TheoryofDeepLearning.2022

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116 theory of deep learning13.3 Example of AlgorithmsHere is an example of algorithm. Usually the algorithm shouldref some Theorem/Lemma, and also the corresponding Theorem/Lemmashould ref back. This will be easier to verify the correctness.Algorithm 2 Fourier Sparse Recovery Algorithm1: procedure FourierSparseRecovery(x, n, k, µ, R ∗ ) ⊲Theorem 13.1.12: Require that µ = 1 √k‖̂x −k ‖ 2 and R ∗ ≥ ‖̂x‖ ∞ /µ3: H ← 5, ν ← µR ∗ /2, y ←⃗04: Let T = {T (1) , · · · , T (H) } where each T (h) is a list of i.i.d.uniform samples in [p] d5: while true do6: ν ′ ← 2 1−H ν7: z ← LinfinityReduce({x t } t∈T )8: if ν ′ ≤ µ then return y + z ⊲ We found the solution9: y ′ ←⃗010: for f ∈ supp(y + z) do11: y ′ f← Π 0.6ν (y f + z f ) ⊲ We want ‖̂x − y ′ ‖ ∞ ≤ ν and thedependence between y ′ and T is under control12: end for13: y ← y ′ , ν ← ν/214: end while15: end procedure
examples of theorems, proofs, algorithms, tables, figures 11713.4 Example of FiguresWe should make sure all the pictures are plotted by the same software.Currently, everyone feel free to include their own picture. Zhaowill re-plot the picture by tikz finally.x 3x 2x Tz 0z TFigure 13.1: A chasing sequencez 3y 2,4y 2,3y 2,2y 2,1z 2x 1z 1x 0
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C O N T R I B U T O R S : R A M A N
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44 Basics of generalization theory
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612 Representation Learning 11113 E
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810.2 Autoencoder defined using a d
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IntroductionThis monograph discusse
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14 theory of deep learning• Train
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2Basics of OptimizationThis chapter
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basics of optimization 19where the
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basics of optimization 21Therefore,
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3Backpropagation and its VariantsTh
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backpropagation and its variants 25
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4Basics of generalization theoryGen
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basics of generalization theory 33p
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basics of generalization theory 35w
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basics of generalization theory 37N
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6Algorithmic RegularizationLarge sc
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algorithmic regularization 43minimi
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algorithmic regularization 45update
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algorithmic regularization 476.2 Ma
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algorithmic regularization 496.3.2
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algorithmic regularization 51Given
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algorithmic regularization 53to the
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algorithmic regularization 55Since
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58 theory of deep learning7.1 Preli
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60 theory of deep learningcreasing
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62 theory of deep learning“gradie
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64 theory of deep learning7.4 Case
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