Spio

(SPEE-oh) — An experimental CUDA kernel framework unifying typed dimensions, NVRTC JIT specialization, and ML‑guided tuning.

Overview

Spio is an experimental CUDA research playground that packages several forward-looking ideas for building next-generation GPU kernels: strongly typed tensor dimensions, machine-learned performance models, and direct-driver execution.

Spio compiles kernels just-in-time with NVRTC and launches them directly from Python via the CUDA Driver API. No intermediate C++ glue code, no CUDA Toolkit (nvcc), no host compiler (gcc) required.

The Typed Dimension System

Standard tensor libraries use positional indexing like tensor(i, j, k) where argument order determines meaning. The programmer must track which dimensions each tensor has, which variables correspond to which dimensions, and apply this knowledge correctly at every access.

This reflects an incomplete abstraction: the system knows tensor shapes but not the identity of dimensions or their relationships across tensors. That missing information must be reasserted by the programmer continuously.

Spio introduces a strongly typed indexing system that describes dimensions consistently across their use in multiple tensors. Dimension types carry compile-time semantics, enabling dimension operators to do the right thing automatically, relieving the programmer from tedious bookkeeping.

Spio implements typed dimensions in a header-only, CUDA-aware C++ library using template metaprogramming. The abstractions resolve at compile time; in most cases, the generated code matches hand-written kernels.

In the following examples, the comment blocks marked with the @spio tag instruct Spio's code generator to pre-include header files that define the requested dimension, tensor, and compound index classes.

1. Safety and Commutativity

Spio dimensions behave like integers. Because dimensions are types, it is not possible to accidentally mix different dimensions.

File: 01_commutativity.cpp

/*@spio
I = Dim()
J = Dim()
K = Dim()
@spio*/

UTEST(Lesson1, TypeSafety) {

    // Dimensions work like integers.
    EXPECT_TRUE(I(2) + I(4) == I(6));
    EXPECT_TRUE(I(8) < I(10));

    // Each dimension is a different CUDA / C++ type.
    static_assert(!std::is_same_v<I, J>, "I and J are different types");

    // Different dimensions cannot be compared. This prevents accidental mixing:
    //
    // EXPECT_EQ(I(5), J(5));
    // error: no match for ‘operator==’ (operand types are ‘I’ and ‘J’)
    //
    // Orthogonal dimensions can be added to produce a coordinates list:
    //
    EXPECT_TRUE(I(3) + J(4) + K(5) == spio::make_coordinates(I(3), J(4), K(5)));
}

Spio never asks for a dimension's position in the tensor's dimensions list. Instead, Spio uses the dimension variable's static type to determine operator behavior.

For example, many frameworks implement tensor subscripting such that the position of a subscript determines its behavior. In other words, x(i, j, k) != x(k, i, j). Spio enables position-free subscripting where x[i][j][k] == x[i + j + k] == x[k][i][j]. The compiler determines the effect of subscripts i, j, and k using their static types only.

Typed dimensions also enable something we call dimensional projection: a coordinate list comprising many dimensions can be used as a subscript, and only dimensions supported by the tensor will have an effect, while others are ignored.

// Define tensors A and B using dimensions I(16) × K(32) and K(32) × J(64).
//
/*@spio
A = Tensor((I(16), K(32)), dtype.float)
B = Tensor((K(32), J(64)), dtype.float)
@spio*/
UTEST(Lesson1, Commutativity) {

    // Create storage for the matrices.
    A::data_type a_data[A::storage_size()];
    B::data_type b_data[B::storage_size()];

    // Create matrices a and b.
    auto a = A(a_data);
    auto b = B(b_data);

    // Verify matrix sizes.
    EXPECT_TRUE(A::size<I>() == I(16));
    EXPECT_TRUE(A::size<K>() == K(32));
    EXPECT_TRUE(B::size<K>() == K(32));
    EXPECT_TRUE(B::size<J>() == J(64));

    // Define coordinates.
    auto i = I(2);
    auto j = J(3);
    auto k = K(4);

    // Position-free subscripting:
    // Subscript order does not affect the result.
    EXPECT_TRUE(a[i][k].get() == a[k][i].get());
    EXPECT_TRUE(b[k][j].get() == b[j][k].get());

    // Dimensional projection:
    // Coordinates project onto the tensor's supported dimensions.
    auto coords = make_coordinates(i, j, k);
    EXPECT_TRUE(a[coords].get() == a[k][i].get());
    EXPECT_TRUE(b[coords].get() == b[j][k].get());
}

2. Cursors

Spio uses Cursors: lightweight, multi-dimensional pointers that traverse tensor dimensions.

