Optimal Complexity in Decentralized Training

Yucheng Lu ยท Christopher De Sa

**Concept Graph & Resume using Claude 3.5 Sonnet | Chat GPT4o | Llama 3:**

graph LR
classDef decentralized fill:#f9d4d4, font-weight:bold, font-size:14px
classDef optimization fill:#d4f9d4, font-weight:bold, font-size:14px
classDef algorithms fill:#d4d4f9, font-weight:bold, font-size:14px
classDef experiments fill:#f9f9d4, font-weight:bold, font-size:14px
A[Optimal Complexity in

Decentralized Training] --> B[Decentralized

ML] A --> C[Optimization

Challenges] A --> D[Algorithms

and

Methods] A --> E[Experiments

and

Performance] B --> B1[Training models across

distributed

systems. 1] B --> B2[Categorizing decentralized

ML

systems. 2] B --> B3[Privacy-preserving training

on edge

devices. 7] B --> B4[Decentralized communication

between

workers. 8] B --> B5[Various network structures

for

workers. 9] B --> B6[Weighted averaging

in gossip

protocols. 15] C --> C1[Optimal convergence rates

for

algorithms. 3] C --> C2[Challenges in optimizing

complex

models. 11] C --> C3[Random sampling for

efficient

training. 12] C --> C4[Different data distributions

across

workers. 13] C --> C5[Complexity related to

gradient

computations. 18] C --> C6[Complexity in information

exchange. 19] D --> D1[Best possible convergence

rates. 4] D --> D2[Synchronized updates

across

workers. 6] D --> D3[Update model coordinates

via

gradients. 14] D --> D4[Separating computation

and communication

phases. 20] D --> D5[Optimal algorithm using

graph

factorization. 21] D --> D6[Uses accelerated gossip

and gradient

tracking. 22] E --> E1[Improves convergence

rate. 23] E --> E2[Estimates global

gradients. 24] E --> E3[Iterations for algorithm

convergence. 26] E --> E4[Performance evaluation

on image

classification. 27] E --> E5[Stability and convergence

tests. 28] E --> E6[Efficiency in decentralized

training. 30] class A,B,B1,B2,B3,B4,B5,B6 decentralized class C,C1,C2,C3,C4,C5,C6 optimization class D,D1,D2,D3,D4,D5,D6 algorithms class E,E1,E2,E3,E4,E5,E6 experiments

Decentralized Training] --> B[Decentralized

ML] A --> C[Optimization

Challenges] A --> D[Algorithms

and

Methods] A --> E[Experiments

and

Performance] B --> B1[Training models across

distributed

systems. 1] B --> B2[Categorizing decentralized

ML

systems. 2] B --> B3[Privacy-preserving training

on edge

devices. 7] B --> B4[Decentralized communication

between

workers. 8] B --> B5[Various network structures

for

workers. 9] B --> B6[Weighted averaging

in gossip

protocols. 15] C --> C1[Optimal convergence rates

for

algorithms. 3] C --> C2[Challenges in optimizing

complex

models. 11] C --> C3[Random sampling for

efficient

training. 12] C --> C4[Different data distributions

across

workers. 13] C --> C5[Complexity related to

gradient

computations. 18] C --> C6[Complexity in information

exchange. 19] D --> D1[Best possible convergence

rates. 4] D --> D2[Synchronized updates

across

workers. 6] D --> D3[Update model coordinates

via

gradients. 14] D --> D4[Separating computation

and communication

phases. 20] D --> D5[Optimal algorithm using

graph

factorization. 21] D --> D6[Uses accelerated gossip

and gradient

tracking. 22] E --> E1[Improves convergence

rate. 23] E --> E2[Estimates global

gradients. 24] E --> E3[Iterations for algorithm

convergence. 26] E --> E4[Performance evaluation

on image

classification. 27] E --> E5[Stability and convergence

tests. 28] E --> E6[Efficiency in decentralized

training. 30] class A,B,B1,B2,B3,B4,B5,B6 decentralized class C,C1,C2,C3,C4,C5,C6 optimization class D,D1,D2,D3,D4,D5,D6 algorithms class E,E1,E2,E3,E4,E5,E6 experiments

**Resume: **

**1.-** Decentralized machine learning: Training models across distributed systems without centralized control.

**2.-** Layered taxonomy: Categorizing decentralized ML systems into application, protocol, and topology layers.

**3.-** Theoretical limits: Exploring the optimal convergence rates for decentralized algorithms.

**4.-** Optimal decentralized algorithms: Introducing methods that achieve the best possible convergence rates.

**5.-** Data parallelism: Distributing data across multiple workers for parallel processing.

**6.-** Centralized training: Using methods like all-reduce for synchronized updates across all workers.

**7.-** Federated learning: Keeping data on edge devices to preserve privacy while training models.

**8.-** Gossip protocol: A decentralized communication method for information exchange between workers.

**9.-** Arbitrary graph topology: Connecting workers in various network structures beyond fully connected graphs.

**10.-** Empirical risk minimization: Formulating the optimization problem for training machine learning models.

**11.-** Non-convex optimization: Addressing challenges in optimizing complex models like deep neural networks.

**12.-** Stochastic algorithms: Using random sampling methods like SGD for efficient training.

**13.-** Data heterogeneity: Dealing with differences in data distribution across workers.

**14.-** Zero-respecting algorithms: Methods that only update model coordinates through gradients or communication.

**15.-** Gossip matrix: A fixed matrix used for weighted averaging in gossip protocols.

**16.-** Spectral gap: The difference between the largest and second-largest eigenvalues of the gossip matrix.

**17.-** Lower bounds: Theoretical minimum complexity for decentralized training algorithms.

**18.-** Sampling complexity: The component of algorithmic complexity related to gradient computations.

**19.-** Communication complexity: The component of algorithmic complexity related to information exchange between workers.

**20.-** Biphase communication: A paradigm separating computation and communication phases for improved consistency.

**21.-** DeFacto algorithm: An optimal decentralized algorithm using graph factorization techniques.

**22.-** DeTAG algorithm: An optimal decentralized algorithm using accelerated gossip and gradient tracking.

**23.-** Accelerated gossip: A technique to improve the convergence rate of gossip protocols.

**24.-** Gradient tracking: A method to estimate global gradients in decentralized settings.

**25.-** Mixing time: The time required for a Markov chain to approach its stationary distribution.

**26.-** Iteration complexity: The number of iterations required for an algorithm to converge.

**27.-** CIFAR-10 experiment: Evaluating algorithm performance on image classification with different data shuffling strategies.

**28.-** ResNet on CIFAR-100: Testing algorithm stability and convergence under various spectral gap conditions.

**29.-** Optimal face length: The ideal duration of communication phases in biphase communication.

**30.-** Throughput preservation: Maintaining computational efficiency while improving consistency in decentralized training.

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