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arxiv: 2605.29592 · v1 · pith:67UIWI76new · submitted 2026-05-28 · 💻 cs.CV

Non-Forgetting Knowledge Allocation with Bi-level Competition for Class-Incremental Learning

Xiang Tan , Run He , Yawen Cui , Mengchen Zhao , Yan Wu , Tianyi Chen , Huiping Zhuang , Xiaonan Luo
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Guanbin Li
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Pith reviewed 2026-06-29 08:15 UTC · model grok-4.3

classification 💻 cs.CV
keywords class-incremental learningnon-forgetting allocatorbi-level competitionrecursive least-squaresadapter-based learningwinner-takes-allknowledge allocation
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The pith

A recursive least-squares allocator in class-incremental learning matches the accuracy of one trained on all data simultaneously.

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

The paper establishes that class-incremental learning with adapters can avoid forgetting by reformulating allocator training as a recursive least-squares problem, yielding performance equivalent to having all task data available at once. It then introduces bi-level competition mechanisms to allocate knowledge from task-specific adapters more effectively during inference by selecting the strongest contributor within each task and suppressing weaker ones across tasks. A sympathetic reader would care because this addresses the core tension in continual learning where models must adapt to new categories without losing old ones, using only pre-trained models and limited new data. The approach includes a stability enhancement process for old tasks.

Core claim

NoFA-BC constructs a non-forgetting allocator (NFA) by transforming the allocator training into a recursive least-squares problem and achieves an allocator equivalent to that trained with all data. Based on the NFA, a Bi-Level Competition (BLC) including an intra-task level Winner-Takes-All (WTA) mechanism and inter-task Last-Ones-Fall (LOF) elimination is proposed to provide better allocation of adapter knowledge. WTA extracts the most significant logit within a task to represent the adapter's contribution and LOF suppresses the irrelevant adapters. With BLC, participation ratio of each adapter can be tailored for each input. Moreover, a Stability Enhancement (SE) process is incorporated to

What carries the argument

The non-forgetting allocator (NFA) obtained by solving a recursive least-squares problem, which maintains equivalence to full-data training while respecting the no-access-to-past-data constraint in class-incremental learning.

If this is right

  • The allocator does not forget previous tasks as new ones are added.
  • Intra-task Winner-Takes-All selects the most significant logit per task to represent adapter contribution.
  • Inter-task Last-Ones-Fall eliminates irrelevant adapters across tasks.
  • Participation ratios of adapters are tailored per input.
  • Stability Enhancement improves old task performance.

Where Pith is reading between the lines

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

  • The recursive least-squares method could extend to other components prone to forgetting in continual learning setups.
  • Bi-level competition might apply to knowledge allocation in other multi-task or incremental scenarios beyond adapters.
  • Testing on a wider range of pre-trained models could reveal if the equivalence holds generally.

Load-bearing premise

The recursive least-squares formulation produces an allocator that does not forget previous tasks when new tasks are added sequentially under the class-incremental learning constraint that prevents access to past data.

What would settle it

Comparing the allocator trained recursively on sequential tasks to one trained on all tasks combined, using the same evaluation metrics on a held-out test set; a significant performance gap would falsify the equivalence claim.

Figures

Figures reproduced from arXiv: 2605.29592 by Guanbin Li, Huiping Zhuang, Mengchen Zhao, Run He, Tianyi Chen, Xiang Tan, Xiaonan Luo, Yan Wu, Yawen Cui.

Figure 1
Figure 1. Figure 1: When aggregating multiple adapters for inference, uniform utilization of all adapters leads to insufficient application of task-relevant knowledge. Conversely, prop￾erly allocating adapters optimally leverages task-specific knowledge, thereby enhancing classification accuracy. with the capability of learning new tasks when new categories arise continually, i.e., the ability of class-incremental learning (C… view at source ↗
Figure 2
Figure 2. Figure 2: The Overview of NoFA-BC. Left: Training Phase, assuming current task is 3. Task-specific adapters are trained per incremental stage while the autocorrelation and cross correlation matrix is continuously updated with the help of adapter A1. Right: The NoFA-BC dynamically regulates the participation of each adapters with the help of Bi-level Competition mechanism. SE is utilized to enhance the stability of f… view at source ↗
Figure 3
Figure 3. Figure 3: Accuracy curve of compared methods during CIL. We annotate the relative improvement of NoFA-BC above the runner-up method with numerical numbers at the last incremental stage. 4.3 Stability Enhancement Maintaining stability is a prevalent challenge in CIL scenarios. Conventionally, updates or expansions of model/modules (e.g., IA in our method) embody plas￾ticity through continual knowledge acquisition, wh… view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of the impact of Stability Compensation in ImageNet￾A B0 Inc20, ImageNet-R B0 Inc20. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Complementation ratio 70 75 80 85 Accuracy(%) ImageNet-R B0-Inc5 A AT [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualizations of NFA and BLC. Managing the utilization of different adapters improves classification [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

Class-Incremental Learning (CIL) with pre-trained models (PTMs) aims to sequentially adapt PTMs to new categories without forgetting old knowledge. Built upon PTMs, existing adapter-based methods mainly train models via distinct task-specific adapters, and present a uniform knowledge allocation for each adapter during inference. However, this allocation mechanism ignores the nature of task discrepancy and leads to suboptimal utilization of adapters. Also, under CIL constraint, an allocator is prone to forgetting when tasks evolve. To address these issues, we propose a Non-Forgetting Allocation with Bi-Level Competition (NoFA-BC). NoFA-BC constructs a non-forgetting allocator (NFA) by transforming the allocator training into a recursive least-squares problem and achieves an allocator equivalent to that trained with all data. Based on the NFA, a Bi-Level Competition (BLC) including an intra-task level Winner-Takes-All (WTA) mechanism and inter-task Last-Ones-Fall (LOF) elimination is proposed to provide better allocation of adapter knowledge. WTA extracts the most significant logit within a task to represent the adapter's contribution and LOF suppresses the irrelevant adapters. With BLC, participation ratio of each adapter can be tailored for each input. Moreover, a Stability Enhancement (SE) process is incorporated to further improve the performance of old tasks.