File: 02_cursor_movement.cpp

/*@spio
I = Dim()
J = Dim()
A = Tensor((I(10), J(10)), dtype.float)
@spio*/

UTEST(Lesson2, RelativeMovement) {
    // Create storage for matrix A.
    A::data_type a_data[A::storage_size()];

    // Create matrix A.
    auto a = A(a_data);

    // Create base cursor at (i=2, j=2).
    auto b = a[I(2)][J(2)];

    // Verify the offset from the base pointer.
    EXPECT_TRUE(b.get() - a_data == 2 * 10 + 2);

    // Move b.
    b.step(I(1));
    b.step(J(1));

    // Verify movement.
    EXPECT_TRUE(b.get() - a_data == 3 * 10 + 3);
}

UTEST(Lesson2, AccumulationLoop) {

    // Create matrix A.
    A::data_type a_data[A::storage_size()];
    auto a = A(a_data);

    // Create cursor at (i=2, j=4).
    auto b = a[I(2)][J(4)];

    for (int step = 0; step < 5; ++step) {
        // Verify the current position.
        EXPECT_TRUE(b.get() == a_data + (2 + step) * 10 + 4);

        // Step by 1 in the I dimension.
        b.step(I(1));
    }
}

3. Folded Dimensions

The generator Dims(K / 8, I, K % 8) creates a tensor with physical layout $(K/8) \times I \times (K \bmod 8)$. Here, K / 8 and K % 8 together address the full logical range $K(0) \ldots K(31)$: K/8 selects which chunk of 8 (the quotient), and K % 8 selects within that chunk (the remainder). This decomposition enables interleaved and vectorized memory layouts while letting you write loops over the logical dimension $K$.

File: 03_folding.cpp

// Define a Tensor with a folded dimension K and interleaved layout.
// Layout: (K / 8) x I x (K % 8)

/*@spio

# Define dimensions
I = Dim()
K = Dim()

# Define sizes.
i = I(4)
k = K(32)

# Define tensor with folded dimensions.
A = Tensor((k / 8, i, k % 8), dtype.float)

# Define a fold alias.
K8 = K / 8

@spio*/

UTEST(Lesson3, Folding) {

    // Create tensor a.
    A::data_type data[A::storage_size()];
    auto a = A(data);

    // Dimensions are compatible with their folds:
    EXPECT_TRUE(K8(3) == K(3 * 8));
    EXPECT_TRUE(K8(3) + K(4) == K(3 * 8 + 4));

    // Use constant I ..
    auto i = I(2);

    // .. and loop over K in range [0 .. 31] inclusive.
    for (auto k : range(K(32))) {

        // The loop variable has type K.
        static_assert(std::is_same_v<decltype(k), K>, "k should be of type K");

        // Spio accepts logical dimension K
        // and folds it into the tensor's K8 and K dimensions automatically ..
        auto b = a[i][k];

        // .. saving the user from folding it manually.
        auto k8 = K8(k.get() / 8);
        auto km8 = K(k.get() % 8);
        auto c = a[i][k8][km8];

        EXPECT_TRUE(b.get() == c.get());
    }
}

Spio accumulates subscripts in logical coordinates before folding, so repeated subscripts are equivalent to their sum. This enables correct carry-over when subscripts cross fold boundaries:

// Example: K(4) + K(4) = K(4 + 4), which carries into K8.
EXPECT_TRUE(*a[i][K(4)][K(4)] == *a[i][K(4 + 4)]);

// This also works when the sum crosses fold boundaries.
// K(7) + K(5) = K(12) = K8(1) + K(4)
EXPECT_TRUE(*a[i][K(7)][K(5)] == *a[i][K(7 + 5)]);
EXPECT_TRUE(*a[i][K(7)][K(5)] == *a[i][K8(1)][K(4)]);

4. Dimensional Projection

A Spio tensor acts as a filter. It accepts a world state (a superset of coordinates) and automatically projects onto the supported dimensions.

