How does backpropagation compute gradients?

Backpropagation traverses the computation graph from the output back to inputs, applying the chain rule at each node: multiply the downstream gradient by the local derivative to accumulate each child's contribution (explanation and examples start at 171 and chain-rule discussion at 2288).

What is a Value object in micrograd?

A Value wraps a scalar number and stores its children, the op that produced it, its data and the grad; Value instances are the nodes of the computation graph used for forward and backward passes (construction and intent described at 1160).

How do you add operator support (like +, *) to Value?

Define Python dunder methods (__add__, __mul__, etc.) that create new Value nodes whose children point to the operands and assign a backward closure implementing the local derivative; the lecture demonstrates addition and multiplication implementation (see the operator discussion beginning at 1226).

How can I visualize the computation graph?

You can trace nodes and edges from the root value and render them with a graphing library (the video demos a drawdot routine that creates op and value nodes and uses a graph-visualization API to show structure, shown at 1509).

What is topological sort and why is it necessary for backward?

Topological sorting orders nodes so every node appears after its dependencies; using this order (then iterating reversed) guarantees that when you call a node's backward closure all downstream gradients have been accumulated (explanation and implementation at 4161).

How do I implement custom operations like tanh?

You can implement tanh either as a single op with its forward and local derivative in backward, or build it from primitives (exp, add, div) — micrograd shows both approaches and proves they produce identical gradients (see the tanh implementation and reconstruction at 3599 and 5592).

How is micrograd related to PyTorch?

micrograd implements the same fundamental math (forward graphs, local derivatives, chain rule, gradient descent) at a scalar level; PyTorch generalizes these ideas to tensor kernels and device-optimized implementations — the lecture compares APIs and shows parity on small examples (see PyTorch comparison at 5972).

What does a minimal training loop look like?

A minimal loop is: forward pass to compute loss, zero parameter gradients, backward() to accumulate grads, then update each parameter by stepping opposite the gradient (p.data -= lr * p.grad); the working loop is shown and discussed around 7039 and 7724.

Why must I call zero_grad before backward?

micrograd's backward accumulates into p.grad with +=, so if you don't reset grads between steps you will accumulate previous steps' gradients and get incorrect updates; the common bug and fix (zeroing grads) are explained at 7724–7949.

How should I pick a learning rate for gradient descent?

Start with a modest lr and monitor loss: if the lr is too small training is slow; if it's too large updates can overshoot and explode the loss — the lecture demonstrates stable vs unstable choices and recommends tuning while watching the loss (see discussion around 7429–7524).

Where can I find the micrograd source, demos, and tests?

The author published micrograd on GitHub; the repo contains engine.py (autograd core), nn.py (tiny NN API), demos, and tests — file structure and repo pointers are shown near the repo walkthrough (see 423 and earlier GitHub mention at 29).

The spelled-out intro to neural networks and backpropagation: building micrograd

Andrej Karpathy

Science & Technology3 min read146 min video

Aug 16, 2022|3,277,648 views|66,089|2,438

neural network backpropagation lecture

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Key Moments

TL;DR

Build a toy autograd (micrograd) from scratch and see backprop in action.

Key Insights

Autograd computes gradients by traversing a computation graph with the chain rule.

Micrograd uses a simple Value class to wrap scalars and overloads operators to build graphs.

Forward pass computes outputs; backward pass computes gradients w.r.t inputs and weights, through topological sort.

Visualization and gradient checks (numerical gradients) help verify backprop correctness.

Real-world libraries (PyTorch) implement similar ideas with tensors and modules; micrograd illustrates concepts in ~150 lines.

Training a neural net reduces to assembling a small expression (neuron, layer, MLP), a loss, backward pass, then gradient descent; pitfalls include zeroing grads and learning rate choices.

INTRO TO MICROGRAD AND AUTOGRAD

André presents micrograd as a tiny autograd engine designed to reveal training mechanics under the hood. The aim is to build a scalar computation graph that can be forward-evaluated and then backpropagated to obtain gradients with respect to inputs and weights. The core idea—that modern libraries rest on automatic differentiation—gets distilled into an approachable, minimal implementation. The talk emphasizes intuition over tensors, and shows that roughly 150 lines of Python can capture the essential autograd behavior.

BUILDING BLOCKS: THE VALUE CLASS AND COMPUTATION GRAPHS

The foundation is the Value class, which wraps a single scalar value, its gradient, and pointers to the values that contributed to it. Operators like add and mul are overloaded so expressions naturally form a graph: each new Value records its children and the operation that produced it. Forward passes compute the final output, while backward passes propagate gradients by following the graph in reverse, enabling backpropagation through the chain rule. This section also introduces graph visualization to see how a simple expression unfolds.

