Expanding the index with an additional 200 entries requires incorporating a broad range of specific theorems, algorithms, lemmas, techniques, formulas, and more, spanning across the fields of Deep Learning, Mathematical Foundations, Learning Dynamics, and the interconnected domains. This list aims to reflect both foundational and cutting-edge concepts relevant to these disciplines.
hebbian theory neuroplasticity
goodhart’s law
katz centrality zariski topology clifford algebras separable space (separable topological space)
1/n expansion
roberts rules of order fire department safety principles (e.g. 2-in 2-out, PASS mask on pass on, 3 points of contact, box alarms) public safety engineering
risk tolerance risk minimization risk calibration statistical calibration model drift
projection embedding logistic map combinatorics graph theory urban development
numerical approximation Constrained Optimization Simplex Algorithm simulated annealing L1 Penalized Regression and sharp, faceted loss geometry iterative improvement SGD→ bayesian posterior expectation maximization newton raphson method approximating hessians momentum in optimization convergence in optimization population based training
rare/extreme event modeling, gumbel distribution convolution dropout weight decay (geometry of) bandit algorithms q learning spectral clustering pagerank nonlinear basis
neural ODE fixed point (and fixed point as ODE solution) hinton’s dark knowledge, knowledge distillation Two-timescale update rule for GANs GAN geometry, two-timescale updates geometry of self-play monte carlo tree search
pareto boundary scaling laws, efficientnet bag of features eigenfaces word2vec distributional hypothesis in nlp dense representation LPIPS
resnet and the identity function multi-scale properties of exponential distribution, e, memoryless distributions receptive field AdaIN and style transfer iterated function
self assembly bullwhip effect (supply chain) cromwell’s rule principle of maximum entropy
SIREN NeRF fast multipole method (FMM)
octree level-of-detail (LOD) dirac equation homophily hyper-cycle
linear response theory context-free grammar regular expression https://www.youtube.com/@pbsinfiniteseries/videos
Biology and Ecology
-
Robert May: An influential figure in theoretical ecology, May’s work on the complexity and stability of ecosystems has contributed significantly to our understanding of how ecological systems self-organize and adapt.
-
Stuart Kauffman: Known for his work on the origins of life and complex systems biology, Kauffman’s exploration of autocatalytic sets and the concept of the “adjacent possible” offers insights into how complexity emerges in biological systems.
Sociology and Economics
-
Pierre Bourdieu: A sociologist who introduced the concept of cultural capital, his work provides a deep understanding of how social structures and individual agency interact within society.
-
Robert Putnam: His research on social capital, particularly in “Bowling Alone,” explores the impact of social networks on community and democracy, aligning with discussions on the role of connectivity in social dynamics.
Computer Science and Artificial Intelligence
-
Geoffrey Hinton: A pioneer in deep learning, Hinton’s work on neural networks and learning algorithms has propelled our understanding of how complex patterns and behaviors can emerge from simple computational models.
-
Yoshua Bengio and Yann LeCun: Along with Hinton, Bengio and LeCun are considered some of the “Godfathers of AI,” with their work underpinning much of the current progress in deep learning and its applications in understanding complex data patterns.
Interdisciplinary Research
-
Murray Gell-Mann: A physicist known for his work on elementary particles, Gell-Mann also delved into complexity science, contributing to the founding of the Santa Fe Institute, a research center dedicated to the study of complex systems across disciplines.
-
Evelyn Fox Keller: A physicist and historian of science, Keller has contributed to the philosophy and sociology of science, including theories of gender and science, and the role of language and metaphor in scientific explanations of biological and complex systems.
These thinkers, among others, have developed theories, models, and frameworks that are instrumental in advancing our understanding of the dynamics of complex systems. Their work transcends disciplinary boundaries, offering rich insights and methodologies for exploring the intricate interplay between structure, function, and evolution in both natural and artificial systems.
