2D Mesh QA

What is 2D mesh network parallel algorithm

A 2D mesh network is a type of network topology where processors are arranged in a grid-like fashion, enabling efficient parallel computing. Multiple algorithms have been developed for various computational tasks on 2D mesh networks. Here are some key points and examples of parallel algorithms designed for 2D mesh networks:

Key Characteristics of 2D Mesh Networks:

• Topology: A 2D mesh network consists of processors arranged in a grid, where each processor can communicate with its four immediate neighbors (top, bottom, left, right) [6].
• Scalability: The area required for a 2D mesh on a VLSI chip increases linearly with the number of processors [1].

Examples of Parallel Algorithms on 2D Mesh Networks:

-Prefix Computation Algorithm**: - An improved parallel algorithm for prefix computation on a 2D mesh network runs in (2n + 5) times, making it comparable with other efficient algorithms [1][8].

2. Matrix Multiplication:
   • A parallel algorithm for multiplying two (n n) arrays using (n^2) processors in a specific amount of time [2].
   • Another algorithm by Bae, Shinn, and Takaoka for matrix multiplication on a 2D mesh array focuses on efficient communication between the processors [6].
3. Summation Algorithm:
   • An improved parallel summation algorithm on a 2D mesh network with (N = n^2) processing elements performs summation of (N) summands in (n + 2) times [5].
4. All-to-All Broadcast Algorithm:
   • This algorithm uses the ring algorithm, treating rows and columns of the mesh as rings. Each row first performs an all-to-all broadcast, followed by a similar operation on the columns [3].
5. Sorting Algorithm:
   • Sorting (N = n^2) numbers on an (N)-node 2D mesh can be done in time (kn) (where (k) is a constant between 2 and 3), which is optimal up to a multiplicative constant [15].

Advantages of 2D Mesh Networks:

• Efficient Communication: Due to the structured layout, communication between processors is efficient.
• Scalability: The network can easily be scaled up by increasing the number of processors, maintaining efficient communication patterns.

Applications:

• Scientific Computation: Used in areas where large-scale computations are necessary, such as simulations and numerical analysis.
• Image Processing: Beneficial for tasks that involve processing large images or video frames.
• Machine Learning: Certain data parallel ML models can benefit from the structured communication pattern of 2D mesh networks [9].

In essence, 2D mesh networks provide a highly structured and efficient means of performing parallel computations, making them suitable for a wide range of applications in scientific and engineering domains.

References:

1. Improved parallel algorithm for prefix computation on 2D mesh network [1].
2. Algorithm for multiplying two (n n) arrays using (n^2) processors [2].
3. All-to-all broadcast algorithm using the ring algorithm [3].
4. Improved parallel summation algorithm on 2D mesh network [5].
5. Structure of a cell in a 2D mesh array [6].
6. Improved parallel prefix computation algorithm on (n n) mesh network [8].
7. Data parallel ML models on 2D mesh networks [9].
8. Optimal sorting algorithm on (N)-node 2D mesh [15].

Citations: 1. https://www.sciencedirect.com/science/article/pii/S2212017313006002 2. https://www.tutorialspoint.com/parallel_algorithm/matrix_multiplication.htm 3. http://www.cs.csi.cuny.edu/~yumei/csc744/Examples/parallelchapter5.pdf 4. http://www.cs.ucf.edu/courses/cop3530/sum2005/parallel4.pdf 5. https://www.researchgate.net/publication/332607833_FAST_ALL_SUM_ALGORITHM_OVER_2D-MESH_NETWORK 6. https://www.sciencedirect.com/science/article/pii/S1877050914003858 7. https://link.springer.com/chapter/10.1007/978-981-10-8633-5_57 8. https://www.researchgate.net/publication/259672034_An_Improved_Parallel_Prefix_Computation_on_2D-Mesh_Network 9. http://mlforsystems.org/assets/papers/neurips2020/highly_kumar_2020.pdf 10. https://www.researchgate.net/figure/2-D-algorithm-for-allreduce-on-2-D-meshes-Here-there-are-two-concurrent-reductions_fig4_345654115 11. https://stackoverflow.com/questions/59940318/find-min-with-a-message-passing-parallel-algorithm-in-a-2d-mesh-of-cpus 12. https://en.wikipedia.org/wiki/Parallel_mesh_generation 13. https://link.springer.com/chapter/10.1007/0-306-46964-2_11 14. https://www.sciencedirect.com/science/article/abs/pii/S1383762103001401 15. https://pages.cs.wisc.edu/~tvrdik/15/html/Section15.html

