Lucid² 💎

Lucid is a minimalist deep learning framework built entirely from scratch in Python. It offers a pedagogically rich environment to explore the foundations of modern deep learning systems, including autodiff, neural network modules, and GPU acceleration — all while staying lightweight, readable, and free of complex dependencies.

Whether you're a student, educator, or an advanced researcher seeking to demystify deep learning internals, Lucid provides a transparent and highly introspectable API that faithfully replicates key behaviors of major frameworks like PyTorch, yet in a form simple enough to study line by line.

📑 Lucid Documentation

🔥 What's New

• EfficientFormer implemented: lucid.models.EfficientFormer

  Detailed variants: efficientformer_l1, efficientformer_l3, and efficientformer_l7

• Added Porting System: lucid.save, lucid.load

  Supports lucid.Tensor and state-dict(OrderedDict) save/load (For lucid.nn.Module, it automatically extracts its state-dict and then saves the dict)

• Faster R-CNN implemented: lucid.mdoels.FasterRCNN

  Also comes with two ResNet-FPN backbone variants:

  • Faster R-CNN ResNet-50 FPN: models.faster_rcnn_resnet_50_fpn
  • Faster R-CNN ResNet-101 FPN: models.faster_rcnn_resnet_101_fpn

• Fast R-CNN implemented: lucid.models.FastRCNN

🔧 How to Install

Lucid is designed to be light, portable, and friendly to all users — no matter your setup.

▶️ Basic Installation

Lucid is available directly on PyPI:

pip install lucid-dl

Alternatively, you can install the latest development version from GitHub:

pip install git+https://github.com/ChanLumerico/lucid.git

This installs all the core components needed to use Lucid in CPU mode using NumPy.

⚡ Enable GPU (Metal / MLX Acceleration)

If you're using a Mac with Apple Silicon (M1, M2, M3), Lucid supports GPU execution via the MLX library.

To enable Metal acceleration:

1. Install MLX:

pip install mlx

2. Confirm you have a compatible device (Apple Silicon).
3. Run any computation with device="gpu".

✅ Verification

Here's how to check whether GPU acceleration is functioning:

import lucid
x = lucid.ones((1024, 1024), device="gpu")
print(x.device)  # Should print: 'gpu'

📐 Tensor: The Core Abstraction

At the heart of Lucid is the Tensor class — a generalization of NumPy arrays that supports advanced operations such as gradient tracking, device placement, and computation graph construction.

Each Tensor encapsulates:

• A data array (ndarray or mlx.array)
• Gradient (grad) buffer
• The operation that produced it
• A list of parent tensors from which it was derived
• Whether it participates in the computation graph (requires_grad)

🔁 Construction and Configuration

from lucid import Tensor

x = Tensor([[1.0, 2.0], [3.0, 4.0]], requires_grad=True, device="gpu")

• requires_grad=True adds this tensor to the autodiff graph.
• device="gpu" allocates the tensor on the Metal backend.

🔌 Switching Between Devices

Tensors can be moved between CPU and GPU at any time using .to():

x = x.to("gpu")  # Now uses MLX arrays for accelerated computation
y = x.to("cpu")  # Moves data back to NumPy

You can inspect which device a tensor resides on via:

print(x.device)  # Either 'cpu' or 'gpu'

📉 Automatic Differentiation (Autodiff)

Lucid implements reverse-mode automatic differentiation, which is commonly used in deep learning due to its efficiency for computing gradients of scalar-valued loss functions.

It builds a dynamic graph during the forward pass, capturing every operation involving Tensors that require gradients. Each node stores a custom backward function which, when called, computes local gradients and propagates them upstream using the chain rule.

📘 Computation Graph Internals

The computation graph is a Directed Acyclic Graph (DAG) in which:

• Each Tensor acts as a node.
• Each operation creates edges between inputs and outputs.
• A _backward_op method is associated with each Tensor that defines how to compute gradients w.r.t. parents.

The .backward() method:

1. Topologically sorts the graph.
2. Initializes the output gradient (usually with 1.0).
3. Executes all backward operations in reverse order.

🧠 Example

import lucid

x = lucid.tensor([1.0, 2.0, 3.0], requires_grad=True)
y = x * 2 + 1
z = y.sum()
z.backward()
print(x.grad)  # Output: [2.0, 2.0, 2.0]

This chain-rule application computes the gradient $\frac{\partial z}{\partial x} = \frac{\partial z}{\partial y}\cdot\frac{\partial y}{\partial x} = [2, 2, 2]$.