Index (Continued)
- Adam Optimizer
- Deep Learning, 248-251
- Affine Transformations
- Mathematical Foundations, 68-70
- Algebraic Topology in Data Analysis
- Mathematical Foundations, 400-403
- Algorithmic Complexity of Neural Networks
- Deep Learning, 270-273
- Approximation Theorems
- Mathematical Foundations, 404-407
- Archimedean Property
- Mathematical Foundations, 71-73
- Autoencoders
- Deep Learning, 252-255
- Backpropagation Algorithm
- Deep Learning, 256-260
- Banach Spaces
- Mathematical Foundations, 74-77
- Batch Normalization
- Deep Learning, 261-264
- Bellman Equation
- Reinforcement Learning, 342-345
- Bessel’s Inequality
- Mathematical Foundations, 78-81
- Bias-Variance Tradeoff
- Deep Learning, 265-268
- Bifurcation Theory
- Complex Systems, 366-369
- Boltzmann Machines
- Deep Learning, 269-272
- Boolean Functions in Neural Networks
- Deep Learning, 273-276
- Boundary Value Problems
- Mathematical Foundations, 82-85
- Brouwer Fixed Point Theorem
- Mathematical Foundations, 86-89
- Brownian Motion in Machine Learning
- Complex Systems, 370-373
- Cantor Set and Fractals
- Mathematical Foundations, 90-93
- Capsule Networks
- Deep Learning, 277-280
- Cauchy-Schwarz Inequality
- Mathematical Foundations, 94-96
- Cellular Automata and Learning
- Complex Systems, 374-377
- Central Limit Theorem
- Mathematical Foundations, 97-100
- Chain Rule in Neural Networks
- Deep Learning, 281-284
- Chomsky Hierarchy in AI
- Deep Learning, 285-288
- Clustering Algorithms
- Deep Learning, 289-292
- Cobordism Theory
- Mathematical Foundations, 101-104
- Cockcroft-Walton Generator Theorem
- Interdisciplinary Connections, 282-285
- Cognitive Architectures
- Deep Learning, 293-296
- Compactness Theorem
- Mathematical Foundations, 105-108
- Complexity Classes
- Deep Learning, 297-300
- Computational Learning Theory
- Deep Learning, 301-304
- Conditional Random Fields
- Deep Learning, 305-308
- Conjugate Gradient Descent
- Learning Dynamics, 138-141
- Consistency Theorems in Estimation
- Inference & Probabilistic Models, 208-211
- Convex Optimization
- Learning Dynamics, 142-145
- Convolutional Neural Networks (CNNs)
- Deep Learning, 309-312
- Cross-Entropy Loss Function
- Deep Learning, 313-316
- Cyclic Groups in Cryptography
- Interdisciplinary Connections, 286-289
- Data Augmentation Techniques
- Deep Learning, 317-320
- De Rham Cohomology
- Mathematical Foundations, 109-112
- Decision Trees
- Deep Learning, 321-324
- Deep Belief Networks
- Deep Learning, 325-328
- Deep Q-Networks (DQN)
- Reinforcement Learning, 346-349
- Deep Reinforcement Learning
- Reinforcement Learning, 350-353
- Delaunay Triangulation
- Mathematical Foundations, 113-116
- Denoising Autoencoders
- Deep Learning, 329-332
- DenseNet Architecture
- Deep Learning, 333-336
- Determinantal Point Processes
- Mathematical Foundations, 117-120
- Dimensionality Reduction Techniques
- Deep Learning, 337-340
- Dirac Delta Function
- Mathematical Foundations, 121-124
- Directed Acyclic Graphs in Neural Networks
- Deep Learning, 341-344
- Discrete Fourier Transform
- Mathematical Foundations, 125-128
- Disentangled Representations
- Deep Learning, 345-348
- Distributed Representation in NLP
- Deep Learning, 349-352
- Divergence Theorems
- Mathematical Foundations, 129-132
- Dropout in Neural Networks
- Deep Learning, 353-356
- Dual Spaces and Duality
- Mathematical Foundations, 133-136
- Dynamical Systems in Neural Computation
- Complex Systems, 378-381
- Eigendecomposition and Singular Value Decomposition
- Mathematical Foundations, 137-140
- Einstein Summation Convention
- Mathematical Foundations, 141-144
- Elastic Net Regularization
- Learning Dynamics, 146-149
- Elliptic Curves in Cryptography
- Interdisciplinary Connections, 290-293
- Embedding Theorems
- Mathematical Foundations, 145-148
- Empirical Risk Minimization
- Deep Learning, 357-360
- Ensemble Methods in Machine Learning