Code generation on 2D Chips

Both Cerebras and Tenstorrent have made significant advancements in 2D mesh chip architectures, which are particularly relevant for AI and machine learning applications. Here is an overview of their technologies and how they handle code generation:

Cerebras

Cerebras Systems is renowned for its Wafer-Scale Engine (WSE) chips, which utilize a 2D mesh topology to interconnect a massive number of cores on a single chip. Here's a breakdown of relevant features and their impact on code generation:

• Wafer-Scale Engine (WSE): The WSE-2, which is the second-generation chip from Cerebras, is designed for AI applications and features a 2D mesh topology that connects its cores on a single wafer [9][10][12].
• On-Chip SRAM: The design philosophy emphasizes mapping the entire model onto a large on-chip SRAM, thereby minimizing the need for expensive DRAM and IO transfers [6].
• Code Generation: Cerebras provides a software stack that supports seamless code generation for their hardware, enabling developers to easily port their AI models to the WSE platform. This includes tools for optimizing neural network execution and leveraging the chip's unique architecture [9].

Tenstorrent

Tenstorrent focuses on scalable AI chip designs, with a strong emphasis on flexibility and performance. Here are some of the key aspects:

• Resizable Chip Architecture: Tenstorrent's approach involves a resizable chip architecture that can be customized for various sizes, making it suitable for both small and large-scale deployments [3].
• Wormhole Chip: One of their notable products, the Wormhole chip, is designed to scale across multiple chips, servers, and racks without software overhead, which is a significant advantage over competitors like Nvidia [14].
• Code Generation: Tenstorrent supports code generation through a software stack tailored for their hardware. This stack is optimized for AI workloads and includes tools for model deployment and performance optimization [14].

Code Generation Tools and Practices

For both Cerebras and Tenstorrent, efficient code generation is crucial to leverage the full potential of their 2D mesh architectures. Here are some common practices and tools:

• High-Level APIs: Both companies provide high-level APIs that abstract the complex hardware details, allowing developers to focus on model development rather than low-level optimizations.
• Compiler Support: Advanced compilers specifically designed for their architectures help in translating high-level code into optimized machine code that can run efficiently on the 2D mesh network.
• Optimization Libraries: Libraries that include pre-optimized routines for common machine learning operations (e.g., matrix multiplications, convolutions) are provided to ensure that the most computationally intensive parts of the code are highly efficient.

Conclusion

Cerebras and Tenstorrent's innovations in 2D mesh chip architectures offer significant advantages for AI and machine learning applications. Their focus on providing robust software stacks and tools for efficient code generation makes it easier for developers to harness the power of these advanced chips.

References:

• Cerebras Wafer-Scale Engine and its design philosophy [6][9][10][12].
• Tenstorrent's resizable chip architecture and the Wormhole chip [3][14].

Citations: 1. https://www.techrxiv.org/articles/preprint/HASP_Hierarchical_Asynchronous_Parallelism_for_Multi-NN_Tasks/22338757/1/files/39744157.pdf 2. https://www.anandtech.com/show/16354/jim-keller-becomes-cto-at-tenstorrent-the-most-promising-architecture-out-there 3. https://medium.com/@adi.fu7/ai-accelerators-part-iv-the-very-rich-landscape-17481be80917 4. https://www.semianalysis.com/p/cerebras-wafer-scale-hardware-crushes 5. https://www.zdnet.com/article/startup-tenstorrent-and-competitors-show-how-computing-is-changing-ai-and-vice-versa/ 6. https://khairy2011.medium.com/tpu-vs-gpu-vs-cerebras-vs-graphcore-a-fair-comparison-between-ml-hardware-3f5a19d89e38 7. https://www.researchgate.net/figure/Conventional-2D-mesh-of-cores-a-reorganized-into-a-functionally-sliced-arrangement-of_fig1_342914141 8. https://www.tomshardware.com/news/tenstorrent-shares-roadmap-of-ultra-high-performance-risc-v-cpus-and-ai-accelerators 9. https://spectrum.ieee.org/cerebras-wafer-scale-engine 10. https://www.cerebras.net/blog/cerebras-architecture-deep-dive-first-look-inside-the-hw/sw-co-design-for-deep-learning 11. https://www.researchgate.net/publication/340850381_Accelerating_Deep_Learning_Inference_with_Hardware_and_Software_Parallelism 12. https://www.cerebras.net/blog/cerebras-wafer-scale-engine-why-we-need-big-chips-for-deep-learning/ 13. https://www.cbinsights.com/company/tenstorrent/alternatives-competitors 14. https://www.semianalysis.com/p/tenstorrent-wormhole-analysis-a-scale ## Learn more about compilers and code generation project on 2D Mesh Network on Chip Architecture.

