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📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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∑MathIntermediate

Markov Chains

A Markov chain models a system that moves between states where the next step depends only on the current state, not the past.

#markov chain#transition matrix#stationary distribution+11
⚙️AlgorithmAdvanced

Matrix Exponentiation - Advanced

Matrix exponentiation turns repeated linear transitions into fast O(n^{3} log k) computation using exponentiation by squaring.

#matrix exponentiation
Advanced
Filtering by:
#matrix exponentiation
#adjacency matrix
#walk counting
+12
∑MathIntermediate

Fast Exponentiation

Fast exponentiation (binary exponentiation) computes a^n using repeated squaring in O(log n) multiplications.

#binary exponentiation#fast power#modular exponentiation+11
⚙️AlgorithmIntermediate

Matrix Exponentiation

Matrix exponentiation turns repeated linear transitions into a single fast power of a matrix using exponentiation by squaring.

#matrix exponentiation#binary exponentiation#companion matrix+11
⚙️AlgorithmAdvanced

DP with Probability

DP with probability models how chance flows between states over time by repeatedly redistributing mass according to transition probabilities.

#markov chain#probability dp#absorbing state+12
∑MathAdvanced

Linear Recurrence

A linear recurrence defines each term as a fixed linear combination of a small, fixed number of previous terms.

#linear recurrence#matrix exponentiation#kitamasa+12
🗂️Data StructureAdvanced

Aho-Corasick - DP Applications

Aho–Corasick (AC) turns a set of forbidden patterns into a finite automaton that lets you process or generate strings while tracking whether any pattern appears.

#aho-corasick#automaton dp#forbidden substrings+12