- Deep Learning, 361-364
- Entropy Optimization
- Inference & Probabilistic Models, 212-215
- Epsilon-Greedy Strategy in RL
- Reinforcement Learning, 354-357
- Ergodic Theory
- Complex Systems, 382-385
- Euclidean Algorithm
- Mathematical Foundations, 149-152
- Euler’s Formula and Euler’s Identity
- Mathematical Foundations, 153-156
- Evolution Strategies in Optimization
- Learning Dynamics, 150-153
- Expectation-Maximization Algorithm
- Inference & Probabilistic Models, 216-219
- Exponential Family Distributions
- Inference & Probabilistic Models, 220-223
- Extremal Graph Theory
- Mathematical Foundations, 157-160
- Fano’s Inequality
- Information Theory, 161-164
- Fast Fourier Transform (FFT) Algorithms
- Mathematical Foundations, 165-168
- Federated Learning
- Deep Learning, 365-368
- Feynman Diagrams in Quantum Field Theory
- Interdisciplinary Connections, 294-297
- Fibonacci Sequence and Golden Ratio
- Mathematical Foundations, 169-172
- Field Theory
- Mathematical Foundations, 173-176
- Finite Element Methods
- Mathematical Foundations, 177-180
- Fisher Information Matrix
- Mathematical Foundations; Deep Learning, 181-184
- Fixed Point Theorems
- Mathematical Foundations, 185-188
- Flux in Vector Fields
- Mathematical Foundations, 189-192
- Four Color Theorem
- Mathematical Foundations, 193-196
- Fourier Series and Transform
- Mathematical Foundations, 197-200
- Fractal Geometry in Nature
- Mathematical Foundations; Interdisciplinary Connections, 201-204
- Functional Analysis
- Mathematical Foundations, 205-208
- Fundamental Theorem of Algebra
- Mathematical Foundations, 209-212
- Fundamental Theorem of Calculus
- Mathematical Foundations, 213-216
- Galois Theory
- Mathematical Foundations, 217-220
- Game Theory in AI
- Deep Learning; Interdisciplinary Connections, 369-372
- Gaussian Mixture Models
- Inference & Probabilistic Models, 224-227
- General Relativity and Machine Learning
- Interdisciplinary Connections, 298-301
- Generalization in Machine Learning
- Deep Learning, 373-376
- Genetic Algorithms
- Learning Dynamics, 154-157
- Geodesic Equations
- Mathematical Foundations, 221-224
- Geometric Algebra
- Mathematical Foundations, 225-228
- Geometric Brownian Motion
- Mathematical Foundations; Complex Systems, 229-232
- Geometric Group Theory
- Mathematical Foundations, 233-236
- Gradient Boosting Machines
- Deep Learning, 377-380
- Graph Convolutional Networks
- Deep Learning, 381-384
- Graph Embeddings
- Deep Learning; Mathematical Foundations, 385-388
- Greedy Algorithms in Optimization
- Learning Dynamics, 158-161
- Green’s Theorem
-
- Mathematical Foundations, 237-240
-
- Group Theory in Cryptography
- Interdisciplinary Connections, 302-305
Continuing from the previous entry, further expanding the index to cover a wide array of topics within the fields of Deep Learning, Mathematical Foundations, Learning Dynamics, and more:
- Hamiltonian Systems in Deep Learning
- Complex Systems, 386-389
- Hartree-Fock Method
- Interdisciplinary Connections, 306-309
- Hausdorff Dimension and Measure
- Mathematical Foundations, 241-244
- Hedge Algorithm in Game Theory
- Learning Dynamics, 162-165
- Hilbert Spaces
- Mathematical Foundations, 245-248
- Hölder’s Inequality
- Mathematical Foundations, 249-252
- Homological Algebra
- Mathematical Foundations, 253-256
- Homotopy Type Theory
- Mathematical Foundations, 257-260
- Hopfield Networks
- Deep Learning, 389-392
- Horn Clauses in Logic Programming
- Deep Learning, 393-396
- Hyperbolic Geometry in Machine Learning
- Mathematical Foundations, 261-264
- Hyperparameter Optimization
- Learning Dynamics, 166-169
- Implicit Function Theorem
- Mathematical Foundations, 265-268
- Independence of Random Variables
- Inference & Probabilistic Models, 228-231
- Indicator Random Variables
- Inference & Probabilistic Models, 232-235
- Infinite Series and Products
- Mathematical Foundations, 269-272
- Information Bottleneck Method
