Distributed Parameter Synchronization in DNN Hucheng Zhou (MSRA) Zheng Zhang (MSRA) Minjie Wang (SJTU)

Model Training Data several GBs of model size several layers millions of edges between two layers thousands of neurons per layer for the imagenet model, the neuron number varies from 56x56x96 to 6x6x256 in convolution layers and 4096 in fully-connected layers 2TB data in ImageNet for 22K classification Training Data TBs of data

DNN model training could take weeks or even more

What if we can train the DNN model in one day? It is still a dream If you wish to get the same error rate we train a 9-layered locally connected sparse autoencoder with pooling and local contrast normalization on a large dataset of images (the model has 1 billion connections, the dataset has 10 million 200x200 pixel images downloaded from the Internet). We train this network using model parallelism and asynchronous SGD on a cluster with 1,000 machines (16,000 cores) for three days. Fast training needs parallelism, even in a distributed fashion

Model Parallelism Model is partitioned and trained in parallel Model Training Data Machine

Model Parallelism Network traffic bounded Non-linear speedup Training Data Network traffic bounded Non-linear speedup Training is still slow with large data sets

Another dimension of parallelism, data parallelism, is required

Data Parallelism 1. Training data is partitioned, and multi-models are trained in parallel (1) Downpour: Asynchronous Distributed SGD (2) Sandblaster: Distributed L-BFGS 2. Intermediate trained results (model parameters) are synchronized

Outline Problem statement Design goals Design Evaluation

It is not a good idea to combine model training and model synchronization

Separate the model training and model synchronization Parameter Server Application Separate the model training and model synchronization Build a dedicated system PS (Parameter Server) to synchronize the intermediate model parameters DistBlief (NIPS 2012)

Outline Problem statement Design goals Design Evaluation

How to build a scalable, reliable and still efficient parameter server?

A Centralized Approach p’’ = p’ + ∆p’ p’ = p + ∆p Parameter Server ∆p’ ∆p p’ p Model workers Jinliang Wei, Wei Dai, Abhimanu Kumar, Xun Zheng, Qirong Ho and E. P. Xing, Consistent Bounded-Asynchronous Parameter Servers for Distributed ML, Manuscript, arXiv:1312.7869, communicated 30 Dec 2013). Asynchronous Stochastic Gradient Descent (A-SGD) Data

A Centralized Approach p’ = p + ∆p Parameter Server ∆p ∆p is vector or matrix with float type, rather than key-value pair p’ = p + ∆p is commutative and associate, which makes synchronization in bulk is possible Model workers Jinliang Wei, Wei Dai, Abhimanu Kumar, Xun Zheng, Qirong Ho and E. P. Xing, Consistent Bounded-Asynchronous Parameter Servers for Distributed ML, Manuscript, arXiv:1312.7869, communicated 30 Dec 2013). Data

However, it is non-scalable if large-scale model workers exist

…… Parameter Server Depends on: The size of model parameters (240MB) The model update rate (3times/s, thus 720MB/s) The number of model workers (overloaded if n is large) GPU scenario Model Workers Data Shards ∆pi ∆p1 ∆pn ……

…… Model parameter partition helps Parameter Server ∆pn Shards ∆p1 ∆pi Workers Data Shards ∆pi ∆p1 ∆pn …… Wei Dai, Jinliang Wei, Xun Zheng, Jin Kyu Kim, Seunghak Lee, Junming Yin, Qirong Ho and E. P. Xing,Petuum: A Framework for Iterative-Convergent Distributed ML, Manuscript, arXiv:1312.7651, communicated 30 Dec 2013).

… A local cache (model slaves) of model parameters helps Parameter Server Model Workers Data Shards ∆pi ∆p1 ∆pn … parameter master parameter slaves

However, parameter master may still be the bottleneck A decentralized (peer-2-peer) system design is motivated

And, what if faults happened?

…… Parameter Server 1. Networking delay or down Model Workers Data Shards ∆pi ∆p1 ∆pn …… 1. Networking delay or down 2. Machine crash and restart 3. Software crash, data lost, job preempted

Again, it is not reliable without fault-tolerance support A fault-tolerant system design is motivated

How about performance if staleness (consistency) is required?

Staleness is required p1 = p + ∆p1 Parameter Server ∆p1 p Model Workers Data Shards p ∆p1

p1 = p + ∆p1 Parameter Server ∆p2 Model Workers Data Shards p1 slower slowest fast Model Workers Data Shards

Staleness is required for fast model convergence Update by worker 1 Update by worker 2 Model synchronization With coordination initialization 𝑡 1 𝑡 2 𝑡 3 global optimal Without coordination (Worker 2 works on a over-staled model) initialization 𝑡 1 𝑡 2 𝑡 3 global optimal local optimal

The working pace of each worker should be coordinated Parameter Server Model Workers Data Coordinator L-BFGS

However, a centralized coordinator is costly, and the system performance (parallelism) is not fully exploited Balance between the system performance and model convergence rate is motivated

Outline Problem statement Design goals Design Evaluation

1. Each worker machine has a local parameter server (model replica), and the system is responsible for parameter synchronization

System Architecture … Parameter Server Reduced network traffic by only exchanging the accumulated updates (commutative and associative) Non-blocking of training Asynchronization Parameter Server

2. How to mutually exchange parameter updates between two connected local parameter servers, with fault-tolerance on network delay or even down?

