arxiv: 2604.08939 · v1 · submitted 2026-04-10 · 💻 cs.LG

Recognition: no theorem link

Delve into the Applicability of Advanced Optimizers for Multi-Task Learning

Chunyan Miao, Linxiao Cao, Peilin Zhao, Pengcheng Wu, Zhipeng Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:39 UTC · model grok-4.3

classification 💻 cs.LG

keywords multi-task learningadvanced optimizersadaptive momentumMuon optimizergradient updatesoptimization-based MTLAPT framework

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The pith

Advanced optimizers underperform in multi-task learning because instant-derived gradients contribute only marginally to parameter updates.

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

The paper argues that optimization-based multi-task learning methods lose effectiveness with advanced optimizers. The gradients computed at each step end up contributing little to the actual changes in model parameters. This mismatch stops the methods from properly balancing or de-conflicting tasks during training. The authors further observe that the Muon optimizer naturally behaves like a multi-task learner, so the gradients supplied to its orthogonalization step become especially important. To correct the mismatch, they introduce the APT framework, which adds an adaptive momentum mechanism to better combine advanced optimizers with MTL objectives and includes a light direction preservation step to help Muon. Experiments on four standard MTL datasets show consistent gains when APT is added to existing approaches.

Core claim

We empirically identify that their effectiveness is often undermined by an overlooked factor when employing advanced optimizers: the instant-derived gradients play only a marginal role in the actual parameter updates. This discrepancy prevents MTL frameworks from fully releasing its power on learning dynamics. Furthermore, we observe that Muon-a recently emerged advanced optimizer-inherently functions as a multi-task learner, which underscores the critical importance of the gradients used for its orthogonalization. To address these issues, we propose APT (Applicability of advanced oPTimizers), a framework featuring a simple adaptive momentum mechanism designed to balance the strengths of the

What carries the argument

The APT framework, consisting of an adaptive momentum mechanism that balances advanced optimizers with MTL goals plus a light direction preservation method to aid Muon's orthogonalization.

If this is right

Existing optimization-based MTL methods gain performance by incorporating APT without changing their core logic.
The marginal influence of instant gradients accounts for underperformance in many advanced-optimizer MTL pairings.
Muon can serve as an effective multi-task learner once its orthogonalization receives preserved directions.
Performance improvements appear consistently across four mainstream MTL datasets and multiple base methods.

Where Pith is reading between the lines

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

The same marginal-gradient issue may appear in other optimization settings that involve conflicting objectives, such as continual learning.
Adaptive-momentum corrections similar to APT could be tested with newer optimizers or in single-task regimes to check generality.
Direction preservation might extend to other methods that rely on orthogonalization or projection steps.

Load-bearing premise

That the marginal role of instant-derived gradients is the primary cause of limited performance when using advanced optimizers in MTL, and that adding adaptive momentum plus direction preservation will resolve it without creating new instabilities or artifacts.

What would settle it

An experiment that measures the actual fraction of parameter update attributable to instant gradients in MTL with and without APT, or that removes the adaptive momentum component and checks whether the reported performance gains disappear.

Figures

Figures reproduced from arXiv: 2604.08939 by Chunyan Miao, Linxiao Cao, Peilin Zhao, Pengcheng Wu, Zhipeng Zhou.

**Figure 1.** Figure 1: Illustration of the impact of EMA in advanced optimizer for MTL. Here we adopt gupdate = 0.9 ∗ gmom + 0.1 ∗ gmtl as the example. Furthermore, Muon—a recently proposed advanced optimizer—requires additional consideration. We show that Muon can be interpreted as an implicit MTL learner, as its orthogonalization operation tends to amplify components shared among task gradients. This property places stricte… view at source ↗

**Figure 2.** Figure 2: Similarity and project norm comparison. 0 100 200 300 400 500 600 700 Singular Value Index 10 10 10 8 10 6 10 4 10 2 10 0 Normalized Singular Value (Log Scale) Gradient Spectrum Analysis: MGDA vs Muon (Re-balancing Demonstration) MGDA (Eff Rank: 415.35) Muon Transformed (Eff Rank: 601.98) Task B Pure (Eff Rank: 396.20) Task A Pure (Eff Rank: 402.21) (a) MGDA. 0 100 200 300 400 500 600 700 Singular Value In… view at source ↗

**Figure 3.** Figure 3: Effective rank comparison. or Nash-MTL, etc). In the following, we first reveal a fundamental mismatch between the momentum mechanism used in advanced optimizers and the objectives of MTL. We then further discuss the applicability and unique characteristics of the Muon optimizer in the MTL setting. 3.2 Does MTL Work Like We Expect? Previous work has rarely examined the impact of EMA–based momentum mechanis… view at source ↗

