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REVIEW 4 major objections 5 minor 45 references

Unprejudiced Training Auxiliary Tasks Makes Primary Better: A Multi-Task Learning Perspective

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Auxiliary tasks trained without bias improve the primary task in multi-task learning.

desk verdict Solid empirical MTL paper with a new two-stage weighting idea, but an undefined mapping and some inconsistent tables keep it from being reproducible as submitted. read the letter →

arxiv 2412.19547 v1 pith:3MKEAPOD submitted 2024-12-27 cs.CV

Yuanze Li , Chun-Mei Feng , Qilong Wang , Guanglei Yang , Wangmeng Zuo This is my paper · ORCID
classification cs.CV
keywords multi-tasklearningauxiliarytaskstaskweightinguncertaintyestimationgradientbalancingpseudo-labelrobustnessdensepredictionencoder-decodernetworks
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Multi-task learning with auxiliary tasks usually gives the auxiliary losses much smaller weights than the primary loss, so the auxiliary decoders are undertrained. This paper argues that undertrained auxiliary tasks actively hurt the primary task, and proposes Impartial Auxiliary Learning (IAL), which trains every task's decoder with weights derived only from that task's uncertainty, then feeds the encoder with auxiliary gradients that are re-normalized to the primary gradient norm and scaled by an uncertainty-dependent weight below 1. The central claim is that this makes auxiliary tasks better trained, and that this in turn improves the generalization and accuracy of the primary task. The paper reports that IAL achieves the best relative multi-task improvement (delta-MTL) among compared methods on NYUv2, Cityscapes, PASCAL-Context, and Multi-CIFAR100, and remains beneficial when noisy pseudo-labels from large pre-trained models are added as auxiliary tasks. If the paper is right, a simple weighting scheme can replace careful auxiliary-task selection and still lift primary-task performance.

What carries the argument

The central object is the two-stage loss decomposition around the shared encoder. In the decoder stage, task-dependent homoscedastic uncertainty $\sigma_t$ is estimated from each task's own loss via the objective $L_{\mathrm{MTL}}=\sum_t \frac{1}{2\sigma_t^2}L_t + \log\sigma_t$, so each decoder's weight depends only on its own output. In the encoder stage, the auxiliary task's contribution is $f(\sigma_t)\operatorname{Norm}(\nabla_z L_t)$, where $\operatorname{Norm}(\nabla_z L_t)=\frac{|\nabla_z L_{\mathrm{pri}}|}{|\nabla_z L_t|}\nabla_z L_t$ re-scales the auxiliary gradient to the primary gradient's magnitude, and $f(\sigma_t)=\min(1,g(1-\sigma_t))$ maps uncertainty to a weight in $[0,1)$; the mapping $g(\cdot)$ is not specified. This mechanism lets the framework train auxiliary decoders without prejudice while still guaranteeing the primary task's dominance in the shared encoder, so that better-trained auxiliary tasks can transfer knowledge to the primary task.

What would settle it

Train IAL on a dense-prediction benchmark while replacing the uncertainty weights with a deliberately scrambled ordering of the same per-task uncertainty values: if delta-MTL stays roughly the same, uncertainty ranking is not what drives the gain; if it drops, the ordering is load-bearing. A complementary test is to add an auxiliary task whose labels are randomized after it is well learned; the method should downweight it and keep primary performance near the no-auxiliary baseline, whereas a method that merely trains all tasks equally would suffer negative transfer.

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Extended reading notes

Core claim

The paper's load-bearing claim is that inadequate training of auxiliary tasks is a main cause of poor primary-task performance in multi-task learning, and that fixing this rather than merely filtering out task interference is what unlocks positive transfer. Its proposed IAL framework splits optimization into two stages: in the decoder stage, each task loss is weighted by $1/(2\sigma_t^2)$ with a learned task-dependent uncertainty $\sigma_t$, so auxiliary decoders are trained as thoroughly as the primary decoder; in the encoder stage, auxiliary gradients are first re-normalized to the magnitude of the primary gradient and then weighted by $f(\sigma_t)=\min(1,g(1-\sigma_t))$, keeping the primary task dominant while letting well-trained auxiliary tasks contribute more. The reported experiments support the claim: on NYUv2 IAL records the best delta-MTL among all compared methods ($-0.44\%$), on Cityscapes it records $+8.22\%$, and in a noisy setting where two pseudo-tasks built from pre-trained model predictions are added, IAL still improves the primary tasks ($+1.99\%$ on NYUv2 and $+8.90\%$ on Cityscapes) while baselines degrade. The paper concludes that better-optimized auxiliary tasks lead to improved primary-task performance, and that uncertainty estimated from each task's own loss is a usable measure of the auxiliary task's training level.

