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How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts172

Groups

๐Ÿ“Linear Algebra15๐Ÿ“ˆCalculus & Differentiation10๐ŸŽฏOptimization14๐ŸŽฒProbability Theory12๐Ÿ“ŠStatistics for ML9๐Ÿ“กInformation Theory10๐Ÿ”บConvex Optimization7๐Ÿ”ขNumerical Methods6๐Ÿ•ธGraph Theory for Deep Learning6๐Ÿ”ตTopology for ML5๐ŸŒDifferential Geometry6โˆžMeasure Theory & Functional Analysis6๐ŸŽฐRandom Matrix Theory5๐ŸŒŠFourier Analysis & Signal Processing9๐ŸŽฐSampling & Monte Carlo Methods10๐Ÿง Deep Learning Theory12๐Ÿ›ก๏ธRegularization Theory11๐Ÿ‘๏ธAttention & Transformer Theory10๐ŸŽจGenerative Model Theory11๐Ÿ”ฎRepresentation Learning10๐ŸŽฎReinforcement Learning Mathematics9๐Ÿ”„Variational Methods8๐Ÿ“‰Loss Functions & Objectives10โฑ๏ธSequence & Temporal Models8๐Ÿ’ŽGeometric Deep Learning8

Category

๐Ÿ”ทAllโˆ‘Mathโš™๏ธAlgo๐Ÿ—‚๏ธDS๐Ÿ“šTheory

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AllBeginnerIntermediate
โš™๏ธAlgorithmAdvanced

Minkowski Sum

The Minkowski sum A โŠ• B adds every point of set A to every point of set B, and for convex polygons it can be computed in O(n + m) by merging edge directions.

#minkowski sum#convex polygon#edge merge+12
โš™๏ธAlgorithmAdvanced

DSU on Tree (Sack)

DSU on Tree (also called the Sack technique) answers many subtree queries in O(n \log n) by keeping data from the heavy child and temporarily re-adding light subtrees.

#dsu on tree
910111213
Advanced
#sack technique
#subtree queries
+12
โš™๏ธAlgorithmAdvanced

Rectangle Union Area

The union area of many axis-aligned rectangles can be computed efficiently using a sweep line over x and a segment tree tracking covered y-length.

#rectangle union area#line sweep#segment tree+12
โš™๏ธAlgorithmAdvanced

Suffix Array Construction

A suffix array stores the starting indices of all suffixes of a string in lexicographic order, enabling fast substring queries and many string operations.

#suffix array#lcp array#kasai+12
โš™๏ธAlgorithmAdvanced

Lyndon Factorization

A Lyndon word is a string that is strictly smaller (lexicographically) than all of its nontrivial rotations.

#lyndon word#duval algorithm#booth algorithm+12
โš™๏ธAlgorithmAdvanced

Broken Profile DP

Broken Profile DP is a dynamic programming technique that sweeps a grid one cell or one column at a time while encoding the boundary between processed and unprocessed cells as a compact state.

#broken profile dp#profile dp#plug dp+11
โš™๏ธAlgorithmAdvanced

Slope Trick

Slope Trick is a technique to maintain a convex piecewise-linear function implicitly using two heaps and a running constant.

#slope trick#convex dp#piecewise linear+11
โš™๏ธAlgorithmAdvanced

Aliens Trick (WQS Binary Search)

Aliens Trick (WQS Binary Search) converts a hard โ€œexactly k itemsโ€ optimization into an unconstrained problem by adding a penalty ฮป per chosen item.

#aliens trick#wqs binary search#parametric search+11
โš™๏ธAlgorithmAdvanced

Subset Sum Convolution

Subset Sum Convolution (often called Subset Convolution) computes C[S] by summing A[T]ร—B[U] over all disjoint pairs T and U whose union is S.

#subset convolution#subset sum convolution#sos dp+11
โš™๏ธAlgorithmAdvanced

Divide and Conquer DP Optimization

Divide and Conquer DP optimization speeds up DP transitions of the form dp[i][j] = min over k of dp[i-1][k] + C(k, j) when the optimal k is monotone in j.

#divide and conquer dp#monge array#quadrangle inequality+10
โš™๏ธAlgorithmAdvanced

Convex Hull Trick - Dynamic (LineContainer)

Dynamic Convex Hull Trick (LineContainer) maintains the lower or upper envelope of lines y = m x + b with O(log n) insertion and O(log n) query for arbitrary insertion order.

#convex hull trick#dynamic cht#linecontainer+12
โš™๏ธAlgorithmAdvanced

Convex Hull Trick (CHT)

The Convex Hull Trick (CHT) speeds up dynamic programs where each state is a minimum over linear functions, such as dp[i] = min_j (dp[j] + b[j] ร— a[i]).

#convex hull trick#cht#dynamic programming optimization+12