**Figure 4.** Figure 4: Effect of momentum on toy example. Furthermore, as illustrated in Figures 2(a)-(c), while momentum may undermine the immediate de-conflicting capabilities of MTL, it maintains a relatively balanced similarity across all tasks. This suggests that the momentum mechanism effectively mitigates the dominance of any single task. We define this behavior as amortized deconflicting, where the benefits of MTL are … view at source ↗

**Figure 5.** Figure 5: Toy example comparison. Evaluation Metric: In addition to individual task performance, we incorporate a widely used aggregate metric, ∆m% [Maninis et al., 2019]. This metric evaluates the overall performance degradation relative to independently trained models, which serve as reference oracles. The formal definition of ∆m% is: ∆m% = 1 K X K k=1 (−1)δk (Mm,k − Mb,k) Mb,k × 100 (13) [PITH_FULL_IMAGE:figures… view at source ↗

read the original abstract

Multi-Task Learning (MTL) is a foundational machine learning problem that has seen extensive development over the past decade. Recently, various optimization-based MTL approaches have been proposed to learn multiple tasks simultaneously by altering the optimization trajectory. Although these methods strive to de-conflict and re-balance tasks, we empirically identify that their effectiveness is often undermined by an overlooked factor when employing advanced optimizers: the instant-derived gradients play only a marginal role in the actual parameter updates. This discrepancy prevents MTL frameworks from fully releasing its power on learning dynamics. Furthermore, we observe that Muon-a recently emerged advanced optimizer-inherently functions as a multi-task learner, which underscores the critical importance of the gradients used for its orthogonalization. To address these issues, we propose APT (Applicability of advanced oPTimizers), a framework featuring a simple adaptive momentum mechanism designed to balance the strengths between advanced optimizers and MTL. Additionally, we introduce a light direction preservation method to facilitate Muon's orthogonalization. Extensive experiments across four mainstream MTL datasets demonstrate that APT consistently augments existing MTL approaches, yielding substantial performance improvements.

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.

Desk Editor's Note private letter to a colleague

The paper flags that current gradients get sidelined in advanced optimizers for MTL and offers APT as a fix, but the evidence for the core mechanism is thin on quantification and controls.

read the letter

This paper points out that advanced optimizers in multi-task learning often sideline the current gradient in parameter updates, limiting how well MTL balancing works, and introduces APT to address it with adaptive momentum and direction preservation for Muon. The new parts are the identification of that gradient marginality problem and the APT framework that tries to balance advanced optimizer strengths with MTL needs. They also highlight that Muon inherently supports multi-task learning through its orthogonalization step. The experiments across four standard datasets show that adding APT improves existing MTL approaches, which is a practical plus for anyone training shared models. It does well in grounding the proposal in observed optimization behavior and delivering consistent gains in the tests. The Muon insight adds a useful angle on why certain optimizers might already help with task interference. The main weakness is that the marginal role of instant gradients is stated as an empirical finding but without a clear quantitative measure or isolated ablation. It's possible the performance lifts come from other aspects of the adaptive mechanism or tuning rather than specifically giving more weight to current gradients. The direction preservation method for Muon lacks a controlled test confirming it maintains the multi-task benefits without side effects. This work is for people in the MTL optimization area looking for incremental improvements to training dynamics. Readers who care about practical enhancements in vision and NLP shared backbones will find value in the results. It deserves peer review because the experiments provide evidence of gains and the problem is relevant, though revisions could strengthen the mechanistic claims. I would send it to referees.

Referee Report

3 major / 2 minor

Summary. The paper empirically identifies that advanced optimizers in optimization-based multi-task learning (MTL) undermine effectiveness because instant-derived gradients contribute only marginally to parameter updates. It further observes that the Muon optimizer inherently functions as a multi-task learner due to its orthogonalization step. To address these issues, the authors propose the APT framework, which includes an adaptive momentum mechanism to balance advanced optimizers with MTL and a light direction preservation method for Muon. Experiments on four mainstream MTL datasets show that APT augments existing MTL approaches with substantial performance improvements.

Significance. If the central empirical observation about marginal gradient contributions is rigorously quantified and the APT mechanisms are shown via controlled ablations to specifically restore gradient influence without new instabilities, the work could offer a practical enhancement for integrating advanced optimizers into MTL pipelines, leading to better learning dynamics across tasks. The observation that Muon acts as an inherent multi-task learner is a potentially useful insight if substantiated.

major comments (3)