Load-bearing premise

The load-bearing premise is that the uncertainty $\sigma_t$ estimated from a task's own loss is a faithful measure of that task's training quality, so lower uncertainty means the auxiliary task is well trained and will transfer positively to the primary task; the mapping $g(\cdot)$ that turns uncertainty into an encoder weight is never specified, so if uncertainty does not track useful transfer, the encoder weighting has no sound basis.

Editorial extensions

If this is right

  • If IAL is right, a single weighting scheme—uncertainty for decoders, uncertainty plus gradient norm for the encoder—is enough to beat task-specific weighting heuristics and meta-learned weights on standard dense-prediction benchmarks.
  • Because the method improves the primary task by improving auxiliary-task training, even auxiliary tasks chosen for their similarity to the primary task are only useful if they are trained to a comparable degree.
  • The pseudo-task experiments imply that noisy auxiliary labels from large pre-trained models can be exploited rather than discarded; the weighting can suppress harmful tasks while letting informative ones contribute, expanding the available auxiliary data without manual annotation.
  • The results across NYUv2, Cityscapes, PASCAL-Context, and Multi-CIFAR100 suggest the benefit is not limited to dense prediction; classification and multi-domain settings also see primary-task gains.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves $g(\cdot)$ unspecified; a natural test is whether any monotone mapping that ranks tasks by uncertainty reproduces the gains, which would show that the ordering, not the exact function, is what matters.
  • The pseudo-task setup opens a semi-supervised variant the paper does not explore: use a frozen large model to label an unlabeled dataset, and rely on the weighting to suppress domain-shifted labels while keeping primary-task training stable.
  • The failure-case analysis suggests equal training alone can cause negative transfer; a direct comparison of decoder-impartial-only versus encoder-gated variants on a strongly conflicting task pair would isolate where the encoder gate matters.
  • One could connect this to gradient-projection methods by replacing the norm re-scaling with orthogonal projection while keeping the uncertainty ranking; the ablations suggest uncertainty ordering would still be the main driver.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes an Impartial Auxiliary Learning (IAL) framework for multi-task learning with a designated primary task. The method operates in two stages: in the decoder stage, task-specific decoders are trained with uncertainty-based weighting (Eq. 3) so that each task's decoder is trained independently of the primary task; in the encoder stage, auxiliary-task gradients are reweighted by a function of the same uncertainty (Eq. 9) and normalized in norm to the primary-task gradient (Eq. 8) before being summed with the primary-task gradient (Eq. 7). The authors evaluate on NYUv2, Cityscapes, PASCAL-Context, and Multi-CIFAR100, including settings where two large-scale pre-trained models provide noisy pseudo auxiliary tasks, and report that the method improves primary-task performance relative to existing task-weighting baselines. The central claim is that inadequately trained auxiliary tasks hurt the primary task, and that balancing auxiliary-task training through uncertainty weights and gradient-norm normalization improves the primary task.

Significance. If the central claim holds, the paper offers a simple and computationally light mechanism for improving a primary task in multi-task learning, with a distinctive focus on the training quality of auxiliary tasks rather than only on minimizing interference. The empirical evaluation is a genuine strength: four benchmarks, multiple tasks per benchmark, five random seeds, reimplemented baselines, and a set of ablations (Tables VIII-XI) that separately assess gradient normalization, uncertainty-based weighting, and impartial decoder training. The pseudo-task experiments address an interesting and practically relevant robustness question. However, the load-bearing mechanism is incompletely specified: the mapping g in Eq. (9) is never defined, and the claim that uncertainty sigma_t measures a task's 'training level' is not validated beyond a correlation with training loss. If the missing specification and the internal inconsistencies in the pseudo-task and ablation tables are fixed, the empirical contribution could be valuable for the multi-task learning community.

