metalcore 0.1.13

Foundational Metal Linear Algebra Primitives for PyTorch

metalcore

Foundational Metal Linear Algebra Primitives for PyTorch on Apple Silicon.

Overview

metalcore provides a unified backend for high-performance linear algebra operations on macOS devices, bypassing generic MPS fallbacks to use optimized custom Metal kernels.

Supported Operations

1. Decompositions

• SVD (svd): One-sided Jacobi algorithm. Highly optimized for both batched small matrices and large "tall" matrices (e.g., LLM weights).
• QR (qr, qr_batched): Blocked Householder reflection. Significantly faster for batched operations.
• Eigh (eigh): Symmetric eigenvalue decomposition using Jacobi rotations.
• Cholesky (cholesky): MAGMA-style shared memory optimization for Positive Definite matrices.

2. Solvers

• Linear Solve (solve): Batched linear system solver using LU factorization. Supports fp16/bf16 (auto-promoted to fp32 for stability).
• Triangular Solve (trsm): Solve $AX=B$ where $A$ is triangular.

3. Training Ops ⚡ NEW

• RMSNorm (MetalRMSNorm): Fused RMS normalization with 2.5x speedup over PyTorch.
• AdamW (MetalAdamW): Fused optimizer step with 2.9x speedup.
• Activations (metal_gelu, metal_silu): Vectorized float4 GELU/SiLU with fast backward pass.
• SDPA (metal_scaled_dot_product_attention): Flash Attention v2 with tiling and causal masking (experimental).

4. Primitives

• Householder Reflections: Core orthogonalization primitives (geqr2, larft, larfb).

Installation

pip install metalcore

Usage

import torch
import metalcore

device = 'mps'

# SVD
A = torch.randn(100, 50, device=device)
U, S, V = metalcore.svd(A)

# Batched QR
B = torch.randn(100, 16, 16, device=device)
Q, R = metalcore.qr(B)

# Cholesky
C = torch.randn(10, 32, 32, device=device)
C = C @ C.mT + 1e-4 * torch.eye(32, device=device)  # Make PD
L = metalcore.cholesky(C)

# Linear Solve (batched, supports fp16/bf16)
A = torch.randn(100, 32, 32, device=device)
b = torch.randn(100, 32, device=device)
x = metalcore.solve(A, b)  # x such that A @ x = b

# Training Ops
from metalcore import MetalRMSNorm, MetalAdamW, metal_gelu

# RMSNorm (2.5x faster)
norm = MetalRMSNorm(512).to(device)
x = torch.randn(32, 128, 512, device=device)
y = norm(x)

# AdamW (2.9x faster)
model = torch.nn.Linear(512, 256).to(device)
optimizer = MetalAdamW(model.parameters(), lr=1e-3)

# GELU activation
y = metal_gelu(x)

Performance Highlights

Operation	Speedup vs PyTorch/CPU
Cholesky Batched	10x faster
Solve Batched	5-10x faster
QR Batched	20x faster
RMSNorm	2.5x faster
AdamW	2.9x faster
SiLU/GELU	2-4x faster

Requirements

• macOS 12.0+ with Apple Silicon (M1/M2/M3/M4)
• Python 3.9+
• PyTorch 2.0+

Author

Kris Bailey

License

MIT