Analytical Model

Analytical Model#

tritonBLAS uses an analytical model called Origami to predict optimal kernel configurations without autotuning.

Overview#

Traditional Triton kernels rely on @triton.autotune which performs a greedy search through configuration spaces. This approach:

  • Requires expensive runtime evaluation of many configurations

  • Produces numerous JIT-compiled kernel variants

  • Lacks predictability and explainability

tritonBLAS eliminates autotuning by using Origami, an analytical model that predicts the optimal configuration based on:

  • Matrix dimensions (M, N, K)

  • Data types

  • Hardware characteristics

  • Memory hierarchy

Origami#

Origami is AMD’s analytical performance model for GEMM kernels. Instead of searching through configuration spaces via autotuning, Origami analytically determines the optimal kernel configuration.

Learn More#

For detailed information about Origami:

How Origami Works in tritonBLAS#

Configuration Selection#

Given matrix dimensions and data types, Origami:

  1. Analyzes the problem characteristics (M, N, K, data types)

  2. Evaluates configuration options analytically based on hardware model

  3. Selects the configuration with predicted best performance

  4. Returns a MatmulHeuristicResult object with optimal parameters

Example Usage#

import torch
import tritonblas

# The analytical model works behind the scenes
m, n, k = 4096, 4096, 4096
selector = tritonblas.MatmulHeuristicResult(
    m, n, k,
    a_dtype=torch.float16,
    b_dtype=torch.float16,
    c_dtype=torch.float16
)

# The selector contains the optimal configuration
# predicted by the analytical model
A = torch.randn(m, k, dtype=torch.float16, device='cuda')
B = torch.randn(k, n, dtype=torch.float16, device='cuda')
C = tritonblas.matmul_lt(A, B, selector=selector)

Model Accuracy#

The analytical model has been validated against:

  • Autotuned configurations

  • Vendor BLAS libraries (hipBLAS, rocBLAS)

  • Empirical performance measurements

Results show that the model consistently selects near-optimal configurations while eliminating autotuning overhead.

Learn More#

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