major comments (4)
  1. [III-C, Eq. (9)] The function g(.) in Eq. (9) is never defined. This is load-bearing because f(sigma_t) determines the encoder-stage weight of every auxiliary task, and the statement in Section IV-G5 that 'these weights typically do not exceed 0.6' cannot be checked or reproduced without knowing g. Please provide the explicit form of g, its hyperparameters, and the admissible range of sigma_t; if sigma_t can exceed 1, the argument (1 - x) to g must also be defined and its behavior outside the nominal range clarified.
  2. [III-B and IV-G3] The claim that task uncertainty sigma_t measures a task's 'training level' (defined in Section III-B as generalization performance) is not established. From Eqs. (3)-(4), the stationary point satisfies sigma_t^2 approx L_t, so sigma_t tracks the instantaneous training loss, not validation performance or positive transfer to the primary task. The fixed-head experiment in Section IV-G3 is intended to support this, but the text says the uncertainty of the fixed (broken) depth task 'obviously drops', which is the opposite of what the proposed weighting direction would predict if the fixed task is poorly trained. Moreover, Table X appears to report the pseudo-task results rather than the standard NYUv2 numbers (see Major Comment 4). Please provide a direct correlation or intervention analysis, for example plotting sigma_t against per-task validation metrics over training, or deliberately degrading an auxiliary task and showing that f(sigma_t) decreases and the primary-task weight protects the encoder.
  3. [III-C, Eqs. (6)-(10)] The encoder-stage update is not the gradient of the loss in Eq. (6). Eq. (7) replaces each gradient nabla_z L_t with the normalized gradient Norm(nabla_z L_t) from Eq. (8), which is not a gradient of L_t, so the method does not optimize a single well-defined objective. Additionally, the algorithm in Section III-C first updates the decoders and uncertainty (step 2) and then computes shared-feature gradients from Eq. (6) using the same forward activations (step 3); after the decoder update, those activations are stale. Please specify the exact computation order, for example whether nabla_z L_t is computed before the decoder update and whether a second forward pass is used, and state explicitly that Eq. (7) is a modified update rule rather than a gradient of Eq. (6).
  4. [IV-D2/D3 and Tables IV, V, X] The noisy-task results are internally inconsistent. Table IV reports Ours with Delta-MTL +1.99% on NYUv2 and Table V reports +8.90% on Cityscapes, yet Section IV-D2 states that 'with token labels -0.45% v.s. -0.44% without auxiliary tasks' and Section IV-D3 states that the pseudo tasks 'do not promote but drop in some tasks'. In addition, Table X (ablation 'Influence of Worse Auxiliary Tasks') lists Ours as 0.5732/44.82/19.36 with Delta-MTL +2.43%, which is exactly the Table IV pseudo-task row, not the standard NYUv2 row from Table I (0.5751/44.60/20.62, -0.44%). The ablation conclusions in Section IV-G3 therefore appear to be based on a configuration that is not the standard NYUv2 benchmark. Please correct the tables and text, and label each table with the exact task configuration (with or without pseudo tasks, with or without token labels).
minor comments (5)
  1. [III-C, Eq. (4)] Eq. (4) contains '1/x' where the derivative of log sigma_t should appear; this should be 1/sigma_t.
  2. [IV-C1, Eq. (11)] The definition of Delta-MTL is garbled: 'For the task li = 1, the lower values of M_i (classification accuracies), the better performance' and 'For the task li = 0, the higher values of M_i (L1 errors for depth prediction)' mix the two cases. It should read: li = 1 for lower-is-better metrics such as errors, li = 0 for higher-is-better metrics such as accuracies.
  3. [IV-G4] The heading 'Inplacement of the uncertainty in the encoder stage' should be 'Replacement of the uncertainty in the encoder stage'.
  4. [Abstract and Introduction] The phrase 'regardless the noise auxiliary tasks' pseudo labels' is grammatically incomplete; suggest 'regardless of noise in the auxiliary tasks' pseudo labels'.
  5. [III-C, step 3] Step 3 of the algorithm refers to Eq. (6) as the objective, but the actual encoder update uses the normalized gradient in Eq. (7) and Eq. (8); please reference the equations consistently so the reader can reproduce the update.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the encoder-stage weighting is a heuristic proxy for auxiliary-task quality, not a fitted prediction of the primary result, and no load-bearing self-citations were found.