[Abstract, §3] Abstract and §3: The central claim that 'instant-derived gradients play only a marginal role in the actual parameter updates' is load-bearing for the motivation but is presented as an unquantified empirical observation. No explicit metric (e.g., ratio of ||current_grad|| to total update norm or cosine similarity between current gradient and final update) is defined or reported, preventing isolation of this factor from other optimizer effects.
[§4] §4 (APT framework): The adaptive momentum mechanism is proposed to balance advanced optimizers and MTL by addressing the marginal gradient role, yet no ablation holds all other components fixed while varying only this mechanism. This leaves open the possibility that reported gains arise from generic hyper-parameter tuning or the direction-preservation term rather than the claimed restoration of instant-gradient influence.
[Experiments] Experiments section: Improvements are claimed across four MTL datasets, but the abstract and provided details give no information on baselines, number of runs, statistical tests, effect sizes, or controls for the Muon-specific direction preservation preserving the orthogonalization's multi-task property. This undermines evaluation of whether APT specifically resolves the identified issue.

minor comments (2)

[Title] The title uses inconsistent capitalization ('oPTimizers'); standardize for clarity.
[§4] Notation for the 'light direction preservation method' and its interaction with Muon's orthogonalization could be formalized with an equation or pseudocode to improve reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback, which highlights important areas for improving the rigor and clarity of our empirical claims and experimental validation. We have revised the manuscript to address each major comment directly.

read point-by-point responses

Referee: [Abstract, §3] Abstract and §3: The central claim that 'instant-derived gradients play only a marginal role in the actual parameter updates' is load-bearing for the motivation but is presented as an unquantified empirical observation. No explicit metric (e.g., ratio of ||current_grad|| to total update norm or cosine similarity between current gradient and final update) is defined or reported, preventing isolation of this factor from other optimizer effects.

Authors: We agree that an explicit metric strengthens the central claim. In the revised manuscript, we introduce and report the ratio of the L2 norm of the instant-derived gradient to the L2 norm of the total update (averaged over training steps in §3), along with cosine similarity between the current gradient and final update. These values confirm the marginal contribution (typically <10% of update norm) when advanced optimizers are used in MTL, isolating this factor from other effects. revision: yes
Referee: [§4] §4 (APT framework): The adaptive momentum mechanism is proposed to balance advanced optimizers and MTL by addressing the marginal gradient role, yet no ablation holds all other components fixed while varying only this mechanism. This leaves open the possibility that reported gains arise from generic hyper-parameter tuning or the direction-preservation term rather than the claimed restoration of instant-gradient influence.

Authors: We acknowledge the value of isolated ablations. The revised §4 now includes a controlled ablation that disables only the adaptive momentum mechanism while holding direction preservation, hyperparameters, and all other components fixed. Results demonstrate a clear performance degradation without momentum balancing, confirming its specific role in restoring instant-gradient influence rather than arising from tuning or the preservation term. revision: yes
Referee: [Experiments] Experiments section: Improvements are claimed across four MTL datasets, but the abstract and provided details give no information on baselines, number of runs, statistical tests, effect sizes, or controls for the Muon-specific direction preservation preserving the orthogonalization's multi-task property. This undermines evaluation of whether APT specifically resolves the identified issue.

Authors: We have expanded the Experiments section with full details: complete baseline descriptions and references, results from 5 independent runs (mean ± std), paired t-tests for significance (p < 0.05 reported), effect sizes (Cohen's d), and a dedicated control experiment verifying that the light direction preservation maintains Muon's orthogonalization multi-task property without new instabilities. These additions confirm APT specifically addresses the marginal gradient issue. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on empirical observations and independent experimental validation.

full rationale

The paper's derivation begins with an empirical observation about the marginal role of instant-derived gradients under advanced optimizers in MTL, notes Muon's inherent multi-task behavior from its orthogonalization step, and introduces APT as a new adaptive momentum mechanism plus light direction preservation. These elements are then validated through experiments on four MTL datasets showing performance gains. No load-bearing step reduces a prediction to a fitted parameter by construction, invokes self-citation as the sole justification for a uniqueness claim, or renames a known result via new coordinates. The framework components are presented as additions tested against baselines rather than tautological redefinitions of the inputs, rendering the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The paper relies on standard machine learning optimization assumptions and introduces new empirical mechanisms without first-principles derivation or external independent evidence beyond the reported experiments.

axioms (1)

standard math Standard assumptions about gradient-based optimization dynamics and convergence in neural network training.
Invoked implicitly when discussing how instant-derived gradients interact with parameter updates in advanced optimizers.

invented entities (2)

APT framework with adaptive momentum mechanism no independent evidence
purpose: To balance strengths of advanced optimizers and MTL by addressing gradient marginality
Newly proposed construct without derivation from prior theory or external validation beyond the four datasets.
Light direction preservation method for Muon no independent evidence
purpose: To facilitate Muon's orthogonalization process
Newly introduced technique without independent falsifiable prediction outside the paper's experiments.

pith-pipeline@v0.9.0 · 5506 in / 1616 out tokens · 49547 ms · 2026-05-10T16:39:10.811824+00:00 · methodology

discussion (0)

Reference graph

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