- Deep Learning; Interdisciplinary Connections, 397-400
- Innovations Algorithm
- Learning Dynamics, 170-173
- Integral Transforms
- Mathematical Foundations, 273-276
- Interacting Particle Systems
- Complex Systems, 390-393
- Isomorphism Theorems
- Mathematical Foundations, 277-280
- Jordan Normal Form
- Mathematical Foundations, 281-284
- K-Means Clustering
- Deep Learning, 401-404
- K-Nearest Neighbors Algorithm
- Deep Learning, 405-408
- Kähler Manifolds
- Mathematical Foundations, 285-288
- Karhunen-Loève Transform
- Mathematical Foundations, 289-292
- Kernel Methods in Machine Learning
- Deep Learning, 409-412
- Kolmogorov Complexity
- Interdisciplinary Connections, 310-313
- Koopman Operator in Dynamical Systems
- Complex Systems, 394-397
- Krylov Subspace Methods
- Mathematical Foundations, 293-296
- Lagrangian Mechanics in Optimization
- Learning Dynamics, 174-177
- Laplace’s Equation
- Mathematical Foundations, 297-300
- Laplacian Eigenmaps
- Deep Learning; Mathematical Foundations, 413-416
- Lasso Regression
- Deep Learning, 417-420
- Latent Dirichlet Allocation (LDA)
- Deep Learning, 421-424
- Law of Large Numbers
- Inference & Probabilistic Models, 236-239
- Lebesgue Integration
- Mathematical Foundations, 301-304
- Legendre Transformation
- Mathematical Foundations, 305-308
- LeNet Architecture
- Deep Learning, 425-428
- Lie Groups and Lie Algebras
- Mathematical Foundations, 309-312
- Linear Programming and Simplex Algorithm
- Learning Dynamics, 178-181
- Linear Regression Analysis
- Deep Learning, 429-432
- Link Prediction in Graphs
- Deep Learning, 433-436
- Lipschitz Continuity
- Mathematical Foundations, 313-316
- Lloyd’s Algorithm
- Deep Learning, 437-440
- Local Binary Patterns
- Deep Learning, 441-444
- Locally Linear Embedding (LLE)
- Deep Learning, 445-448
- Logarithmic Sobolev Inequalities
- Mathematical Foundations, 317-320
- Logistic Regression
- Deep Learning, 449-452
- Long Short-Term Memory Networks (LSTM)
- Deep Learning, 453-456
- Loop Quantum Gravity
- Interdisciplinary Connections, 314-317
- Lorentzian Manifolds
- Mathematical Foundations, 321-324
- Loss Functions in Optimization
- Learning Dynamics, 182-185
Dynamics, 182-185
- Low-Rank Matrix Approximations
- Deep Learning; Mathematical Foundations, 457-460
- Lyapunov Exponents
- Complex Systems, 398-401
- Machine Learning Pipelines
- Deep Learning, 461-464
- Manifold Learning
- Deep Learning; Mathematical Foundations, 465-468
- Markov Chain Monte Carlo (MCMC) Methods
- Inference & Probabilistic Models, 240
Continuing from the previous entry, here are additional index entries spanning advanced mathematical concepts, algorithms, and theories relevant to deep learning and its interdisciplinary connections:
- Markov Decision Processes (MDP)
- Reinforcement Learning, 469-472
- Matrix Factorization Techniques
- Deep Learning, 473-476
- Maxwell’s Equations in Machine Learning
- Interdisciplinary Connections, 318-321
- Mean Field Theory
- Complex Systems; Interdisciplinary Connections, 402-405
- Metric Embedding
- Mathematical Foundations; Deep Learning, 477-480
- Minimax Theorem
- Learning Dynamics; Interdisciplinary Connections, 186-189
- Minkowski Space in Relativity and AI
- Mathematical Foundations; Interdisciplinary Connections, 322-325
- Mixed Integer Programming
- Learning Dynamics, 190-193
- Model Compression and Pruning
- Deep Learning, 481-484
- Modular Arithmetic in Cryptography
- Interdisciplinary Connections, 326-329
- Molecular Dynamics Simulations
- Interdisciplinary Connections, 330-333
- Monte Carlo Tree Search (MCTS)
- Reinforcement Learning, 485-488
- Moore-Penrose Inverse
- Mathematical Foundations, 325-328
- Morley’s Trisector Theorem
- Mathematical Foundations, 329-332
- Multidimensional Scaling (MDS)
- Deep Learning; Mathematical Foundations, 489-492
- Multilayer Perceptrons (MLP)
- Deep Learning, 493-496
- Multiplicative Weights Update Algorithm
