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arxiv: 2605.15877 · v1 · pith:DXL46QJ7new · submitted 2026-05-15 · 💻 cs.LG · cs.AI

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

Mohammad Ali Vahedifar , Abhisek Ray , Qi Zhang This is my paper

Pith reviewed 2026-05-20 20:24 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords continual learningcatastrophic forgettingShapley valuesneuron importancebuffer-free learningclass incremental learningtask incremental learning
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The pith

Shapley values can identify which neurons to freeze so a network learns new tasks without forgetting old ones or storing data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Shapley Neuron Valuation to score how much each neuron contributes to performance on tasks already learned. High-scoring neurons are frozen while others stay free to change, letting the same fixed network handle a sequence of tasks. This removes the need for replay buffers or growing the model size, two common costs in continual learning. A reader cares because many real systems must keep improving on new data without losing what they already know, yet most current fixes either use extra memory or change the architecture. The approach grounds the choice of which parts to protect in cooperative game theory rather than ad-hoc rules.

Core claim

We present Shapley Neuron Valuation (SNV), a framework that treats neurons as players in a cooperative game and computes their marginal contribution to the network's output on prior tasks. SNV then freezes neurons with the highest values to protect earlier knowledge while leaving lower-value neurons plastic for new learning. On ImageNet-1k this yields +2.88 percent accuracy in class-incremental learning and +6.46 percent in task-incremental learning over the strongest buffer-free baseline.

What carries the argument

Shapley Neuron Valuation (SNV), which assigns each neuron a value equal to its average marginal contribution across all possible coalitions of neurons, to decide which neurons must remain unchanged during subsequent training.

If this is right

  • SNV enables continual learning on large image datasets without storing past examples.
  • Accuracy gains appear in both class-incremental and task-incremental protocols.
  • The network size stays constant because only selected neurons are frozen rather than new layers added.
  • Neuron importance is computed once per task and then used to set a binary freeze mask.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same scoring could be applied to other layer types if an equivalent notion of 'neuron' is defined.
  • Periodic re-calculation of Shapley values after several tasks might further reduce forgetting under distribution shift.
  • Combining SNV with lightweight regularization on the plastic neurons could produce additive gains.

Load-bearing premise

That the importance ranking of neurons computed on past tasks will still mark the right neurons to protect when entirely new tasks arrive.

What would settle it

Run the same continual-learning schedule on ImageNet-1k but freeze neurons chosen at random instead of by SNV scores; if the accuracy gap over baselines vanishes, the method's advantage is not explained by the Shapley ranking.

Figures

Figures reproduced from arXiv: 2605.15877 by Abhisek Ray, Mohammad Ali Vahedifar, Qi Zhang.

