Knowledge Vault 2/23 - ICLR 2014-2023
Anima Anandkumar ICLR 2016 - Keynote - Guaranteed Non-convex Learning Algorithms through Tensor Factorization
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Concept Graph & Resume using Claude 3 Opus | Chat GPT4 | Gemini Adv | Llama 3:

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ICLR 2016] --> B[Tensor methods: non-convex solutions,
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to orthogonal tensor 9] A --> K[Tensor methods: probabilistic models,
topic modeling, networks 10] K --> L[Tensor methods outperform
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incoherent dictionary 12] K --> N[Convolutional constraints: shift invariance,
FFT computation 13] K --> O[Tensor methods: sentence embeddings,
paraphrase detection 14] K --> P[Tensor methods: reinforcement learning,
POMDP framework 15] K --> Q[Tensor methods: Atari games,
better rewards 16] K --> R[Tensor methods: one-layer network,
input-output guarantees 17] K --> S[Tensor representations: compress layers,
higher rates 18] K --> T[Tensor factorization: analyze
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semantic decoding 20] A --> V[Randomized sketching: scalable tensors,
avoid exponential blowup 21] A --> W[Communication-efficient, blocked computations:
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benefit applications, deep learning 23] A --> Y[Smoothing, homotopy, local search:
non-convex optimization guarantees 24] A --> Z[Diffusion processes: speed up
RNN training, generalization 25] A --> AA[Saddle points: challenges in
high-dimensional non-convex optimization 26] AA --> AB[Escaping higher-order saddle points:
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unsupervised learning potential 28] A --> AD[Research-industry collaboration: accelerate
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scalable complex learning solutions 30] class A,B tensor; class C,D,E,F,G,H,I,J decomposition; class K,L,M,N,O,P,Q,R,S,T applications; class U,V,W,X,Y,Z,AA,AB,AC,AD,AE future;


1.-Tensor methods offer effective solutions to non-convex learning problems and local optima by replacing the objective function.

2.-Tensor decomposition preserves global optimum with infinite samples, providing a consistent solution.

3.-Simple algorithms can solve tensor decomposition under transparent conditions, which are natural for learning problems.

4.-Matrix decomposition has limitations such as non-uniqueness and inability to have over-complete representations.

5.-Tensor decomposition allows for shared decomposition of multiple matrices, leading to better identification and quantifiability.

6.-Tensor decomposition is NP-hard in general, but efficient algorithms exist for a natural class of tensors.

7.-Tensor contractions extend the notion of matrix product and enable solving the decomposition problem.

8.-For orthogonal tensors, the tensor power method converges to stable stationary points, which are the components.

9.-Pre-processing the input tensor can transform a general tensor into an orthogonal form for efficient decomposition.

10.-Tensor methods can efficiently solve probabilistic models like topic modeling and community detection in social networks.

11.-Tensor methods outperform variational inference in terms of running time and likelihood for various applications.

12.-Tensor methods can learn overcomplete representations in sparse coding when dictionary elements are incoherent.

13.-Convolutional constraints in tensor decomposition allow for shift invariance and efficient computation through FFT operations.

14.-Tensor methods applied to sentence embeddings achieve good performance in paraphrase detection with limited training data.

15.-Tensor methods can solve partially observable processes in reinforcement learning by incorporating a POMDP framework.

16.-Tensor methods show potential for better rewards compared to convolutional networks in Atari game play.

17.-Tensor methods can train a one-layer neural network with guarantees by looking at input-output relationships.

18.-Tensor representations can effectively compress dense layers of neural networks, achieving higher compression rates than low-rank representations.

19.-Tensor factorization can be used to analyze the expressive power of different neural network architectures.

20.-Tensors have been explored for memory models and semantic decoding, showing promising directions for further research.

21.-Randomized sketching can make tensor methods scalable by avoiding exponential blowup with increasing tensor order.

22.-Communication-efficient schemes and blocked tensor computations can extend matrix computations for improved performance.

23.-Strong library support and hardware acceleration for tensor methods can benefit a range of applications, including deep learning.

24.-Smoothing and homotopy methods can be combined with local search techniques for non-convex optimization with guarantees.

25.-Diffusion processes can speed up training and improve generalization in recurrent neural networks compared to stochastic gradient descent.

26.-Saddle points pose challenges in high-dimensional non-convex optimization, slowing down stochastic gradient descent.

27.-Escaping higher-order saddle points arising from over-specified models can speed up non-convex optimization.

28.-Tensor methods have been applied to a wide range of applications, showing their potential for unsupervised learning.

29.-Collaborations between researchers and industry partners can accelerate the development and adoption of tensor methods.

30.-Further research on tensor methods can lead to more efficient and scalable solutions for complex learning problems.

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