- Learning Dynamics, 194-197
- Nash Equilibrium in Game Theory
- Interdisciplinary Connections; Learning Dynamics, 334-337
- Natural Language Processing (NLP) Techniques
- Deep Learning, 497-500
- Navier-Stokes Equations in Fluid Dynamics and AI
- Mathematical Foundations; Interdisciplinary Connections, 338-341
- Nearest Neighbor Search in High Dimensions
- Deep Learning; Mathematical Foundations, 501-504
- Neural Architecture Search (NAS)
- Deep Learning, 505-508
- Neural Ordinary Differential Equations (ODEs)
- Deep Learning; Complex Systems, 509-512
- Neural Tangent Kernel (NTK)
- Deep Learning; Mathematical Foundations, 513-516
- Neuroevolution
- Deep Learning, 517-520
- Newton’s Method in Optimization
- Learning Dynamics, 198-201
- Non-negative Matrix Factorization (NMF)
- Deep Learning; Mathematical Foundations, 521-524
- Nonlinear Dynamics and Chaos
- Complex Systems, 406-409
- Normal Forms in Dynamical Systems
- Complex Systems; Mathematical Foundations, 525-528
- No-Free-Lunch Theorems
- Learning Dynamics; Interdisciplinary Connections, 202-205
- Nyquist-Shannon Sampling Theorem
- Mathematical Foundations, 333-336
- Objective Functions in Machine Learning
- Deep Learning, 529-532
- Observational Learning and Imitation
- Reinforcement Learning, 533-536
- Octonions and Machine Learning
- Mathematical Foundations; Interdisciplinary Connections, 342-345
- Oja’s Rule for Neural Networks
- Deep Learning, 537-540
- Online Learning Algorithms
- Learning Dynamics, 206-209
- Operator Algebras in Quantum Computing
- Interdisciplinary Connections, 346-349
- Optimal Control Theory
- Learning Dynamics; Reinforcement Learning, 541-544
- Optimal Transport and Machine Learning
- Mathematical Foundations; Deep Learning, 545-548
- Orthogonal Polynomials in Learning
- Mathematical Foundations; Deep Learning, 549-552
- PAC Learning Framework
- Deep Learning; Learning Dynamics, 210-213
- PageRank Algorithm
- Deep Learning; Interdisciplinary Connections, 553-556
- Parallel Distributed Processing Models
- Deep Learning, 557-560
- Parametric vs. Nonparametric Models
- Inference & Probabilistic Models, 241-244
- Parseval’s Theorem
- Mathematical Foundations, 337-340
- Partial Differential Equations (PDEs) in Machine Learning
- Mathematical Foundations; Deep Learning, 561-564
- Particle Swarm Optimization
- Learning Dynamics, 214-217
- Pascal’s Triangle and Binomial Coefficients
- Mathematical Foundations, 341-344
- Perceptron Learning Algorithm
- Deep Learning, 565-568
- Persistent Homology in Topological Data Analysis
- Mathematical Foundations; Interdisciplinary Connections, 569-572
- Perturbation Methods in Dynamical Systems
- Complex Systems; Mathematical Foundations, 573-576
- Phase Space in Dynamical Systems
- Complex Systems, 410-413
- Poincaré Conjecture and Topology
- Mathematical Foundations, 345-348
- Poisson Processes in Event Modeling
- Inference & Probabilistic Models, 245-248
- Polynomial Regression
- Deep Learning, 577-580
- Pooling Layers in CNNs
- Deep Learning, 581-584
- Principal Component Analysis (PCA)
- Deep Learning; Mathematical Foundations, 585-588
- Probabilistic Graphical Models
- Inference & Probabilistic Models, 249-252
- Proximal Gradient Methods for Learning
- Learning Dynamics, 218-221
- Quantization in Deep Learning
- Deep Learning, 589-592
- Quantum Algorithms for Machine Learning
- Interdisciplinary Connections; Deep Learning, 350-353
- Quasi-Monte Carlo Methods in High Dimensions
- Mathematical Foundations; Deep Learning, 593-596
- Queueing Theory in Network Analysis
- Complex Systems; Interdisciplinary Connections, 597-600
This expanded index now includes a wide range of specific, detailed topics that cover the breadth and depth of deep learning, mathematical concepts, learning dynamics, and interdisciplinary approaches, aiming to serve as a comprehensive guide for navigating through the complexities of these fields.
