Prerequisite · Matrix Algebra Foundations

Einsum in TensorFlow

Colab Notebook · ~40 min
Google Colab Notebook
Einsum in TensorFlow
Python · ~40 min
Open in Colab
Lab Objectives
1
Verify that tf.einsum produces numerically identical results to torch.einsum for all canonical operations using np.allclose.
2
Build a custom Keras EinsumDense layer and confirm it trains correctly with standard optimizers.
3
Implement multi-head attention (score + weighted sum + projection) using tf.einsum and verify output shapes.
4
Use tf.GradientTape to compute the gradient of a quadratic form expressed with einsum and verify it analytically.
5
Measure the speedup of @tf.function over eager mode for einsum-based attention on realistic tensor sizes.
6
Articulate when to prefer tf.linalg vs tf.einsum in production TensorFlow code.

Lab: Einstein Summation in TensorFlow

tf.einsum is syntactically identical to torch.einsum — the same notation string works in both frameworks, as well as in NumPy and JAX. This lab focuses on what is different in the TensorFlow context: how einsum composes with Keras custom layers, how GradientTape differentiates through it, and how tf.function compilation affects performance.

What You'll Build

  • Parity verification: every operation from the PyTorch lab reproduced in TensorFlow with np.allclose checks
  • A custom EinsumDense Keras layer that replicates tf.keras.layers.Dense using tf.einsum — fully trainable, gradient-compatible
  • A multi-head attention forward pass implemented with einsum and integrated into a Keras model
  • A GradientTape walkthrough: compute the gradient of f(x)=x⊤Axf(\mathbf{x}) = \mathbf{x}^\top A \mathbf{x} and verify it equals 2Ax2A\mathbf{x} analytically
  • A benchmark of eager vs @tf.function-compiled einsum attention

Key Concepts Practiced

By the end you will understand that einsum strings are framework-agnostic, know when to prefer tf.linalg over tf.einsum (standard ops in perf-critical paths) vs when einsum wins (novel contractions, readability), and be able to drop an einsum operation into a Keras model without any special gradient handling.