full rationale

The paper's derivation chain is a two-stage weighting scheme. In the decoder stage, Eq. (3) uses Kendall et al.'s uncertainty weighting to train each task-specific decoder independently, with sigma_t updated from that task's own loss via Eq. (4). In the encoder stage, Eqs. (6)-(9) weight auxiliary-task gradients by f(sigma_t), where sigma_t is inherited from the decoder stage. The skeptical worry is that sigma_t is fit to the auxiliary training loss, so f(sigma_t) is ultimately a function of that same loss, making the encoder weighting a loss-based reweighting rather than a genuine measure of 'training level'. This is a legitimate correctness concern, but it is not circularity under the paper's own equations: the claimed outcome is primary-task performance measured on held-out benchmarks (Tables I, III-VII) against external baselines, and that outcome is not defined in terms of sigma_t. Even if one rewrites f(sigma_t) as a function of L_t at the stationary point of Eq. (4), the measured Delta-MTL is not a tautology; it is an empirical result that could have gone the other way. The paper additionally provides external, falsifiable checks of the proxy: the fixed-head experiment in Sec. IV-G3 and the alternative-metric comparison in Table XI (Sec. IV-G4). Those checks may be imperfect, and the mapping g(.) in Eq. (9) is indeed left unspecified, but this is a reproducibility/rigor limitation rather than an input-output equivalence. The only self-citation is reference [6] (ControlVideo), which appears as part of a general range citation in the introduction and is not load-bearing for any of the paper's claims. The Conclusion's statement that the shared-encoder enhancement mechanism is underexplored is an honest scope limitation. No step in the derivation reduces by construction to its own input, so the circularity score is 0.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the assumption that uncertainty estimated from a task's own loss is a valid proxy for how well that task is trained and how positively it transfers to the primary task. This is not derived, only checked empirically in the fix-head ablation. The decoder uncertainty weights are borrowed verbatim from Kendall et al. [16]; the encoder weight function is a heuristic whose map g is never specified.

free parameters (4)
  • Initial auxiliary task weight = 0.1
    All task weightings initialized to 0.1 (Sec. IV-B), a hand-set hyperparameter.
  • Uncertainty weight learning rate = hand-selected per dataset
    Sec. IV-B states the learning rate to update these weightings is hand-selected for each dataset.
  • Task-dependent uncertainty sigma_t = optimized during training
    sigma_t is learned from each task's loss via Eq. (3) and then used to weight the same task in the encoder stage.
  • Mapping function g in Eq. (9) = unspecified
    The exact form of g(.) is never given; the resulting auxiliary weights are stated to stay below 0.6 in experiments, implying a specific hand-chosen mapping.
assumptions (4)
  • domain assumption Task-dependent homoscedastic uncertainty is a valid measure of auxiliary task training level
    Invoked via Eq. (9); support comes only from the fix-head ablation in Sec. IV-G3.
  • domain assumption Normalizing auxiliary gradient norms to the primary task gradient norm preserves primary-task dominance without distorting useful gradient information
    Introduced in Eq. (8); a heuristic with no theoretical justification.
  • domain assumption Better-trained auxiliary tasks transfer positively to the primary task
    Core premise of Sec. I and III-B; supported only by the empirical ablations.
  • domain assumption Kendall et al.'s uncertainty weighting correctly balances decoder training
    Adopted verbatim in Eq. (3) from [16].