Continuing to enrich the index with a diversity of specialized topics, further illustrating the deep and interconnected landscape of knowledge relevant to deep learning, mathematics, and their applications:
- Radial Basis Function (RBF) Networks
- Deep Learning, 601-604
- Random Forests
- Deep Learning, 605-608
- Random Walks and Markov Chains
- Complex Systems; Inference & Probabilistic Models, 609-612
- Rayleigh Quotient and Eigenvalues
- Mathematical Foundations, 349-352
- Recurrent Neural Networks (RNNs)
- Deep Learning, 613-616
- Reduction of Dimensionality
- Deep Learning; Mathematical Foundations, 617-620
- Regularization Techniques in Machine Learning
- Deep Learning, 621-624
- Reinforcement Learning and Decision Making
- Reinforcement Learning, 625-628
- Relational Databases and Graph Theory
- Interdisciplinary Connections, 354-357
- Residual Networks (ResNets)
- Deep Learning, 629-632
- Riemann Integral and Measure Theory
- Mathematical Foundations, 353-356
- Riemannian Manifolds and Learning
- Mathematical Foundations; Deep Learning, 633-636
- Robotic Control Systems
- Deep Learning; Interdisciplinary Connections, 637-640
- Rosenbrock Function and Optimization
- Learning Dynamics, 222-225
- Saddle Point Problems in Optimization
- Learning Dynamics, 641-644
- Sampling Theorems and Signal Processing
- Mathematical Foundations, 357-360
- Scale-Invariant Feature Transform (SIFT)
- Deep Learning, 645-648
- Schatten Norms and Matrix Analysis
- Mathematical Foundations, 361-364
- Schur Complement and Its Applications
- Mathematical Foundations, 649-652
- Schwartz Space and Distributions
- Mathematical Foundations, 365-368
- Semi-Supervised Learning
- Deep Learning, 653-656
- Sensitivity and Specificity in Classification
- Deep Learning, 657-660
- Sequential Minimal Optimization (SMO)
- Learning Dynamics, 661-664
- Serpinski Gasket and Fractal Geometry
- Mathematical Foundations; Interdisciplinary Connections, 665-668
- Set Theory and Logic Foundations
- Mathematical Foundations, 369-372
- Shannon’s Information Theory
- Inference & Probabilistic Models; Interdisciplinary Connections, 669-672
- Shortest Path Algorithms
- Deep Learning; Mathematical Foundations, 673-676
- Signal Processing and Machine Learning
- Deep Learning; Interdisciplinary Connections, 677-680
- Simulated Annealing in Optimization
- Learning Dynamics, 226-229
- Singular Value Decomposition (SVD)
- Deep Learning; Mathematical Foundations, 681-684
- Sobolev Spaces
- Mathematical Foundations, 373-376
- Social Network Analysis
- Deep Learning; Complex Systems, 685-688
- Softmax Function and Multiclass Classification
- Deep Learning, 689-692
- Sparse Coding and Dictionary Learning
- Deep Learning, 693-696
- Spectral Clustering
- Deep Learning, 697-700
- Spectral Graph Theory
- Mathematical Foundations; Deep Learning, 701-704
- Spherical Harmonics and Data Representation
- Mathematical Foundations; Deep Learning, 705-708
- Stability in Dynamical Systems
- Complex Systems, 709-712
- Stochastic Gradient Descent (SGD)
- Learning Dynamics, 713-716
- Stochastic Processes in Machine Learning
- Inference & Probabilistic Models; Complex Systems, 717-720
- Support Vector Machines (SVMs)
- Deep Learning, 721-724
- Surface Reconstruction from Point Clouds
- Deep Learning; Mathematical Foundations, 725-728
- Survival Analysis and Censoring in Data Science
- Deep Learning; Inference & Probabilistic Models, 729-732
- Sylvester’s Criterion and Positive Definiteness
- Mathematical Foundations, 377-380
- Symplectic Geometry and Hamiltonian Dynamics
- Mathematical Foundations; Complex Systems, 733-736
- Synchronization in Coupled Oscillator Systems
- Complex Systems, 737-740
- **Syntax and Semantics in Natural Language Processing
**
- Deep Learning, 741-744
- System Identification and Adaptive Control