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 NoFA-BC for class-incremental learning (CIL) with pre-trained models and task-specific adapters. It introduces a Non-Forgetting Allocator (NFA) obtained by recasting allocator training as a recursive least-squares (RLS) problem, claimed to yield an allocator identical to the batch solution trained on all data seen so far. On top of the NFA it defines a Bi-Level Competition (BLC) consisting of an intra-task Winner-Takes-All (WTA) mechanism and an inter-task Last-Ones-Fall (LOF) elimination rule, together with a Stability Enhancement (SE) process, to produce input-dependent participation ratios for the adapters.

Significance. If the RLS equivalence can be shown to hold exactly under the CIL memory constraint and the BLC rules demonstrably improve allocation without introducing new forgetting, the method would supply a principled, memory-bounded alternative to uniform or heuristic adapter selection in PTM-based CIL.

major comments (2)
  1. [Abstract / §3] Abstract and §3 (NFA construction): the central claim that the RLS formulation produces an allocator 'equivalent to that trained with all data' is load-bearing for the non-forgetting guarantee, yet no derivation, normal-equation update, or proof that the chosen allocator loss admits an exact, fixed-size sufficient-statistic update under sequential task arrival is supplied; any loss of cross-task terms or rank deficiency would invalidate the identity.
  2. [§4 / Experiments] §4 (BLC) and experimental section: the WTA and LOF rules are presented as improving allocation, but without an ablation that isolates their contribution from the NFA itself or from the SE process, it is impossible to determine whether the reported gains are attributable to the bi-level competition or to other factors.
minor comments (1)
  1. [Abstract] The abstract contains no quantitative results or dataset names, which is atypical for a methods paper in this area and makes the strength of the empirical claims difficult to gauge from the opening paragraph.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and commit to revisions that strengthen the presentation of the NFA equivalence and the empirical validation of BLC.

read point-by-point responses

  1. Referee: [Abstract / §3] Abstract and §3 (NFA construction): the central claim that the RLS formulation produces an allocator 'equivalent to that trained with all data' is load-bearing for the non-forgetting guarantee, yet no derivation, normal-equation update, or proof that the chosen allocator loss admits an exact, fixed-size sufficient-statistic update under sequential task arrival is supplied; any loss of cross-task terms or rank deficiency would invalidate the identity.

    Authors: We agree that an explicit derivation is necessary to substantiate the equivalence claim under the memory constraints of CIL. In the revision we will add a dedicated subsection in §3 that derives the RLS update from the normal equations, shows that the chosen allocator loss (quadratic in the participation weights) admits an exact fixed-size sufficient statistic, and proves that no cross-task terms are lost when tasks arrive sequentially. This will directly address potential concerns about rank deficiency or approximation. revision: yes

  2. Referee: [§4 / Experiments] §4 (BLC) and experimental section: the WTA and LOF rules are presented as improving allocation, but without an ablation that isolates their contribution from the NFA itself or from the SE process, it is impossible to determine whether the reported gains are attributable to the bi-level competition or to other factors.

    Authors: We acknowledge the value of isolating the BLC components. The revised experimental section will include a new ablation table that evaluates (i) NFA alone, (ii) NFA + WTA, (iii) NFA + LOF, (iv) NFA + SE, and (v) the full NoFA-BC, reporting both accuracy and forgetting metrics. This will allow readers to attribute performance gains specifically to the intra-task WTA and inter-task LOF rules. revision: yes

Circularity Check

0 steps flagged

No circularity: RLS equivalence claim is a standard construction, not a reduction to inputs

full rationale

The abstract states that transforming allocator training into a recursive least-squares problem 'achieves an allocator equivalent to that trained with all data.' This is the standard exact property of RLS when the normal equations are updated via sufficient statistics; it does not reduce the claimed non-forgetting property to a fitted parameter or self-citation by construction. The BLC mechanisms (WTA, LOF) are presented as separate proposals for allocation and do not rely on the equivalence claim for their justification. No equations, self-citations, or ansatzes are quoted that would make any central result tautological. The derivation chain is therefore self-contained against external benchmarks for RLS.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach assumes the recursive least-squares solution provides the non-forgetting property without additional mechanisms beyond those stated.

axioms (1)
  • domain assumption The allocator training can be transformed into a recursive least-squares problem that maintains equivalence to full data training under incremental constraints.
    This is the core of the non-forgetting allocator as described in the abstract.

pith-pipeline@v0.9.1-grok · 5793 in / 1216 out tokens · 46447 ms · 2026-06-29T08:15:14.453562+00:00 · methodology

discussion (0)

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Reference graph

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