Sange Mehrab

Exciton Diffusion as a Blind Search

Tue, 14 Apr 2026 10:30:00 +0300

Master's thesis note on exciton diffusion, blind search, and first-hitting versus first-return statistics in disordered semiconductor environments.

1.1 From Scalars to Vectors: Data Points, Rows, Columns, and Transpose

Mon, 27 Apr 2026 00:00:00 +0000

A careful introduction to how a single house measurement becomes a scalar, how many measurements become a vector, how rows become datasets, and how vectors are used in machine learning and neural networks.

1.2 From Matrices to Tensors: Tables, Images, Batches, and Multilinear Structure

Tue, 28 Apr 2026 00:00:00 +0000

A deep introduction to matrices and tensors for AI mathematics: data matrices, images as matrices, color images and batches as tensors, matrix operations, linear maps, rank, norms, eigenvalues, SVD, tensor order, modes, unfolding, n-mode products, tensor contractions, CP decomposition, Tucker decomposition, and the formal tensor-product view.

1.3 Probability Distributions, Noise, Markov Chains, SDEs, and Stochastic PDEs

Wed, 29 Apr 2026 00:00:00 +0000

A careful introduction to distributions and noise for AI mathematics, starting from real-world uncertainty and moving toward Gaussian random vectors, white and colored noise, Markov chains, Brownian motion, Itô SDEs, Fokker–Planck equations, stochastic PDEs, Euler–Maruyama, Milstein methods, and the mathematical foundation of diffusion generative models.

1.4 Mathematics of Large Language Models: Training, Inference, Attention, Scaling, and Alignment

Fri, 01 May 2026 00:00:00 +0000

A beginner-to-advanced mathematical introduction to LLMs, covering autoregressive language modeling, tokenization, vector embeddings, positional encodings, transformer blocks, attention, softmax, cross-entropy, maximum likelihood, backpropagation, AdamW, scaling laws, compute-optimal training, MoE, efficient attention, KV caching, speculative decoding, quantization, LoRA, RLHF, DPO, PPO, and inference-time reasoning.

1.5 Mathematics of Machine Learning and Deep Learning for Time Series

Fri, 01 May 2026 00:00:00 +0000

A beginner-to-advanced mathematical introduction to time-series machine learning and deep learning, covering classical forecasting, stochastic processes, spectral analysis, supervised time-series learning, recurrent neural networks, LSTMs, GRUs, temporal convolutional networks, transformers, PatchTST, iTransformer, TimesNet, TimeMixer, state-space models, S4, Mamba, DeepAR, N-BEATS, N-HiTS, Temporal Fusion Transformers, diffusion-based forecasting, neural ODEs, neural CDEs, foundation models, probabilistic losses, conformal prediction, anomaly detection, classification, and imputation.

Section 2.1