This allows you to create a single coordinates variable that includes all relevant dimensions. Each tensor projects the coordinates onto its supported dimensions, and arithmetic and comparison operators follow the same projection rules.

With dimensional projection, individual dimensions disappear from the program. Tensor definitions carry all the information about how dimensions are used, and dimensional projection automatically harvests the relevant dimensions from world coordinates.

File: 04_projection.cpp

// Define tensors A, B, C, and C_tile
/*@spio

# Define dimensions.
I = Dim()
J = Dim()
K = Dim()

# Define tensors for matrices A, B, and C.
A = Tensor((I(16), K(32)), dtype.float)
B = Tensor((K(32), J(64)), dtype.float)
C = Tensor((I(16), J(64)), dtype.float)

# Define a tensor for tiles of matrix C with custom stride.
C_tile = Tensor((I(8), J(32)), dtype.float, strides=I(64))
@spio*/
UTEST(Lesson4, DimensionalProjection) {
    // Create data for matrices a, b, and c.
    A::data_type a_data[A::storage_size()];
    B::data_type b_data[B::storage_size()];
    C::data_type c_data[C::storage_size()];

    // Initialize with counting numbers.
    std::iota(std::begin(a_data), std::end(a_data), 1.0f);
    std::iota(std::begin(b_data), std::end(b_data), 1.0f);
    std::iota(std::begin(c_data), std::end(c_data), 1.0f);

    // Construct matrices a, b, and c.
    auto a = A(a_data);
    auto b = B(b_data);
    auto c = C(c_data);

    // Select coordinates (I, J) for the tiles.
    //
    auto origin = spio::make_coordinates(I(12), J(60));

    // Operations on coordinates use a technique we call dimensional projection:
    // - arithmetic applies to pairs of matching dimensions and passes through others
    // - comparison tests all pairs of matching dimensions
    // - subscript applies matching dimensions and ignores others

    // For matrix a ~ I × K, subscript I matches, and J is ignored.
    auto a_tile = a[origin];

    // For matrix b ~ K × J, subscript J matches, and I is ignored.
    auto b_tile = b[origin];

    // For matrix c ~ I × J, both I and J match.
    auto c_tile = C_tile(c[origin].get());

    // Iterate over the range I(8) × J(32).
    for (auto idx : spio::range(c_tile)) {

        // Iterate over the range K(32).
        for (auto k : spio::range(a.size<K>())) {

            // local and world have dimensions (I, J, K)
            auto local = idx + k;
            auto world = origin + local;

            // Check that world coordinates I and K are less than a's extents.
            // Ignore world coordinate J in the comparison and subscript operations.
            if (world < a.extents()) { EXPECT_TRUE(*a_tile[local] == *a[world]); }

            // Check that world coordinates J and K are less than b's extents.
            // Ignore world coordinate I in the comparison and subscript operations.
            if (world < b.extents()) { EXPECT_TRUE(*b_tile[local] == *b[world]); }
        }

        // Check that world coordinates I and J are less than c's extents.
        if (origin + idx < c.extents()) { EXPECT_TRUE(*c_tile[idx] == *c[origin + idx]); }
    }
}

5. Compound Index

Spio uses a compound index to fold a linear offset into multiple dimensions. A common use case is folding CUDA blockIdx and threadIdx into logical tensor coordinates.

File: 05_compound_index.cpp

/*@spio

# Define the dimensions.
I = Dim()
J = Dim()

# Define the sizes.
i = I(512)
j = J(512)

# Define compound indices for blocks and threads.
BlockIndex = CompoundIndex(i / 16, j / 16)
ThreadIndex = CompoundIndex(i % 16, j % 16)

# Define tensor A using dimensions i x j
A = Tensor((i, j), dtype.float)

# Define aliases for I / 16 and J / 16.
I16 = I / 16
J16 = J / 16

@spio*/
UTEST(Lesson5, CompoundIndex) {

    // Initialize matrix a.
    A::data_type a_data[A::storage_size()];
    std::iota(std::begin(a_data), std::end(a_data), 1.0f);
    auto a = A(a_data);