🔄 Hooks & Shape Alignment

Lucid supports:

• Hooks for gradient inspection or modification.
• Shape broadcasting and matching for non-conforming tensor shapes.

🚀 Metal Acceleration (MLX Backend)

Lucid supports Metal acceleration on Apple Silicon devices using MLX. This integration allows tensor operations, neural network layers, and gradient computations to run efficiently on the GPU, leveraging Apple’s unified memory and neural engine.

📋 Key Features

• Tensors with device="gpu" are allocated as mlx.core.array.
• Core mathematical operations, matrix multiplications, and backward passes use MLX APIs.
• No change in API: switching to GPU is as simple as .to("gpu") or passing device="gpu" to tensor constructors.

💡 Example 1: Basic Acceleration

import lucid

x = lucid.randn(1024, 1024, device="gpu", requires_grad=True)
y = x @ x.T
z = y.sum()
z.backward()
print(x.grad.device)  # 'gpu'

💡 Example 2: GPU-Based Model

import lucid.nn as nn
import lucid.nn.functional as F

class TinyNet(nn.Module):
    def __init__(self):
        super().__init__()
        self.fc = nn.Linear(100, 10)

    def forward(self, x):
        return F.relu(self.fc(x))

model = TinyNet().to("gpu")
data = lucid.randn(32, 100, device="gpu", requires_grad=True)
output = model(data)
loss = output.sum()
loss.backward()

When training models on GPU using MLX, you must explicitly evaluate the loss tensor after each forward pass to prevent the MLX computation graph from growing uncontrollably.

MLX defers evaluation until needed. If you don’t force evaluation (e.g. calling .eval()), the internal graph may become too deep and lead to performance degradation or memory errors.

Recommended GPU Training Pattern:

loss = model(input).sum()
loss.eval()  # force evaluation on GPU
loss.backward()

This ensures that all prior GPU computations are flushed and evaluated before backward pass begins.

🧱 Neural Networks with lucid.nn

Lucid provides a modular PyTorch-style interface to build neural networks via nn.Module. Users define model classes by subclassing nn.Module and defining parameters and layers as attributes.

Each module automatically registers its parameters, supports device migration (.to()), and integrates with Lucid’s autodiff system.

🧰 Custom Module Definition

import lucid.nn as nn

class MLP(nn.Module):
    def __init__(self):
        super().__init__()
        self.fc1 = nn.Linear(784, 128)
        self.fc2 = nn.Linear(128, 10)

    def forward(self, x):
        x = self.fc1(x)
        x = nn.functional.relu(x)
        x = self.fc2(x)
        return x

🧩 Parameter Registration

All parameters are registered automatically and can be accessed:

model = MLP()
print(model.parameters())

🧭 Moving to GPU

model = model.to("gpu")

This ensures all internal parameters are transferred to GPU memory.

🏋️‍♂️ Training & Evaluation

Lucid supports training neural networks using standard loops, customized optimizers, and tracking gradients over batches of data.

✅ Full Training Loop

import lucid
from lucid.nn.functional import mse_loss

model = MLP().to("gpu")
optimizer = lucid.optim.SGD(model.parameters(), lr=0.01)

for epoch in range(100):
    preds = model(x_train)
    loss = mse_loss(preds, y_train)
    loss.eval()  # force evaluation

    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    print(f"Epoch {epoch}, Loss: {loss.item()}")

🧪 Evaluation without Gradients

with lucid.no_grad():
    out = model(x_test)

Prevents gradient tracking and reduces memory usage.

🧬 Educational by Design

Lucid is not a black box. It’s built to be explored. Every class, every function, and every line is designed to be readable and hackable.

• Use it to build intuition for backpropagation.
• Modify internal operations to test custom autograd.
• Benchmark CPU vs GPU behavior on your own model.
• Debug layer by layer, shape by shape, gradient by gradient.

Whether you're building neural nets from scratch, inspecting gradient flow, or designing a new architecture — Lucid is your transparent playground.

🧠 Conclusion

Lucid serves as a powerful educational resource and a minimalist experimental sandbox. By exposing the internals of tensors, gradients, and models — and integrating GPU acceleration — it invites users to see, touch, and understand how deep learning truly works.

📜 Others

Dependencies:

Library	Purpose
numpy	Core Tensor operations for CPU
mlx	Core Tensor operations for GPU(Apple Silicon)
pandas, openml	Dataset download and fetching
matplotlib	Various visualizations
networkx	Graph construction of Tensors and modules for visualizations

Inspired By: