly convex, PL/KL, heavy-tailed noise, proximal). It also covers special cases (Gaussian/RKHS), extends to Hilbert manifolds/Banach spaces, analyzes discretizations (stability/consistency), and includes four applications (QM ground states, elasticity, optimal control, inverse problems) with pseudocode and explicit constants. Open problems at the end invite feedback. PDF is free to redistribute if cited. Happy to answer questions on assumptions that are actually needed in infinite-D, how the spectral picture influences rates, and what breaks outside Hilbert structure. If you want a quick start, skim the convergence summary and the applications sections.
Does the same job
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More life & fun this month
the category →- TL
Life & fun · 10d ago · louisabraham.github.io
Photosynthesis fires two of your iPhone
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SoloUno▲310Take control of hair pulling, nail biting & skin picking
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Scroll through all 43,252,003,274,489,856,000 reachable Rubik's Cube permutations.
Life & fun · 26d ago · everycube.alen.is
Hi HN, I built Eigendrum, a web tool that solves the 2D wave equation for arbitrary shapes so you can hear what they sound like as drums. How it works: * Solves -∇²u = λu using finite element analysis (Kφ = λMφ) on a triangle mesh. * Validated to <0.1% error against closed-form solutions for circles (Bessel zeros) and rectangles. * Sound model factors in strike location, Rayleigh damping, and mallet width. * Includes Kac drums I & II to demonstrate identical sound spectra from different geometries. * No frameworks, build steps, or dependencies. Repo and tests:…
Life & fun · 26d ago · baselashraf81.github.io
Launched alongside, October 2025
the whole month →
- SA
I went down the rabbit hole on a side project and ended up building this: Strange Attractors(https://blog.shashanktomar.com/posts/strange-attractors). It’s built with three.js. Working on it reminded me of the little "maths for fun" exercises I used to do while learning programming in early days. Just trying things out, getting fascinated and geeky, and being surprised by the results. I spent way too much time on this, but it was extreme fun. My favorite part: someone pointed me to the Simone Attractor on Threads. It is a 2D attractor and I asked GPT to extrapolate it to…
AI · Oct 2025 · blog.shashanktomar.com
- ASAutism Simulator▲779
Hey all, I built this. It’s not trying to capture every autistic experience (that’d be impossible). It’s based on my own lived experience as well as that of friends on the spectrum. I'm trying to give people a feel for what masking, decision fatigue, and burnout can look like day-to-day. That’s hard to explain in words, but easier to show through choices and stats. I'm not trying to "define autism". I’ve gotten good feedback here about resilience, meds, and difficulty tuning. I’ll keep tweaking it. If even a few people walk away thinking, "ah, maybe that’s why my coworker struggles in those…
Life & fun · Oct 2025 · autism-simulator.vercel.app