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Cite this review

Pith. "Pith review of Unprejudiced Training Auxiliary Tasks Makes Primary Better: A Multi-Task Learning Perspective." pith.science (2026). https://pith.science/paper/3MKEAPOD

@misc{pith2026241219547,
  author       = {Pith},
  title        = {Pith review of: Unprejudiced Training Auxiliary Tasks Makes Primary Better: A Multi-Task Learning Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3MKEAPOD}},
  note         = {Machine review of arXiv:2412.19547}
}
read the original abstract

Human beings can leverage knowledge from relative tasks to improve learning on a primary task. Similarly, multi-task learning methods suggest using auxiliary tasks to enhance a neural network's performance on a specific primary task. However, previous methods often select auxiliary tasks carefully but treat them as secondary during training. The weights assigned to auxiliary losses are typically smaller than the primary loss weight, leading to insufficient training on auxiliary tasks and ultimately failing to support the main task effectively. To address this issue, we propose an uncertainty-based impartial learning method that ensures balanced training across all tasks. Additionally, we consider both gradients and uncertainty information during backpropagation to further improve performance on the primary task. Extensive experiments show that our method achieves performance comparable to or better than state-of-the-art approaches. Moreover, our weighting strategy is effective and robust in enhancing the performance of the primary task regardless the noise auxiliary tasks' pseudo labels.

Figures

Figures reproduced from arXiv: 2412.19547 by the authors.

Figure 1
Figure 1. Visual comparison between our impartial training framework and OL [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. An comparison between our equally training framework and previous methods. (a) Baseline methods, use a weight estimator to produce auxiliary [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Visualization on NYUv2 [17] with semantic segmentation as the primary task and other two tasks (depth estimation and normal prediction) as auxiliary. The impressive improvements are marked with a purple box. into MTI-Net repository [38], [39], which has different model implement and data pre-process. Concretely, two task categories are defined, i.e., classifica￾tion and pixel-wise prediction, to evaluate the method.… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Visualization on NYUv2 [17] with depth estimation as the primary task and other two tasks (semantic segmentation and normal prediction) as auxiliary. The impressive improvements are marked with a purple box. (a) Image (b) OL-AUX [13] (c) Auto-λ [15] (d) Ours (e) GT [P…
Figure 5
Figure 5. Figure 5: Visualization on NYUv2 [17] with surface normal prediction as the primary task and other two tasks (semantic segmentation and depth estimation) as auxiliary. The impressive improvements are marked with a purple box. (a) Image (b) OL-AUX [13] (c) Auto-λ [15] (d) Ours (e…
Figure 6
Figure 6. Figure 6: Visualization on Cityscapes [18] with semantic segmentation as the primary task and other two tasks (disparity estimation and part segmentation) as auxiliary. The impressive improvements are marked with a purple box. mantic segmentation as the primary task on the Citys…
Figure 7
Figure 7. Figure 7: Visualization on Cityscapes [18] with disparity estimation as the primary task and other two tasks (semantic segmentation and part segmentation) as auxiliary. The impressive improvements are marked with a purple box. (a) Image (b) OL-AUX [13] (c) Auto-λ [15] (d) Ours (…
Figure 8
Figure 8. Figure 8: Visualization on Cityscapes [18] with part segmentation as the primary task and other two tasks (semantic segmentation and disparity estimation) as auxiliary.The impressive improvements are marked with a purple box. Following the same data pre-process, we evaluate 5 ta…
Figure 9
Figure 9. Figure 9: Visualization on Cityscapes [18] with semantic segmentation as the primary task and other two tasks (disparity estimation and part segmentation) and additional pseudo tasks as auxiliary.The impressive improvements are marked with a purple box. (a) Image (b) OL-AUX [13]…
Figure 10
Figure 10. Figure 10: Visualization on Cityscapes [18] with disparity estimation as the primary task and other two tasks (semantic segmentation and part segmentation) and additional pseudo tasks as auxiliary.The impressive improvements are marked with a purple box. (a) Image (b) OL-AUX [13…
Figure 11
Figure 11. Figure 11: Visualization on Cityscapes [18] with part segmentation as the primary task and other two tasks (semantic segmentation and disparity estimation) and additional pseudo tasks as auxiliary.The impressive improvements are marked with a purple box. TABLE VI COMPARISON OF M…
Figure 12
Figure 12. Figure 12: Visualization of Fail cases on Cityscapes. ”GT“ indicates ground truth. ”ours“ refers to a model that uses semantic segmentation as its primary task and depth regression as an auxiliary task, which is trained using the method we proposed. In Table VII, we show the cla…
Figure 13
Figure 13. Figure 13: Uncertainty curve of baseline and fixed head on NYUv2 [ [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 14
Figure 14. Figure 14: Visualization of weight changing over training on [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.