    // Check the size of the compound indices.
    EXPECT_TRUE(BlockIndex::size() == 32 * 32);
    EXPECT_TRUE(ThreadIndex::size() == 16 * 16);

    // Simulate thread-blocks and threads.
    for (int blockIdx = 0; blockIdx < BlockIndex::size(); ++blockIdx) {
        for (int threadIdx = 0; threadIdx < ThreadIndex::size(); ++threadIdx) {

            // Create a compound index for this block ..
            auto block = BlockIndex(blockIdx);

            // .. and thread.
            auto thread = ThreadIndex(threadIdx);

            // Subscripting with the compound indices ..
            auto b = a[block][thread];

            // .. saves the user from computing the coordinates and offset manually.
            auto block_i16 = blockIdx / 32;
            auto block_j16 = blockIdx % 32;

            auto thread_i = threadIdx / 16;
            auto thread_j = threadIdx % 16;

            auto offset = (block_i16 * 16 + thread_i) * 512 + block_j16 * 16 + thread_j;

            // Check that these two methods are equivalent.
            EXPECT_TRUE(*b == a_data[offset]);
        }
    }
}

6. Matrix Multiply Kernel

For a full example of a high-performance matrix multiply kernel using typed dimensions and just-in-time compilation, see:

CUDA Source: mma_checkerboard_16c.cu
Python Generators: test_mma_checkerboard.py

This example demonstrates how dimensional projection manages the complexity of mapping global memory, swizzled shared memory tiles, and tensor core fragments, reaching 94% arithmetic utilization on an RTX 4090 GPU.

Limitations

Tensor dimensions are compile-time constants. This suits workloads with fixed shapes (e.g., vision systems deploying at known resolutions). Runtime-sized dimensions are not yet supported.

Additional Features

Just-in-Time Kernel Generation

Spio compiles kernels at runtime with NVIDIA’s NVRTC (libnvrtc) and uses a trained performance model to select the fastest kernel configuration for your GPU and workload. No CUDA toolkit install is needed because Spio relies on the CUDA headers and NVRTC shared libraries that NVIDIA distributes as Python packages (the same infrastructure PyTorch depends on). Spio launches kernels directly through the CUDA driver API, so no C/C++ launcher wrappers are required.

Performance Models

For each kernel and GPU architecture, Spio trains an XGBoost model to predict execution latency from layer parameters and kernel configuration. At runtime, these predictions guide configuration selection, eliminating expensive auto-tuning.

PyTorch Integration

Seamless integration with PyTorch through custom operators and torch.compile support.

Performance Results

Memory-Efficient Grouped Convolution

The cuDNN Conv2d kernels use "implicit GEMM" with 1D horizontal tiling, causing excessive memory traffic due to overlapping reads in the convolution halo. Spio uses 2D tiling with a circular-buffer overlap-add algorithm that:

Reduces tile overlap and global memory traffic
Maximizes register usage through loop unrolling
Increases occupancy by minimizing local memory footprint
Leverages Tensor Cores with 8×8 matrix operations for a group width of 8

Benchmark Results

On NVIDIA GeForce RTX 3090, Spio approaches theoretical DRAM bandwidth limits for forward pass (FProp), input gradients (DGrad), and weight gradients (WGrad), while PyTorch/cuDNN implementations suffer from excess data transfers.

On NVIDIA GeForce RTX 4090, Spio exceeds the effective DRAM bandwidth limit for small batch sizes. 2D tiling always reduces L2 traffic, and the advantage grows when inputs from the previous layer already reside in the 72 MB cache.

Benchmarks use realistic workloads with layers embedded in ConvFirst or MBConv blocks to accurately reflect real-world performance.

Quick Start

Prerequisites

Linux x86_64
NVIDIA GPU: Ampere (sm_80/sm_86) or Ada (sm_89)
NVIDIA driver (compatible with CUDA 12 runtime)
Python 3.9+

Installation

Install Spio from PyPI using pip:

pip install spio

Notes:

PyTorch (torch>=2.4.0) is an explicit dependency and will be installed automatically when you install Spio; no separate installation step is required.
CUDA toolkit installation is not required. Spio relies on NVIDIA's CUDA runtime and NVRTC libraries and installs them automatically via pip wheels. PyTorch also depends on the same NVIDIA packages.

