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Concepts356

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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

Level

AllBeginnerIntermediate
∑MathIntermediate

Linear Basis for XOR

A linear basis for XOR is a compact set of at most W numbers (W = number of bits) that can generate every XOR value obtainable from a multiset of numbers.

#xor basis#linear basis#gaussian elimination f2+12
∑MathIntermediate

Matrix Rank and Linear Independence

Matrix rank is the number of pivots after Gaussian elimination and equals the dimension of both the column space and the row space.

#matrix rank
2324252627
Advanced
#linear independence
#gaussian elimination
+12
⚙️AlgorithmIntermediate

Bipartite Matching - Hopcroft-Karp

Hopcroft–Karp computes maximum matching in a bipartite graph in O(E \sqrt{V}) time, which is asymptotically faster than repeated DFS (Kuhn's algorithm).

#hopcroft karp#bipartite matching#augmenting path+11
⚙️AlgorithmIntermediate

Bipartite Matching - Kuhn's Algorithm

Kuhn’s algorithm finds a maximum matching in a bipartite graph by repeatedly searching for augmenting paths using DFS.

#bipartite matching#kuhn algorithm#augmenting path+12
⚙️AlgorithmIntermediate

König's Theorem

König's Theorem states that in any bipartite graph, the size of a maximum matching equals the size of a minimum vertex cover.

#konig's theorem#bipartite matching#minimum vertex cover+12
⚙️AlgorithmIntermediate

Flow - Modeling Techniques

Many classic problems can be modeled as a maximum flow problem by building the right network and capacities.

#max flow#dinic#bipartite matching+12
⚙️AlgorithmIntermediate

Min-Cut Max-Flow Theorem

The Max-Flow Min-Cut Theorem says the maximum amount you can push from source to sink equals the minimum total capacity you must cut to disconnect them.

#max flow#min cut#edmonds karp+12
⚙️AlgorithmIntermediate

Maximum Flow - Dinic's Algorithm

Dinic's algorithm computes maximum flow by repeatedly building a level graph with BFS and sending a blocking flow using DFS.

#dinic#maximum flow#blocking flow+11
⚙️AlgorithmIntermediate

Maximum Flow - Ford-Fulkerson

Ford–Fulkerson finds the maximum possible flow from a source to a sink by repeatedly pushing flow along an augmenting path in the residual graph.

#maximum flow#ford-fulkerson#edmonds-karp+10
⚙️AlgorithmIntermediate

LCA - Binary Lifting

Binary lifting precomputes 2^k ancestors for every node so we can jump upward in powers of two.

#lca#binary lifting#tree+12
⚙️AlgorithmIntermediate

Strongly Connected Components

Strongly Connected Components (SCCs) partition a directed graph into maximal groups where every vertex can reach every other vertex in the group.

#strongly connected components#tarjan#kosaraju+12
⚙️AlgorithmIntermediate

Bridge Tree

A bridge tree is built by contracting every 2-edge-connected component of an undirected graph into a single node, leaving only bridges as edges between nodes.

#bridge tree#2-edge-connected components#bridges+12