Nabla - High-Performance Scientific Computing

Nabla is a high-performance scientific computing and machine learning framework combining imperative and functional APIs. Seamlessly drop custom Mojo kernels into the autodiff engine and automatically shard distributed workloads, built on Mojo & MAX.

Active Development: This is the main development branch with distributed SPMD execution and a refined lazy, MAX-native execution model. Read the docs: https://nablaml.com.

Installation

Nabla requires Modular nightly.

python -m venv .venv
source .venv/bin/activate
pip install --pre --extra-index-url https://whl.modular.com/nightly/simple/ modular nabla-ml

GPU Support:

• Linux (AMD/NVIDIA): Supported natively via Modular MAX.
• macOS (Apple Silicon): Requires Xcode Metal toolchain (xcode-select --install).

Development Setup

Installation of all dependencies (torch/jax for testing, mypy/black for linting, etc.)

git clone https://github.com/nabla-ml/nabla.git
cd nabla
python -m venv venv
source venv/bin/activate
pip install -r requirements-dev.txt
pip install -e ".[dev]"

Feature Showcase

1. Tensors & Autodiff

Define Python functions and compute gradients using trace-based automatic differentiation. Read more

import nabla

# Use Accelerator (GPU) or CPU for execution
with nabla.default_device(nabla.Accelerator()):
    x = nabla.uniform((4, 8))
    w = nabla.uniform((8, 16))

    # Define loss function
    def compute_loss(x, w):
        return nabla.mean(nabla.relu(x @ w))

    # Compute loss (implicit .realize() on print)
    loss = compute_loss(x, w)
    print("Loss:", loss)

    # Compute gradients via backward replay
    grad_x, grad_w = nabla.grad(compute_loss, argnums=(0, 1))(x, w)
    print("Gradients:", grad_x.shape, grad_w.shape)

2. SPMD Sharding

Shard tensors on a logical mesh; operations automatically propagate sharding constraints. Read more

# Define 2×4 device mesh (Logical DP × TP)
mesh = nabla.DeviceMesh("my_mini_pod", (2, 4), ("dp", "tp"))

# Shard x on 'dp' (rows), w on 'tp' (columns)
x = nabla.shard(nabla.uniform((32, 128)), mesh, nabla.P("dp", None))
w = nabla.shard(nabla.uniform((128, 256)), mesh, nabla.P(None, "tp"))

def compute_loss(x, w):
    return nabla.mean(nabla.relu(x @ w))

# Automatic AllReduce is inserted for 'tp' sum
loss = compute_loss(x, w)
print("Loss (Sharded):", loss)

3. Mojo Integration

Nabla's core strength is its ability to drop down to Mojo for high-performance custom kernels, bridging the gap between high-level Python and bare-metal execution. Read more

Mojo Kernel (kernels/custom_kernel.mojo)

@compiler.register("my_kernel")
struct MyKernel:
    @staticmethod
    def execute[target: StaticString](
        output: OutputTensor,
        x: InputTensor[dtype = output.dtype, rank = output.rank],
        ctx: DeviceContextPtr,
    ):
        @parameter
        fn add_one[W: Int](idx: IndexList[x.rank]) -> SIMD[x.dtype, W]:
            return x.load[W](idx) + 1

        foreach[add_one, target=target](output, ctx)

Python Usage

class AddOneOp(nabla.UnaryOperation):
    name = "my_kernel"

    def kernel(self, x, **kwargs):
        # Concise invocation: (func_name, path, inputs, out_types)
        return nabla.call_custom_kernel("my_kernel", "./kernels", x, x.type)

x = nabla.Tensor.constant([1., 2., 3.])
y = AddOneOp()(x)

4. Distributed Pipeline Parallelism (GPipe)

Define complex distributed schedules like GPipe using vmap for parallel execution and ppermute for explicit data movement. Read more

# Parallel execution across 'num_stages'
@nabla.vmap(in_axes=(0, 0), spmd_axis_name="stage")
def stage_compute(x, w): 
    return nabla.relu(x @ w)

def pipeline_step(current_state, fresh_input, weights, mask_0):
    # 1. Compute: Run all stages in parallel
    computed = stage_compute(current_state, weights)

    # 2. Communicate: Shift activations to the next stage (i -> i+1)
    shifted = nabla.ppermute(computed, perm=[(i, (i + 1) % stages) for i in range(stages)])

    # 3. Control: Stage 0 takes fresh input; others take shifted data
    return nabla.where(mask_0, fresh_input, shifted)

5. Dynamic Shape Compilation

Compile functions once with symbolic dimensions to handle varying input sizes without recompilation.

# Compile once for ANY batch size (dim 0)
@nabla.compile(dynamic_dims={0: {0: "batch"}})
def square(x):
    return x * x

x_small = nabla.uniform((2, 10))
x_large = nabla.uniform((128, 10))

res1 = square(x_small) # Triggers compilation
res2 = square(x_large) # Reuses compiled graph!

Architecture Overview

Nabla relies on three core principles:

1. Lazy Execution: Shapes are computed eagerly, but the computation graph is built and compiled only when .realize() is called.
   • Read more: Operation Pipeline
2. Trace-Based Autodiff: Gradients are computed by tracing the forward pass and replaying operations in reverse.
   • Read more: Autograd Engine
3. Factor-Based SPMD: Sharding is propagated using "semantic factors" (e.g., batch, heads) rather than physical mesh axes.
   • Read more: Sharding & Solver

Contributing

• Bugs/Docs: Submit PR directly.
• Features: Open an Issue first.
• New Ops: See nabla/ops/README.md.

License

Apache-2.0 — see LICENSE