pith. sign in

arxiv: 2605.17839 · v3 · pith:7NLVGYVWnew · submitted 2026-05-18 · 💻 cs.LG · cs.AI

Balancing Knowledge Distillation for Imbalance Learning with Bilevel Optimization

Anh B.H. Nguyen , Ba Tho Phan , Viet Cuong Ta This is my paper

Pith reviewed 2026-05-20 12:37 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords knowledge distillationimbalanced learningbilevel optimizationlong-tailed dataper-sample weightinghard and soft lossesCIFAR
0
0 comments X

The pith

Bilevel optimization lets a weight network adapt hard and soft loss weights per sample during knowledge distillation on imbalanced data.

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

The paper introduces BiKD, a bilevel framework that trains a weight generation network to produce per-sample weights balancing hard and soft losses in knowledge distillation. The outer loop uses a small balanced validation set to guide the weights, while the inner loop trains the student with the resulting weighted losses. This replaces fixed weightings that become brittle on long-tailed data and allows the student to relax both loss terms. A multi-step SGD update improves optimization of the weight network. Experiments on long-tailed CIFAR-10 and CIFAR-100 show gains over prior balanced distillation approaches across different imbalance ratios.

Core claim

We propose BiKD -- a bilevel framework that dynamically balances hard and soft losses for each sample. We employ a weight generation network that produces adaptive per-sample weights, guided by a small balanced validation set. The student is now trained with an unconstrained combination of weighted hard and soft losses, allowing the student to relax both terms. We further propose a multi-step SGD strategy to optimize the weight model more accurately and efficiently. Experiments on long-tailed CIFAR-10/100 show that our approach surpasses recent balanced distillation methods across imbalance factors.

What carries the argument

BiKD bilevel framework whose weight generation network outputs adaptive per-sample weights for the hard and soft losses, with the outer loop optimized on a small balanced validation set.

If this is right

  • The student learns from imbalanced data without being locked into a single fixed ratio between hard and soft losses.
  • Per-sample weight adaptation produces higher accuracy on long-tailed CIFAR-10 and CIFAR-100 than recent reweighting baselines at multiple imbalance factors.
  • Multi-step SGD updates improve the accuracy and stability of the learned weight generator compared with single-step alternatives.

Where Pith is reading between the lines

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

  • The same bilevel structure could be applied to distillation tasks outside image classification where class imbalance or loss-term conflicts also arise.
  • If the small validation set is drawn from a different distribution than the test data, the learned weights may fail to generalize even when they perform well on the validation set itself.
  • Computational cost of the outer loop may limit direct scaling to very large teacher-student pairs unless the weight network is kept small.

Load-bearing premise

A small balanced validation set is available and sufficiently representative to guide the outer-loop optimization of the weight generation network without introducing bias or overfitting that would invalidate the per-sample weight adaptation on the imbalanced training distribution.

What would settle it

Removing the balanced validation set from the outer loop and retraining on the same long-tailed CIFAR splits, then observing performance no better than fixed-weight distillation baselines, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.17839 by Anh B.H. Nguyen, Ba Tho Phan, Viet Cuong Ta.

Figure 1
Figure 1. Figure 1: This figure illustrates the difference between the online optimization and [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: This figure illustrates our framework. 3.4 Analysis of the meta model weighting mechanism We detail how the meta model generates the weights for the hard and soft losses in the training objective. Under the bilevel framework, w hard prevents the student from biasing toward majority class samples, while w soft encourages the student to follow informative teacher signals during distillation. The meta paramet… view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of the meta outputs after training process with long-tailed [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: In the left subfigure, the confusion matrix for the Vanilla KD and ours [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Knowledge distillation transfers knowledge from a high capacity teacher to a compact student using a mixture of hard and soft losses. On imbalanced data, a fixed weighting between hard and soft losses becomes brittle the learning process. Recent studies try to reweight these components in long-tailed settings. However, most of these methods do not adapt weights at the sample-wise level and do not take into account the students behavior during training. To address this, we propose BiKD -- a bilevel framework that dynamically balances hard and soft losses for each sample. We employ a weight generation network that produces adaptive per-sample weights, guided by a small balanced validation set. The student is now trained with an unconstrained combination of weighted hard and soft losses, allowing the student to relax both terms. We further propose a multi-step SGD strategy to optimize the weight model more accurately and efficiently. Experiments on long-tailed CIFAR-10/100 show that our approach surpasses recent balanced distillation methods across imbalance factors.

