A Redis-wire-compatible (RESP) vector memory engine written from scratch in Rust with zero dependencies beyond libc — works unchanged with redis-cli and existing clients. Hand-rolled HNSW approximate nearest-neighbour index with a single-threaded event-driven I/O core over raw kqueue/epoll and vector search offloaded to a worker pool. Hand-written SIMD distance kernels in NEON (ARM64) and AVX2+FMA (x86_64) with runtime dispatch achieve ~9× speedup at 768 dimensions; WAL + compacting mmap snapshot for crash-safe durability.

A from-scratch differentiable spectral-segmentation library in PyTorch that treats a network's feature map as a graph and learns to segment by cutting graphs, motivated by the Cheeger inequality bounding graph conductance by the Fiedler value λ₂. Implements every spectral operator by hand — learned-metric affinity kernels, three graph-Laplacian variants, k-NN sparsification, and a symmetric eigensolver (cyclic Jacobi + Lanczos), each validated against numpy/scipy oracles. Hand-codes a degeneracy-robust differentiable eigensolver replacing PyTorch's unstable eigh backward with Lorentzian-broadened eigenvalue-gap gradients stable where eigenvalues collapse at segment boundaries. Replaces fixed eigenbasis weighting with a learned, label-supervised spectral response whose noise floor is set from the Marchenko–Pastur bulk edge; benchmarked as a U-Net head on Cityscapes with mIoU / Boundary-IoU metrics.

A minimal autograd engine built from scratch in Rust exploring where neural network performance actually comes from. Implements reverse-mode autograd over a dynamic graph, four matrix multiplication kernels (naive, tiled, packed+SIMD, and an experimental Strassen-form mp variant), a kernel scheduler, and a gradient memory pool with lifetime-based release. CPU-only; SIMD via NEON on arm64 and AVX2+FMA on x86_64.

Research-driven LLM architecture exploring energy-based self-learning for scientific reasoning, symbolic mathematics, and formal logic. Combines contrastive energy functions with autoregressive generation to enable iterative self-correction without external reward models.

Real-time chat system built from scratch over raw WebSocket connections. Persistent message storage, presence detection, typing indicators, and room-based multiplexing — no third-party chat SDKs.

Mobile application that clusters photos using on-device ML for perceptual similarity. Extracts feature embeddings, runs hierarchical clustering, and groups visually related images without uploading data to any external server.

Deterministic spatial interaction engine for generating structured synthetic datasets. Simulates grid-based environments with configurable physics, agent policies, and collision semantics — designed to produce training data for autonomous agent learning.

AI-driven microplastic detection pipeline combining optical particle counters with Bulk Acoustic Wave (BAW) preprocessing. Classifies particle morphology through signal analysis and implements a toxin-free acoustic capture system for microplastic recovery across varied aquatic environments.