Figure 1
Figure 1. Figure 1: An illustration of Shapley Neuron Values where for each task task t − 1, task t, and task t + 1, we identify and freeze the Neurons whose Shapley Values fall within the top r%. Neurons marked with specific colors indicate that the same Neuron appears within the top r% for t specific tasks. τi is each task’s top r% threshold. task can be reliably identified and structurally preserved. We propose Shapley Neu… view at source ↗
Figure 2
Figure 2. Figure 2: ACC evaluation for CIL across 10 tasks on each dataset. Each point represents the average classification accuracy evaluated after learning a given task. For example, the value at task 5 corresponds to the average accuracy of the model on the test sets of tasks 1 through 5 after completing training on task 5. For details, see [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Network parameter usage efficiency across datasets in the CIL scenario for 10 tasks. The dashed vertical lines indicate the critical pruning percentage where each method experiences significant accuracy degradation. A sharper decline at lower pruning percentages indicates more efficient usage of network capacity, as it suggests the method utilizes essential parameters with minimal redundancy. using a fixed… view at source ↗
Figure 4
Figure 4. Figure 4: Capacity analysis on CIFAR-100 and TinyImageNet for SNV. (a) Accuracy as a function of model capacity across incremental tasks. (b) Capacity versus Accuracy. However, WSN reaches only 64.00% on CIFAR-100 and 61.06% on Tiny-ImageNet at the same capacity (c=0.5), trailing SNV by 15.76 and 13.76 points respectively. This gap widens under tighter budgets: at c=0.03, SNV achieves 71.74% versus WSN’s 59.65% on C… view at source ↗
Figure 5
Figure 5. Figure 5: Computational cost of all compared methods across CIFAR-100, Tiny-ImageNet, and ImageNet-1k (Class-IL, 10 tasks). Left: total training FLOPs on a log scale. Right: peak GPU memory. 3.3. Computational Cost Comparison A natural concern with Shapley-based importance estima￾tion is cost: Monte Carlo sampling over Neuron coalitions adds computation that simpler proxies like Fisher infor￾mation avoid entirely [… view at source ↗
Figure 6
Figure 6. Figure 6: Performance evaluation metrics of continual learning methods. RAC is the Random model ACcuracy. 3. Removing the Cumulative Shapley Mask. We ex￾perimented with training without the cumulative Shapley mask and found that performance collapsed. This confirmed that the mask is a core mechanism: without it, the network fails to properly freeze parameters associated with previous tasks. 4. Allowing a Small Perce… view at source ↗
Figure 7
Figure 7. Figure 7: ACC evaluation comparison for the CIL for 20 tasks for each dataset. Each point represents the average classification accuracy evaluated after learning a given task, averaged over all tasks learned up to that point. For example, the value at task 10 corresponds to the average accuracy of the model on the test sets of tasks 1 through 10 after completing training on task 10. For details, see [PITH_FULL_IMAG… view at source ↗
Figure 8
Figure 8. Figure 8: ACC matrix for SNV for the CIL for 10 tasks for each dataset. proaches under current evaluation protocols? Are memory-based approaches even applicable in real￾world scenarios where privacy constraints, data retention policies, or legal regulations restrict storing past examples? F.2. CIL Analysis for CIFAR-100 and Tiny-ImageNet [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: ACC matrix for SNV for the CIL for 20 tasks for each dataset. stantial forgetting that a replay buffer must continuously patch. On Tiny-ImageNet the story is similar: DyTox leads by 3.7 points in accuracy but trails by 0.34 in backward transfer. For any deployment where data retention is re￾stricted, whether by privacy regulation, memory constraints, or both, SNV offers a compelling trade-off: nearly equiv… view at source ↗
Figure 10
Figure 10. Figure 10: Layer-wise Shapley Neuron Importance Across Datasets. T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 Task ID T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 Task ID 1.00 0.07 1.00 0.06 0.05 1.00 0.05 0.07 0.08 1.00 0.10 0.08 0.08 0.05 1.00 0.08 0.08 0.12 0.07 0.06 1.00 0.07 0.07 0.08 0.07 0.07 0.06 1.00 0.06 0.07 0.06 0.05 0.08 0.10 0.05 1.00 0.09 0.07 0.08 0.07 0.08 0.08 0.05 0.10 1.00 0.08 0.05 0.12 0.09 0.05 0.08 0.05 0.08 0.04 1.00 C… view at source ↗
Figure 11
Figure 11. Figure 11: Mask overlap between tasks across datasets for 10 tasks in the CIL scenario. reveal critical insights into SNV’s Neuron allocation strat￾egy: moderate overlap values (typically 0.3–0.5) indicate that SNV achieves an effective balance between knowledge sharing and interference avoidance. Shared Neurons fa￾cilitate positive forward transfer by reusing generalizable features across tasks, while distinct Neur… view at source ↗
read the original abstract

Continual learning enables neural networks to learn tasks sequentially without forgetting previously acquired knowledge. However, neural networks suffer from catastrophic forgetting, where learning new tasks degrades performance on earlier ones. We address this problem with Shapley Neuron Valuation (SNV), a principled framework that quantifies Neuron importance in continual learning, grounded in cooperative game theory. SNV selectively freezes important Neurons while keeping others plastic, enabling buffer-free continual learning without expanding architecture. Experiments on ImageNet-1k show that SNV consistently outperforms existing buffer-free methods. In particular, SNV improves accuracy by +2.88% in the class incremental learning and +6.46% in the task incremental learning scenarios compared to the second baseline.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes Shapley Neuron Valuation (SNV), a framework grounded in cooperative game theory to quantify the importance of individual neurons for continual learning. SNV computes Shapley values using a value function on the current task's data to rank neurons, then selectively freezes the most important ones while keeping others plastic. This approach aims to mitigate catastrophic forgetting in a buffer-free manner without expanding the network architecture. Experiments on ImageNet-1k report accuracy gains of +2.88% in class-incremental learning and +6.46% in task-incremental learning over the second baseline.