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 / 2 minor

Summary. The manuscript introduces BiKD, a bilevel optimization framework for knowledge distillation on imbalanced (long-tailed) data. A weight generation network produces adaptive per-sample weights to balance hard and soft losses; these weights are optimized in the outer loop using a small balanced validation set. The student is trained on an unconstrained combination of the weighted losses, with a multi-step SGD strategy proposed for the weight model. Experiments on long-tailed CIFAR-10/100 report that BiKD surpasses recent balanced distillation baselines across imbalance factors.

Significance. If the central claims hold, the work provides a concrete bilevel mechanism for sample-wise adaptive loss balancing in distillation under class imbalance, moving beyond fixed or class-level reweighting schemes. The multi-step SGD optimization and explicit use of a validation-driven outer loop are technically interesting and could inform follow-on work in adaptive KD. However, the practical significance is tempered by the dependence on a small balanced validation set whose representativeness is not thoroughly validated.

major comments (2)
  1. [Method / bilevel framework] The bilevel setup (described in the abstract and method) claims that the weight generation network produces per-sample adaptations that validly balance hard/soft losses on the imbalanced training distribution. This claim is load-bearing and rests on the assumption that the small balanced validation set is representative and does not induce bias or overfitting in the outer-loop optimization; no sensitivity analysis to validation-set size, no distribution-shift experiments between val and train, and no ablation on bilevel stability are reported.
  2. [Experiments] Experiments section: superiority is asserted over recent balanced distillation methods, yet the manuscript provides no details on hyperparameter search protocols for baselines, no ablation isolating the contribution of the bilevel component versus the multi-step SGD, and no convergence or stability diagnostics for the outer-loop optimization. These omissions make it difficult to attribute gains specifically to the proposed framework.
minor comments (2)
  1. [Method] Notation for the per-sample weight generation and the exact form of the unconstrained combined loss could be stated more explicitly (e.g., with an equation reference) to improve reproducibility.
  2. [Abstract] The abstract states that the student 'relaxes both terms'; a brief clarification of what 'relax' means in the loss formulation would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment point by point below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: [Method / bilevel framework] The bilevel setup (described in the abstract and method) claims that the weight generation network produces per-sample adaptations that validly balance hard/soft losses on the imbalanced training distribution. This claim is load-bearing and rests on the assumption that the small balanced validation set is representative and does not induce bias or overfitting in the outer-loop optimization; no sensitivity analysis to validation-set size, no distribution-shift experiments between val and train, and no ablation on bilevel stability are reported.

    Authors: We agree that the representativeness of the small balanced validation set is a key assumption underlying the bilevel framework. The manuscript follows common practice in long-tailed learning by employing such a set to guide the outer loop. To strengthen the presentation, we will add a sensitivity analysis with respect to validation-set size, include targeted experiments that introduce controlled distribution shifts between validation and training data, and report an ablation examining the stability of the bilevel optimization. revision: yes

  2. Referee: [Experiments] Experiments section: superiority is asserted over recent balanced distillation methods, yet the manuscript provides no details on hyperparameter search protocols for baselines, no ablation isolating the contribution of the bilevel component versus the multi-step SGD, and no convergence or stability diagnostics for the outer-loop optimization. These omissions make it difficult to attribute gains specifically to the proposed framework.

    Authors: We acknowledge that additional experimental details would improve clarity and attribution of results. In the revised manuscript we will document the hyperparameter search protocols applied to all baselines. We will also insert an ablation that isolates the bilevel optimization component from the multi-step SGD strategy, and we will include convergence curves together with stability metrics for the outer-loop optimization. revision: yes

Circularity Check

0 steps flagged

No significant circularity; BiKD bilevel setup is a constructive proposal grounded in external validation set

full rationale

The paper defines BiKD as a bilevel optimization method in which an outer loop optimizes a weight generation network on a small balanced validation set to produce per-sample weights for an unconstrained combination of hard and soft losses in the inner loop. This is an explicit algorithmic construction rather than a reduction of any claimed result to its own inputs by definition. No equations or steps in the abstract or described framework rename fitted quantities as predictions, import uniqueness via self-citation, or smuggle ansatzes; the experimental claims rest on comparisons to baselines rather than tautological equivalence. The derivation chain remains self-contained against the external validation set as independent grounding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters or axioms; the method implicitly assumes the existence of a representative balanced validation set and stable bilevel optimization.

pith-pipeline@v0.9.0 · 5697 in / 1141 out tokens · 46607 ms · 2026-05-20T12:37:36.405995+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.