BACKPROPAGATION AND THE CHAIN RULE IN ACTION

Backpropagation is implemented by applying the chain rule along a topologically sorted graph. The gradient at the output starts at 1 and flows backward, with each node applying its local derivative and distributing gradients to its inputs. Accumulation via plus-equals handles shared inputs that contribute through multiple paths. The discussion covers simple ops (addition with local derivative 1, multiplication with the other input), as well as nonlinear nodes like tanh, underscoring how local derivatives knit together into global gradients.

FROM NEURONS TO MLPS: TRAINING WITH FORWARD, LOSS, BACKPROP, AND UPDATE

Micrograd scales up from scalars to neural-net building blocks: Neuron, Layer, and Multi-Layer Perceptron (MLP). André demonstrates a tiny binary classification dataset, defines a mean-squared-error loss, and walks through forward, backward, and gradient-descent updates. A subtle but instructive bug—failing to zero gradients between iterations—is highlighted, illustrating practical pitfalls in training loops. The example shows how even a small network with ~40 parameters can embody the full training pipeline.

MICROGRAD VS PYTORCH: INSIGHTS, LIMITS, AND TAKEAWAYS

The talk juxtaposes micrograd with PyTorch: autograd, tensors, and backward passes are the same core ideas, but micrograd distills them into a transparent, educational 100–150 line toy. PyTorch extends these concepts to large-scale tensors and modules, enabling production-ready models. The final message is that neural networks are about expressing computations, losses, gradients, and iterative optimization; micrograd demonstrates these principles clearly, while PyTorch handles efficiency and scale.

Mentioned in This Episode

●Products

●Software & Apps

●Tools

●Companies

●People Referenced

micrograd & backprop cheat sheet

Practical takeaways from this episode

Do This

Do implement a small Value class that stores data, grad, op, and children so you can build a computation graph (start at 1160).

Do implement and attach a local backward() closure for each operation that multiplies the incoming gradient by the local derivative and accumulates into children (see 3071).

Do build a topological ordering of the computation graph and run backward() in reverse topological order (see 4161).

Do zero all parameter gradients before each backward pass (zero_grad) to avoid accumulating gradients across steps (see 7724).

Do run small forward/backward/update loops (forward → zero_grad → backward → update) and monitor loss and LR to tune stability (see 7039 & 7429).

Avoid This

Don't overwrite child gradients in backward — use += to accumulate contributions from multiple paths (see 4494).

Don't forget to wrap numeric constants as Value objects if your operator expects Value operands (see 5161).

Don't run backward without resetting gradients (you’ll accumulate old gradients and get incorrect updates — see 7724).

Don't choose an overly large learning rate without monitoring loss; large steps can destabilize or explode training (see 7429).

Common Questions

micrograd is a tiny scalar autograd engine that implements automatic differentiation and backpropagation so you can see how gradient computation works under the hood; it's intentionally simple and pedagogical rather than optimized for production (see explanation at 50).

Topics

Micrograd Autograd Backpropagation Value Object Chain Rule Topological Sort Tanh Neuron MLP Gradient Descent Zero_grad Learning Rate

Mentioned in this video

toolengine.py

One of the two files in the micrograd repo; contains the autograd engine (Value class, ops, backward logic).

tooltanh

A specific activation (hyperbolic tangent) implemented both as a single op and later reconstructed from primitives to show equivalence; its local derivative is used in backpropagation examples.

toolmatplotlib (plt)

Used to visualize example functions (e.g., plotting a parabola) and decision surfaces in demos.

toolnn.py

The second file in micrograd that provides tiny neural network primitives (Neuron, Layer, MLP) built on top of the engine.

toolnn.Module

The module-style API concept (parent class) that micrograd's small neural-library mirrors, referenced while explaining the repo structure.

toolmicrograd

A tiny scalar autograd engine (Python library) that the lecture builds step‑by‑step and demonstrates as a pedagogical implementation of automatic differentiation.

toolNumPy (np)

Used for numeric examples and to show plotting and function evaluation (e.g., np.tanh used when discussing activations).

toolCUDA

Mentioned when tracing PyTorch internals (there are separate CPU and GPU kernels for operations such as tanh backward).

personAndre

The lecture speaker introducing micrograd and walking through implementation and intuition for backpropagation.

toolGraphis

The graph visualization API referenced when showing code to draw computation graphs (the lecture references using a graph visualization tool via its API).