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Concepts13

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šŸ“Linear Algebra15šŸ“ˆCalculus & Differentiation10šŸŽÆOptimization14šŸŽ²Probability Theory12šŸ“ŠStatistics for ML9šŸ“”Information Theory10šŸ”ŗConvex Optimization7šŸ”¢Numerical Methods6šŸ•øGraph Theory for Deep Learning6šŸ”µTopology for ML5šŸŒDifferential Geometry6āˆžMeasure Theory & Functional Analysis6šŸŽ°Random Matrix Theory5šŸŒŠFourier Analysis & Signal Processing9šŸŽ°Sampling & Monte Carlo Methods10šŸ§ Deep Learning Theory12šŸ›”ļøRegularization Theory11šŸ‘ļøAttention & Transformer Theory10šŸŽØGenerative Model Theory11šŸ”®Representation Learning10šŸŽ®Reinforcement Learning Mathematics9šŸ”„Variational Methods8šŸ“‰Loss Functions & Objectives10ā±ļøSequence & Temporal Models8šŸ’ŽGeometric Deep Learning8

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šŸ”·Allāˆ‘Mathāš™ļøAlgošŸ—‚ļøDSšŸ“šTheory

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āš™ļøAlgorithmIntermediate

Efficient Attention Mechanisms

Standard softmax attention costs O(nĀ²) in sequence length because every token compares with every other token.

#linear attention#efficient attention#kernel trick+12
šŸ“šTheoryIntermediate

Scaled Dot-Product Attention

Scaled dot-product attention scores how much each value V should contribute to a query by taking dot products with keys K, scaling by \(\sqrt{d_k}\), applying softmax, and forming a weighted sum.

#scaled dot-product attention
12
Advanced
Filtering by:
#time complexity
#softmax
#transformer
+10
āˆ‘MathIntermediate

Convolution Theorem

The Convolution Theorem says that convolving two signals in time (or space) equals multiplying their spectra in the frequency domain.

#convolution theorem#fft#dft+12
āˆ‘MathIntermediate

Tensor Operations

A tensor is a multi-dimensional array that generalizes scalars (0-D), vectors (1-D), and matrices (2-D) to higher dimensions.

#tensor#multi-dimensional array#broadcasting+12
āš™ļøAlgorithmIntermediate

Complexity Analysis Quick Reference

Use an operation budget of about 10^8 simple operations per second on typical online judges; always multiply by the time limit and number of test files if known.

#time complexity#competitive programming#big-o+12
āš™ļøAlgorithmIntermediate

Debugging Strategies for CP

Systematic debugging beats guesswork: always re-read the statement, re-check constraints, and verify the output format before touching code.

#competitive programming#debugging#stress testing+12
āš™ļøAlgorithmIntermediate

Small-to-Large Principle

Small-to-large means always merge the smaller container into the larger one to keep total work low.

#small-to-large#sack technique#dsu on tree+11
āˆ‘MathIntermediate

Permutations and Combinations

Permutations count ordered selections, while combinations count unordered selections.

#permutations#combinations#binomial coefficient+12
āˆ‘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
āš™ļøAlgorithmIntermediate

Breadth-First Search (BFS)

Breadth-First Search (BFS) explores a graph level by level, visiting all vertices at distance d from the source before any at distance d+1.

#bfs#breadth first search#graph traversal+12
āš™ļøAlgorithmIntermediate

0-1 BFS

0-1 BFS is a shortest path algorithm specialized for graphs whose edge weights are only 0 or 1.

#0-1 bfs#binary weights#shortest path+12
āš™ļøAlgorithmIntermediate

Prefix Sum and Difference Array

Prefix sums precompute running totals so any range sum [l, r] can be answered in O(1) time as prefix[r] - prefix[l-1].

#prefix sum#difference array#imos method+12