Aggregators

Krum provides several Byzantine-resilient gradient aggregation rules (GARs). Each rule follows a keyword-only contract and includes parameter validation and optional theoretical bounds.

Overview

Aggregators

Aggregator	Complexity	Min. Workers	Byzantine Res.
Average	\(\mathcal{O}(nd)\)	\(1\)	None (baseline)
Median	\(\mathcal{O}(nd)\)	\(1\)	Basic
Krum	\(\mathcal{O}(n^2 d)\)	\(2f + 3\)	Moderate
Bulyan	\(\mathcal{O}(n^2 d)\)	\(4f + 3\)	Strong
Brute	\(\mathcal{O}(\binom{n}{n-f}d)\)	\(2f + 1\)	Optimal

where:

• \(n\) = total number of workers

• \(f\) = number of Byzantine workers

• \(d\) = gradient dimension

• \(\binom{n}{k}\) = binomial coefficient

Available Aggregators

Robust Aggregation Rules:

• Average
• Median
• Krum / Multi-Krum
• Bulyan
• Brute

API Reference

Gradient aggregation rules (GARs) for Byzantine-resilient distributed learning.

Each rule combines a keyword-only aggregation function with a validation function and optional metadata used by the training and experiment scripts.

Contract

Each aggregation rule MUST:

1. Accept keyword-only arguments

2. Accept the reserved parameter gradients (non-empty list of gradients)

3. Accept the reserved parameter f (number of Byzantine gradients to tolerate)

4. Accept the reserved parameter model (model with configured defaults)

5. NOT return a tensor that aliases any input tensor

Each rule MUST provide a check function that validates parameters and returns None when valid, or a user-facing error message otherwise.

The module exposes three variants for each rule:

• rule: The default version (checked in debug mode, unchecked in release)

• rule.checked: Always validates parameters

• rule.unchecked: Skips validation (faster in production)

Additional metadata available on each rule:

• rule.check: The validation function

• rule.upper_bound: Theoretical bound on stddev/norm ratio (if available)

• rule.influence: Attack acceptance ratio (if available)