Running code on advanced chips like those from Cerebras and Tenstorrent requires specialized compilers and code generation tools to fully utilize the 2D mesh network architecture. Here’s an overview of how code runs on these chips, along with some projects and tools related to compilers and code generation for 2D Mesh Network on Chip (NoC) architecture:

How Code Runs on Cerebras and Tenstorrent Chips

Cerebras Wafer-Scale Engine (WSE)

1. Software Stack: Cerebras provides a comprehensive software stack that includes a compiler, runtime, and libraries optimized for AI workloads.
   • Model Mapping: The software stack maps neural network models directly onto the WSE cores, leveraging the 2D mesh topology for efficient communication.
   • On-Chip Execution: Models are executed on the chip with minimal off-chip memory access, thanks to the large on-chip SRAM, which reduces latency and increases throughput [9][10].
2. Compiler: Cerebras' compiler translates high-level machine learning models (e.g., TensorFlow, PyTorch) into a representation that can be efficiently executed on the WSE.
   • Optimization: The compiler performs various optimizations specific to the 2D mesh architecture, such as load balancing, data locality, and minimizing communication overhead.

Tenstorrent

1. Scalable Architecture: Tenstorrent chips are designed to scale across multiple devices, making efficient use of the 2D mesh topology for inter-chip communication.
   • Flexible Deployment: Their architecture allows for flexible deployment ranging from single chips to large server clusters, maintaining efficient data flow without software overhead [14].
2. Compiler and Runtime: Similar to Cerebras, Tenstorrent provides a specialized compiler and runtime environment that optimize AI models for execution on their chips.
   • Model Optimization: The compiler optimizes models for the unique characteristics of the Tenstorrent hardware, focusing on maximizing throughput and minimizing latency [14].

Projects and Tools for Compilers and Code Generation in 2D Mesh NoC Architecture

1. Verilog Implementations:
   • Network-on-Chip in Verilog: Projects like the one by xuanz20 include Verilog implementations of 2D mesh NoC, which can be used as a foundation for developing compilers that target such architectures [1].
   • Pipelined Routers: Implementations of 5-stage pipelined routers in Verilog are crucial for understanding the low-level communication mechanisms within a 2D mesh NoC [1].
2. Routing Algorithms:
   • DyAD, O1TURN, and Contention-Aware Input Selection: Research papers analyzing routing algorithms for 2D meshes provide insight into the communication patterns and potential optimizations for compilers [5].
   • Circuit Switching and XY Routing: Understanding these routing strategies is essential for developing efficient compilers that can map high-level code to low-level hardware instructions [2].
3. Compiler Projects:
   • LLVM: The LLVM compiler infrastructure can be extended to support 2D mesh NoC architectures by adding custom passes that optimize for mesh-specific characteristics.
   • Custom Compilers: Developing custom compilers that directly target 2D mesh NoC architectures, incorporating specific optimizations for load balancing, data locality, and communication reduction.
4. Tools and Libraries:
   • Parallel Programming Libraries: Libraries that abstract the complexity of parallel programming on 2D mesh networks, providing high-level APIs for developers.
   • Simulation Tools: Tools that simulate the behavior of 2D mesh networks, allowing for testing and debugging of compilers and generated code before deployment on actual hardware.

Conclusion

Running code on advanced 2D mesh NoC architectures like those from Cerebras and Tenstorrent involves specialized software stacks, compilers, and runtime environments. These tools are designed to optimize AI models for the unique characteristics of the hardware, ensuring efficient execution. Projects and tools related to Verilog implementations, routing algorithms, and compiler frameworks like LLVM are essential for developing and understanding code generation for these architectures.

References:

• Network-on-Chip in Verilog and pipelined routers [1].
• Routing algorithms and circuit switching strategies [2][5].
• Cerebras' WSE and its software stack [9][10][14].
• Tenstorrent's scalable architecture and compiler optimizations [14].

Citations: 1. https://github.com/xuanz20/Network-on-Chip-Verilog 2. https://www.journalmc.com/en/article/id/8389409f-cd40-4064-9430-cd5dcff9c0cc 3. https://www.researchgate.net/figure/2D-mesh-network-on-chip-The-figure-shows-2D-mesh-Network-on-chip-topology-where-a-set_fig1_335981756 4. https://ieeexplore.ieee.org/document/5682890 5. http://cva.stanford.edu/classes/ee382c/research/2DRouting.pdf 6. https://www.design-reuse.com/articles/23347/on-chip-network.html