Development

To install Spio from source, first ensure your system has a C compiler. On Ubuntu:

sudo apt update
sudo apt install -y build-essential

Then clone the Spio repository and install the package in editable mode:

git clone https://github.com/andravin/spio.git
cd spio
pip install -e .

Now run the unit tests:

SPIO_WORKERS=$(nproc) pytest tests

The tutorial requires the CUDA toolkit. If your system has nvcc, you can run the examples like this:

SPIO_ENABLE_CPP_TESTS=1 pytest -s tests/test_tutorial.py

Spio will likely find your CUDA toolkit installation automatically. To specify it manually, set the CUDA_HOME environment variable, or set CUDACXX to the full path of nvcc.

Additional Requirements for torch.compile

Update: New versions of PyTorch will include fix (es) for the issue (s) described below. Starting with PyTorch 2.10 (expected 21 January 2026), PyTorch runtime Docker images will include a C compiler, and Triton Language will link against libcuda.so.1, so torch.compile will work out of the box.

The Spio runtime does not need a host C/C++ compiler or the CUDA developer toolkit. You can use Spio operations with PyTorch on a production system that does not have these.

However, torch.compile (Inductor/Triton) does. Without a C compiler installed, torch.compile will produce the error

torch._inductor.exc.InductorError: RuntimeError: Failed to find C compiler. Please specify via CC environment variable or set triton.knobs.build.impl.

If you intend to use torch.compile, ensure your production environment provides:

GCC or Clang (or a compatible toolchain)
CUDA driver development files (e.g., libcuda.so symlink or stubs)

These commands will add the requirements for torch.compile on an Ubuntu system:

# Install development tools required by PyTorch Inductor + Triton
sudo apt update
sudo apt install -y build-essential

# Ensure the CUDA driver library has the expected unversioned symlink
# (Many cloud images only ship libcuda.so.1)
sudo ln -sf /usr/lib/x86_64-linux-gnu/libcuda.so.1 /usr/lib/x86_64-linux-gnu/libcuda.so

Then test:

python3 -c "import torch; torch.cuda.is_available()"
python3 -c "import torch; torch.compile(lambda x: x**2)(torch.randn(5, device='cuda'))"

Usage

Here is an example of how to use Spio operations with PyTorch:

import torch
import spio.functional

# Define input and weights for grouped convolution
x = torch.randn(32, 64, 56, 56, device='cuda', dtype=torch.float16)
weight = torch.randn(64, 8, 3, 3, device='cuda', dtype=torch.float16)

# Call the Spio custom convolution op with registered autograd support.
# Automatically selects optimal kernel configuration for your GPU. 
output = spio.functional.conv2d_gw8(x, weight, groups=8)

Name		Name	Last commit message	Last commit date
Latest commit History 145 Commits
docs		docs
figures		figures
scripts		scripts
spio		spio
tests		tests
.clang-format		.clang-format
.gitignore		.gitignore
.pre-commit-config.yaml		.pre-commit-config.yaml
CHANGELOG.md		CHANGELOG.md
CLAUDE.md		CLAUDE.md
LICENSE		LICENSE
MANIFEST.in		MANIFEST.in
README.md		README.md
justfile		justfile
pylintrc		pylintrc
pyproject.toml		pyproject.toml
pytest.ini		pytest.ini
setup.py		setup.py

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Spio

Overview

The Typed Dimension System

1. Safety and Commutativity

2. Cursors

3. Folded Dimensions

4. Dimensional Projection

5. Compound Index

6. Matrix Multiply Kernel

Limitations

Additional Features

Just-in-Time Kernel Generation

Performance Models

PyTorch Integration

Performance Results

Memory-Efficient Grouped Convolution

Benchmark Results

Quick Start

Prerequisites

Installation

Development

Additional Requirements for torch.compile

Usage

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Spio

Overview

The Typed Dimension System

1. Safety and Commutativity

2. Cursors

3. Folded Dimensions

4. Dimensional Projection

5. Compound Index

6. Matrix Multiply Kernel

Limitations

Additional Features

Just-in-Time Kernel Generation

Performance Models

PyTorch Integration

Performance Results

Memory-Efficient Grouped Convolution

Benchmark Results

Quick Start

Prerequisites

Installation

Development

Additional Requirements for torch.compile

Usage

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