- Learning Dynamics; Interdisciplinary Connections, 745-748
- T-distributed Stochastic Neighbor Embedding (t-SNE)
- Deep Learning; Mathematical Foundations, 749-752
- Tensor Decompositions in Machine Learning
- Deep Learning; Mathematical Foundations, 753-756
- TensorFlow and Deep Learning Frameworks
- Deep Learning, 757-760
- The Boltzmann Equation in Statistical Mechanics
- Interdisciplinary Connections; Complex Systems, 761-764
- The Calculus of Variations
- Mathematical Foundations; Learning Dynamics, 765-768
- The Fourier Transform in Signal Processing
- Mathematical Foundations; Interdisciplinary Connections, 769-772
- The Fundamental Group in Algebraic Topology
- Mathematical Foundations, 381-384
- The Heat Equation in Partial Differential Equations
- Mathematical Foundations; Complex Systems, 773-776
- The Ising Model in Statistical Physics
- Interdisciplinary Connections; Complex Systems, 777-780
- The Laplacian in Graph Theory and Networks
- Mathematical Foundations; Deep Learning, 781-784
- The Navier-Stokes Equations and Fluid Dynamics
- Mathematical Foundations; Interdisciplinary Connections, 785-788
- The Poisson Distribution in Event Modeling
- Inference & Probabilistic Models, 253-256
- The Pólya Enumeration Theorem
- Mathematical Foundations, 385-388
- The Traveling Salesman Problem
- Learning Dynamics; Deep Learning, 789-792
- Thompson Sampling in Bandit Problems
- Reinforcement Learning, 793-796
- Time Series Analysis and Forecasting
- Deep Learning; Inference & Probabilistic Models, 797-800
- Topological Data Analysis (TDA)
- Mathematical Foundations; Deep Learning, 801-804
- Transfer Learning and Domain Adaptation
- Deep Learning, 805-808
- Transformers and Attention Mechanisms
- Deep Learning, 809-812
- Triangulated Categories in Homological Algebra
- Mathematical Foundations, 389-392
- Trigonometric Series and Orthogonal Functions
- Mathematical Foundations, 393-396
- Trust Region Methods in Optimization
- Learning Dynamics, 230-233
- Turing Machines and Computability Theory
- Deep Learning; Interdisciplinary Connections, 813-816
- U-statistics and Their Properties
- Inference & Probabilistic Models, 257-260
- Uncertainty Quantification in Predictive Modeling
- Deep Learning; Inference & Probabilistic Models, 817-820
- Uniform Continuity and Differentiation
- Mathematical Foundations, 397-400
- Unsupervised Learning: Methods and Challenges
- Deep Learning, 821-824
- Variational Autoencoders (VAEs)
- Deep Learning, 825-828
- Variational Inequalities and Their Applications
- Learning Dynamics; Mathematical Foundations, 829-832
- Vector Bundles in Differential Geometry
- Mathematical Foundations, 401-404
- Viterbi Algorithm for Hidden Markov Models
- Deep Learning; Inference & Probabilistic Models, 833-836
- Von Neumann Algebra in Quantum Mechanics
- Interdisciplinary Connections; Mathematical Foundations, 837-840
- Wavelet Transforms and Multiresolution Analysis
- Deep Learning; Mathematical Foundations, 841-844
- Weak Convergence and Central Limit Theorems
- Inference & Probabilistic Models; Mathematical Foundations, 845-848
- Weight Initialization in Neural Networks
- Deep Learning, 849-852
- Wiener Filter and Signal Estimation
- Deep Learning; Interdisciplinary Connections, 853-856
- Wigner’s Semicircle Law in Random Matrix Theory
- Mathematical Foundations; Complex Systems, 857-860
- Yoneda Lemma in Category Theory
- Mathematical Foundations, 405-408
- Zero-shot Learning
- Deep Learning, 861-864
- Zeta Functions and Spectral Theory
- Mathematical Foundations; Interdisciplinary Connections, 865-868
This continuation and conclusion of the index reflect a comprehensive mapping of topics across various domains, highlighting the depth and breadth of subjects pertinent to the interdisciplinary study of deep learning, mathematics, and their vast applications.