… Parameter Server Pairwise fault-tolerant update exchange protocol

Pairwise Protocol Invariants … Pairwise fault-tolerant update exchange protocol p q r Node p’s “belief” of model (Θ𝑝) equals to its own contribution (𝑥𝑝) and contribution from its neighbors (φqp) Θ𝑝=𝑥𝑝+∑q∊Np φqp (1) 𝑥𝑝 φqp φrp

Pairwise Protocol Invariants … Pairwise fault-tolerant update exchange protocol p q r A node (p) also propagates updates to neighbor (q) from the contribution of itself and the accumulated updates from other neighbors (r) φpq = Θ𝑝 - φqp (2) Θ𝑝 - φqp

Pairwise Protocol Details

3. How about flow control?

Straightforward, just control the timing of synchronization via such as timer, the version gap, or even dynamic adjusted

4. How about the fault-tolerance?

NOT based on redundancy (multiple copies) Mu Li, Li Zhou, Zichao Yang, Aaron Li, Fei Xia, Dave Andersen and Alex Smola. Parameter Server for Distributed Machine Learning, Big Learning Workshop, NIPS 2013

Instead, get the history from its neighbors (Θ𝑝 - φqp ) Or, just keep the accumulated local updates in persistent store

Temporary outage Scheduled failure Permanent failure

Dynamic adding or removing of model replicas has the same logic as fault tolerance

5. How local parameter servers are connected (topology)?

The right topology is hard to determine for system, which depends on the application, such as model size, update rate, network bandwidth, the number of neighbors, etc. Therefore, topology configuration is motivated

Further more, as workers leaves and joins in, the right topology would be adjusted. For example, increasingly added model replicas would be helpful for DNN training Therefore, topology re-configuration is necessary

Master-slave … master Parameter Server Shortest propagation delay (one hop) But high workload in master master Parameter Server

Tree-based topology … Parameter Server Decentralized Longer propagation delay (multiple hops) Without bottleneck Parameter Server Decentralized

Scalability is sensitive to topology The parameter size is 12MB and each worker pushes updates of the same size once per second.

Topology affects staleness

6. And how to set the right staleness to balance the system performance and model convergence rate?

Application-defined staleness is supported, such as Best effort (no extra requirement) Maximal delayed time (block push if previous n pushes not complete) User-defined filters (only push significant update) SSP* (bound the max gap between the fastest and slowest worker) Bound the update version gap Bound the parameter value gap *. Q. Ho, J. Cipar, H. Cui, J.-K. Kim, S. Lee, P. B. Gibbons, G. Gibson, G. R. Ganger and E. P. Xing,More Effective Distributed ML via a Stale Synchronous Parallel Parameter Server, Advances in Neural Information Processing Systems 27 (NIPS 2013). 

Outline Problem statement Design goals Design Evaluation

Learning speed can be accelerated But there is still a long journey to get a better error rate

Recap Re-configurability is the king in system design The layered design is beautiful Pure p2p design Pairwise protocol Flow control Fault tolerance Node joining in or leaving Topology configurable Staleness configurable

Future work Parameter server design is not only for DNN, but also for general inference problems Generalized linear model with a single massive vector Topic model with sparse vectors Graphical model with plates The design is also works for areas other than machine learning The scenarios with structured data and the aggregation is both commutative and associative, such as Sensor network to get aggregated data

Related work Jeffrey Dean, Greg S. Corrado, Rajat Monga, Kai Chen, Matthieu Devin, Quoc V. Le, Mark Z. Mao, Marc’Aurelio Ranzato, Andrew Senior, Paul Tucker, Ke Yang, and Andrew Y. Ng. Large Scale Distributed Deep Networks, NIPS 2012 Q. Ho, J. Cipar, H. Cui, J.-K. Kim, S. Lee, P. B. Gibbons, G. Gibson, G. R. Ganger and E. P. Xing,More Effective Distributed ML via a Stale Synchronous Parallel Parameter Server, NIPS 2013.  Jinliang Wei, Wei Dai, Abhimanu Kumar, Xun Zheng, Qirong Ho and E. P. Xing, Consistent Bounded-Asynchronous Parameter Servers for Distributed ML, Manuscript, arXiv:1312.7869, communicated 30 Dec 2013). Wei Dai, Jinliang Wei, Xun Zheng, Jin Kyu Kim, Seunghak Lee, Junming Yin, Qirong Ho and E. P. Xing,Petuum: A Framework for Iterative-Convergent Distributed ML, Manuscript, arXiv:1312.7651, communicated 30 Dec 2013). Mu Li, Li Zhou, Zichao Yang, Aaron Li, Fei Xia, Dave Andersen and Alex Smola. Parameter Server for Distributed Machine Learning, Big Learning Workshop, NIPS 2013

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