What is the L1 loss gradient?

It's the subgradient of the absolute error |y - ŷ|, which is sign(y - ŷ) except at zero where it's in [-1, 1]. Handles non-differentiability for strong training.

Why use L1 loss instead of L2?

L1 resists outliers better, promotes sparsity, ideal for noisy real-world data like sensors or web images.

How does gradient descent work with L1 loss?

Uses subgradients, stochastic noise, or smooth approximations like Huber to navigate the non-smooth point at zero.

🔬 AI Research

The L1 Loss Gradient Snag: Fixing Gradient Descent's Absolute-Value Headache

Your model's predictions flop on outliers? The L1 loss gradient holds the fix—but it's tricky. Understand it, and you train tougher AIs.

theAIcatchup Apr 10, 2026 4 min read

Step-by-step diagram of L1 loss gradient computation in gradient descent

⚡ Key Takeaways

L1 loss gradients use subgradients to handle the non-differentiable kink at zero, enabling strong training. 𝕏
Unlike L2, L1 promotes sparsity and outlier resistance—key for real-world noisy data. 𝕏
Practical hacks like smoothing and adaptive optimizers make L1 viable in modern deep learning. 𝕏

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Originally reported by Towards AI

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