🤖 machine learning

Shapley Neuron Values for Continual Learning: Which Neurons Matter Most?

This paper introduces Shapley Neuron Valuation (SNV), a game-theoretic framework that identifies and freezes critical neurons to enable effective buffer-free continual learning without architectural expansion, achieving significant accuracy improvements over existing methods on ImageNet-1k.

Original authors: Mohammad Ali Vahedifar, Abhisek Ray, Qi Zhang

Published 2026-05-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mohammad Ali Vahedifar, Abhisek Ray, Qi Zhang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The "Goldfish Memory" of AI

Imagine you are teaching a student (a neural network) a series of subjects: first Math, then History, then Biology.

The Goal: You want the student to learn Biology without forgetting Math or History.
The Reality: In traditional AI, learning Biology often causes the student to "overwrite" their Math notes. This is called Catastrophic Forgetting. The more they learn, the more they forget what came before.

To fix this, most current methods use one of two tricks:

The "Notebook" Method (Memory-based): The student keeps a physical notebook of old Math problems to review while learning Biology. Problem: This notebook gets huge, takes up space, and might contain private info you aren't allowed to keep.
The "Backpack" Method (Dynamic Architecture): The student buys a bigger backpack every time they learn a new subject. Problem: Eventually, the backpack is so heavy and big it becomes impossible to carry.

The Paper's Solution: The "Shapley Neuron Value" (SNV)

This paper proposes a third way: The "Smart Locker" System.

Instead of buying a bigger backpack or carrying a heavy notebook, the student uses the same backpack they started with. The trick is figuring out exactly which items in the backpack are essential for which subject and locking them in place so they can't be lost, while leaving other items free to be used for new subjects.

Here is how they do it:

1. The "Team of Workers" Analogy (Game Theory)

Inside the AI's brain, there are thousands of tiny "workers" called Neurons. When the AI solves a problem, these workers collaborate.

The Question: Who is the most important worker for this specific task?
The Tool: The authors use a mathematical concept from Cooperative Game Theory called Shapley Values.
The Metaphor: Imagine a group of people trying to build a house. Some people are laying bricks, others are painting, and some are just standing around. The Shapley Value is a fair way to calculate exactly how much each person contributed to the final house.
- If you remove a specific worker and the house collapses, that worker had a high value.
- If you remove a worker and the house looks the same, that worker had zero value.

2. The "Freezing" Strategy

Once the AI learns a task (like Math), the SNV system runs a quick calculation to see which Neurons were the "star players" for Math.

The Action: It puts a frozen lock on those specific star Neurons. They are now "frozen" and cannot change.
The Result: When the AI learns History, it can only use the unfrozen Neurons. The Math Neurons are safe in their lockers, so the Math knowledge is preserved.
The Benefit: The AI never needs to store old data (no notebook) and never needs to grow bigger (no new backpack). It just rearranges and locks parts of its existing brain.

3. Why This is Better Than Other Methods

The paper compares this "Smart Locker" system to other methods:

Vs. The "Notebook" (Memory-based): SNV doesn't need to store old photos or data. This is great for privacy (no data leaks) and saves storage space.
Vs. The "Backpack" (Dynamic Architecture): SNV doesn't add new parts to the brain. It fits everything into the original size.
Vs. The "Blind Freeze" (Other Buffer-free methods): Some other methods just freeze random parts of the brain or freeze based on simple guesses. SNV uses the "Shapley Value" math to be precise. It knows exactly which neurons matter most, so it doesn't accidentally freeze a neuron that is needed for the new task.

The Results: "The Goldfish that Remembers"

The researchers tested this on huge image datasets (like ImageNet, which has thousands of types of pictures).

The Outcome: SNV consistently beat other methods that don't use a "notebook."
The Score: In one test, SNV improved accuracy by nearly 6.5% compared to the second-best method that also didn't use a notebook.
The "Zero Forgetting" Claim: In tests where the AI knew which task it was doing (Task Incremental Learning), SNV achieved zero forgetting. It learned new things without losing any old things, all without storing a single old image.

The Catch (Limitations)

The paper admits there is a small cost. Calculating the "Shapley Value" (figuring out who the star workers are) takes a little bit of extra computer time and energy.

The Trade-off: It's like spending 10 extra minutes doing a detailed inventory of your backpack before a trip. It takes a little more time upfront, but it ensures you don't lose your keys later. The paper argues this small time cost is worth it to avoid the massive cost of storing data or building bigger models.

Summary

Think of Shapley Neuron Values as a smart librarian for an AI's brain.
Instead of throwing away old books (forgetting) or buying a new library (expanding), the librarian identifies the most important books for the current topic, locks them in a safe, and lets the AI write new notes in the empty space. This way, the library stays the same size, but the knowledge never gets lost.

Technical Summary: Shapley Neuron Values for Continual Learning

1. Problem Statement

Continual learning (CL) aims to enable neural networks to learn sequential tasks without forgetting previously acquired knowledge. However, standard neural networks suffer from catastrophic forgetting, where learning new tasks degrades performance on earlier ones. Existing solutions face significant limitations:

Memory-based methods (e.g., iCaRL, DER++) store and replay past examples, violating strict CL settings where past data is inaccessible and raising privacy concerns (e.g., GDPR).
Dynamic architecture methods (e.g., PNN, DyTox) expand the model size over time, leading to unbounded parameter growth and computational impracticality.
Regularization-based methods (e.g., EWC, SI) often struggle with highly heterogeneous tasks and may require auxiliary modules or task-specific constraints.