Significance. If the central claim holds, SNV would provide a principled, game-theoretic method for identifying neurons to protect across tasks, advancing buffer-free continual learning. The grounding in cooperative game theory and the scale of the ImageNet-1k experiments are strengths that could influence future work on neuron-level regularization. However, the significance hinges on whether task-local Shapley rankings generalize to prevent forgetting, which requires further substantiation.

major comments (2)
  1. [Abstract and §4 (Experiments)] Abstract and §4 (Experiments): The headline accuracy gains (+2.88% class-incremental, +6.46% task-incremental) are stated without derivation details for the Shapley approximation, baseline descriptions, statistical tests, error bars, or ablation results on the importance threshold or value function. This prevents assessment of whether the central claim is supported or influenced by post-hoc choices.
  2. [§3 (SNV framework)] §3 (SNV framework): The load-bearing assumption that Shapley values computed via value function v on the current task's data identify neurons whose freezing prevents forgetting on future tasks lacks supporting derivation or experiment. No analysis demonstrates that marginal contributions under v on task t correlate with cross-task preservation or stability under distribution shift; the selected neurons could simply be those most active on the current distribution.
minor comments (1)
  1. [§3] The notation for the characteristic function v(S) and how it is defined for neuron coalitions in the continual-learning setting could be clarified with an explicit equation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive suggestions. We address the major comments point by point below, providing clarifications and outlining the revisions we will make to strengthen the manuscript. We believe these changes will better support the central claims of our work on Shapley Neuron Valuation for continual learning.

read point-by-point responses

  1. Referee: [Abstract and §4 (Experiments)] The headline accuracy gains (+2.88% class-incremental, +6.46% task-incremental) are stated without derivation details for the Shapley approximation, baseline descriptions, statistical tests, error bars, or ablation results on the importance threshold or value function. This prevents assessment of whether the central claim is supported or influenced by post-hoc choices.

    Authors: We appreciate this observation and agree that more detailed reporting is necessary for reproducibility and to substantiate the claims. In the revised version, we will include: (1) the specific method for approximating Shapley values, such as the number of samples or the algorithm used (e.g., Monte Carlo sampling); (2) comprehensive descriptions of the baselines, including their implementation details and hyperparameters; (3) results presented with error bars from at least 3 independent runs and statistical tests (e.g., Wilcoxon signed-rank test) to confirm significance of the gains; (4) ablation studies varying the importance threshold (e.g., freezing top 10%, 20%, 30% neurons) and different value functions v (e.g., accuracy vs. loss-based). These additions will be placed in an expanded Section 4 and supplementary material. revision: yes

  2. Referee: [§3 (SNV framework)] The load-bearing assumption that Shapley values computed via value function v on the current task's data identify neurons whose freezing prevents forgetting on future tasks lacks supporting derivation or experiment. No analysis demonstrates that marginal contributions under v on task t correlate with cross-task preservation or stability under distribution shift; the selected neurons could simply be those most active on the current distribution.

    Authors: This is a valid concern regarding the theoretical grounding. The SNV framework posits that neurons with high Shapley values on the current task's data are those that contribute most to the model's performance on that task, and by freezing them, we preserve the representations learned so far. While we do not provide a formal proof that these marginal contributions directly correlate with future task stability, the empirical results demonstrate that this selection leads to better retention of previous knowledge compared to baselines that do not use such principled selection. To address this, in the revision we will add a subsection in §3 providing a more detailed motivation based on the cooperative game theory interpretation, arguing that high-value neurons are critical for the function approximation on the seen data distribution. We will also include an experiment analyzing the overlap of important neurons across tasks or the forgetting rate when using SNV vs. random freezing. However, we maintain that the primary validation comes from the end-to-end performance improvements on ImageNet-1k, which show reduced catastrophic forgetting. revision: partial

Circularity Check

0 steps flagged

SNV applies standard Shapley valuation to neurons with no reduction of the continual-learning claim to fitted inputs or self-citations

full rationale

The paper grounds SNV directly in cooperative game theory by defining neuron importance via the Shapley value of a value function v computed on the current task's data distribution. This construction is independent of the target continual-learning outcome (future-task accuracy after freezing); the link between current-task marginal contributions and cross-task stability is presented as an empirical hypothesis rather than a definitional identity. No equations equate the protection mask to a fit on forgetting metrics, no self-citation supplies a uniqueness theorem that forces the method, and the reported accuracy gains are measured on held-out future tasks rather than being recovered by construction from the valuation step itself. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into parameters and assumptions; the method appears to rest on treating neurons as cooperative-game players and on the existence of a computable importance threshold for freezing.

free parameters (1)
  • importance threshold for freezing
    A cutoff value must exist to decide which neurons to freeze; its selection is not described in the abstract.
axioms (1)
  • domain assumption Shapley values computed over neuron coalitions accurately reflect contribution to task performance in a neural network
    The framework is explicitly grounded in cooperative game theory as stated in the abstract.

pith-pipeline@v0.9.0 · 5648 in / 1197 out tokens · 56219 ms · 2026-05-20T20:24:13.089850+00:00 · methodology

discussion (0)

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