概念
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AI
5Backpropagation
Efficient computation of all gradients ∂L/∂w via the chain rule on the computational graph
Convolutional Neural Network
Shared convolutional filters learn spatially local patterns; efficient for images via weight sharing
Hierarchical Representation Learning
Deep models learn hierarchical representations by composing many nonlinear layers
Neural Networks
Compositions of linear layers + nonlinear activations: output = σ(W_L σ(…σ(W_1 x + b_1)…) + b_L)
Recurrent Neural Network
h_t = σ(W_h h_{t-1} + W_x x_t + b): recurrent cell processes sequences step by step
CS
5Algorithmic Complexity
Algorithmic complexity predicts how runtime or memory grows as input size increases
Dynamic Programming
Solve overlapping subproblems once and cache results to avoid redundant computation
Graph Algorithms
Algorithms operating on graphs G=(V,E): traversal, shortest paths, spanning trees, connectivity
Greedy Algorithms
Make the locally optimal choice at each step, achieving a global optimum when the greedy property holds
Sorting
Arrange elements in order; comparison-based lower bound is Ω(n log n)
ML
5k-Nearest Neighbors
Classify by majority vote of k nearest neighbors; no training phase (lazy learner)
Linear Regression
Fit a hyperplane y = Xβ + ε to minimize squared error ‖y − Xβ‖²
Logistic Regression
Binary classifier: P(y=1|x) = σ(w^T x + b), trained via cross-entropy loss
Supervised Learning
Learn a mapping f: X → Y from labeled training examples (x_i, y_i) pairs
Support Vector Machine
Find the maximum-margin hyperplane: maximize 2/‖w‖ s.t. y_i(w^T x_i + b) ≥ 1
Mathematics
5Eigenvalues & Eigenvectors
Av = λv: eigenvector v is only scaled (not rotated) by matrix A; λ is the eigenvalue
Matrix Multiplication
C = AB where C_{ij} = Σ_k A_{ik}B_{kj}; represents composition of linear maps
Singular Value Decomposition
A = UΣV^T: any matrix factors into rotation × scaling × rotation
Vector Space Basis
A basis is a minimal set of independent vectors that spans a vector space
Vector Spaces
A set closed under vector addition and scalar multiplication (satisfying 8 axioms)
Semiconductor
4BJT Operation
Current-controlled bipolar transistor: base current controls larger collector current via minority carrier injection
CMOS Logic Gates
Complementary NMOS+PMOS pairs form logic gates with near-zero static power and full-swing output
MOSFET Operation
Voltage-controlled transistor: gate voltage modulates channel conductance between drain and source
PN Junction
Junction between p-type and n-type semiconductor forms depletion region and rectifying diode behavior