The core challenge addressed is achieving forget-resistant continual learning within a fixed-capacity backbone network, without revisiting past data and without expanding the architecture.

2. Methodology: Shapley Neuron Values (SNV)

The authors propose Shapley Neuron Values (SNV), a buffer-free framework that leverages the inherent over-parameterization of modern neural networks. The method identifies and preserves "expert subnetworks" for each task using principles from cooperative game theory.

Core Mechanism

Neuron Definition: In convolutional networks, a "Neuron" is defined as a convolutional filter (kernel).
Shapley Valuation: The importance of each neuron is quantified using Shapley Values, which fairly distribute the model's performance metric $V(M)$ $V (M)$ among neurons based on their marginal contributions to various subsets of the network.
- The valuation satisfies four axioms: Efficiency, Null Contribution, Symmetry, and Linearity.
- The Shapley value $\phi_i$ for neuron $i$ is calculated as:
  $\phi_i = \sum_{S \subseteq M \setminus \{i\}} \frac{|S|!(|M| - |S| - 1)!}{|M|!} [V(S \cup \{i\}) - V(S)]$
- Here, $V(S)$ represents the model performance when neurons in $M \setminus S$ are replaced by their mean activations (masking), preserving signal statistics without retraining.
Approximation Strategy: Since exact Shapley computation is exponential, SNV employs three approximations:
- Monte Carlo Estimation: Sampling permutations of neurons to estimate marginal contributions.
- Truncation: Skipping marginal computations for small subsets where performance drops below a threshold (assuming the model is non-functional).
- Multi-Armed Bandit (MAB): Focusing sampling efforts on neurons whose confidence intervals overlap with the top- $k$ estimated values to efficiently identify the most important neurons.
Freezing and Plasticity:
- For each task $t$ , the top $c \cdot N$ neurons (where $c$ is a sparsity ratio and $N$ is total neurons) with the highest Shapley values are selected.
- A cumulative binary mask $B_t$ is maintained, marking all neurons selected for tasks $1$ through $t$ .
- During training for task $t+1$ , gradients are blocked for all neurons in $B_t$ (frozen), while the remaining "plastic" neurons are updated. This ensures stable knowledge retention for past tasks while allowing flexibility for new ones.

3. Key Contributions

Principled Neuron Selection: Introduces a game-theoretic framework (Shapley Values) to identify the most critical neurons for specific tasks, moving beyond heuristic or binary importance scores.
Buffer-Free & Fixed-Capacity: Demonstrates that a fixed-capacity network can learn sequential tasks indefinitely by selectively freezing important neurons, eliminating the need for replay buffers or architectural expansion.
Stability-Plasticity Trade-off: Explicitly disentangles knowledge retention (via frozen stable neurons) from new task learning (via plastic neurons), reducing cross-task interference.
Efficient Estimation: Proposes a practical pipeline (Monte Carlo + Truncation + MAB) to make Shapley value estimation computationally feasible for continual learning.

4. Experimental Results

Experiments were conducted on CIFAR-100, Tiny-ImageNet, and ImageNet-1k using ResNet-18, covering both Class-Incremental Learning (CIL) and Task-Incremental Learning (TIL) scenarios.

Performance Highlights

ImageNet-1k (CIL): SNV achieved 41.30% accuracy on 10 tasks, 34.20% on 20 tasks, and 25.60% on 50 tasks. It consistently outperformed all buffer-free baselines (e.g., NFL+, DCNet) and even surpassed the memory-based method DyTox (which stores 20,000 exemplars) in the 10-task scenario.
ImageNet-1k (TIL): SNV achieved 57.82% accuracy with 0.0 backward transfer (BWT), outperforming all buffer-free methods and matching or exceeding memory-based methods without storing any data.
Comparison to Baselines:
- In CIL, SNV improved accuracy by +2.88% over the second-best buffer-free method (NFL+) on 10 tasks, with the gap widening to +3.20% on 50 tasks.
- In TIL, SNV outperformed WSN (Winning SubNetwork) by 15.76% on CIFAR-100 (at $c=0.5$ ), demonstrating that principled Shapley selection is superior to binary heuristic selection.
Parameter Efficiency: Pruning analysis showed that SNV utilizes parameters more efficiently than methods like PEC or EWC. SNV maintained high accuracy under deeper pruning before collapsing, indicating less redundancy and more critical parameter usage.
Computational Cost: While SNV requires more FLOPs than lightweight regularizers (e.g., EWC), the overhead is modest (~1.24x that of NFL+). It remains significantly more efficient than memory-based methods like DyTox, which require ~2.8x the FLOPs and 2.1x the GPU memory.

5. Significance and Claims

The paper claims that SNV provides a principled, buffer-free solution to catastrophic forgetting that is well-suited for resource-constrained and privacy-sensitive environments.

Privacy: By eliminating the need to store past data, SNV avoids the privacy risks associated with data retention regulations (e.g., GDPR).
Scalability: It avoids the unbounded memory growth of dynamic architecture methods.
Effectiveness: The authors argue that simply storing and replaying samples may not be the optimal strategy; instead, identifying and preserving the "right" neurons within a fixed network is a more robust approach for strict continual learning.
Limitations: The authors acknowledge that the post-task Shapley estimation step adds computational cost, which may become a bottleneck for very large models. Future work aims to approximate these values online to eliminate the separate estimation phase.

The work positions SNV as a strong alternative to memory-based approaches, demonstrating that high performance in continual learning is achievable without violating strict data access constraints.