Table of Contents

Interface ISecondOrderGradientComputable<T, TInput, TOutput>

Namespace
AiDotNet.Interfaces
Assembly
AiDotNet.dll

Extended gradient computation interface for MAML meta-learning algorithms.

public interface ISecondOrderGradientComputable<T, TInput, TOutput> : IGradientComputable<T, TInput, TOutput>

Type Parameters

T

The numeric data type (e.g., float, double).

TInput

The input data type.

TOutput

The output data type.

Inherited Members

Remarks

This interface extends IGradientComputable<T, TInput, TOutput> with second-order gradient computation capability required for full MAML (Model-Agnostic Meta-Learning).

For Beginners: While basic gradient computation tells you how to improve on a single task, second-order gradients tell you how changing your starting point would affect learning on that task.

Think of it like this:

  • First-order: "If I start here, which direction improves this task?"
  • Second-order: "If I started slightly differently, how would my entire learning trajectory change?"

This is computationally expensive but more accurate for meta-learning.

MAML Use Case: Full MAML uses second-order gradients to backpropagate through the inner loop adaptation, computing true meta-gradients that account for how the adaptation process itself changes. Reptile and first-order MAML approximate this with only first-order gradients.

Methods

ComputeSecondOrderGradients(List<(TInput input, TOutput target)>, TInput, TOutput, ILossFunction<T>, T)

Computes second-order gradients (Hessian-vector product) for full MAML meta-learning.

Vector<T> ComputeSecondOrderGradients(List<(TInput input, TOutput target)> adaptationSteps, TInput queryInput, TOutput queryTarget, ILossFunction<T> lossFunction, T innerLearningRate)

Parameters

adaptationSteps List<(TInput input, TOutput target)>

The sequence of adaptation steps (support set training).

queryInput TInput

The query set input for evaluation after adaptation.

queryTarget TOutput

The query set target for evaluation after adaptation.

lossFunction ILossFunction<T>

The loss function to use for gradient computation.

innerLearningRate T

The inner loop learning rate for adaptation.

Returns

Vector<T>

The meta-gradient computed through the entire adaptation process.

Remarks

This computes the true MAML gradient by backpropagating through the inner loop adaptation. This requires computing second-order derivatives (gradients of gradients).

Algorithm: 1. Record the adaptation trajectory (parameter updates during inner loop) 2. Compute query loss gradient at adapted parameters 3. Backpropagate through each adaptation step using chain rule 4. Return gradient w.r.t. original (pre-adaptation) parameters

For Beginners: Full MAML asks: "If I change my starting point slightly, how does that affect my performance after adaptation?"

This requires tracking not just how to improve on this task, but how changing the starting point would have changed the whole adaptation process.

Example: If your starting point makes you learn faster, the second-order gradient captures that benefit. First-order approximations (like Reptile) miss this.

Computational Cost: Significantly more expensive than first-order MAML: - Requires storing intermediate computations from adaptation - Performs additional backward passes through adaptation steps - Memory scales with number of adaptation steps

Use only when accuracy is more important than speed.

Exceptions

ArgumentNullException

If any parameter is null.

ArgumentException

If adaptationSteps is empty.

Edit this page