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REVIEW 4 major objections 5 minor 62 references

Sequence Transferability and Task Order Selection in Continual Learning

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

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Pith's one-line read Two simple transferability scores predict continual-learning accuracy, and a greedy rule built on them picks task orders that beat random selection.

desk verdict TFT/TRT are sensible but incremental sequence transferability measures; the HCTOS ordering rule contradicts its own hard-to-easy rationale and is empirically under-supported. read the letter →

arxiv 2502.06544 v1 pith:HBAKSWXA submitted 2025-02-10 cs.LG cs.CV

Thinh Nguyen , Cuong N. Nguyen , Quang Pham , Binh T. Nguyen , Savitha Ramasamy , Xiaoli Li , Cuong V. Nguyen This is my paper · ORCID
classification cs.LGcs.CV
keywords continuallearningtransferabilityestimationtaskorderselectionforwardtransferbackwardLogMEreplay-basedmethods
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

The paper's aim is to show that the transferability of a task sequence—how easily knowledge flows from earlier tasks to later ones, and from the final model back to earlier ones—can be measured cheaply and that these measurements track the average accuracy of continual learning algorithms. To that end, it introduces TFT and TRT, two sequence-level scores built by averaging an existing pairwise transferability metric across the tasks in order. It then uses the forward score TFT as the basis of HCTOS, a heuristic that picks a task order by repeatedly choosing the remaining task whose transferability to all other remaining tasks is smallest. The paper reports that TFT and TRT correlate well with average accuracy across several replay-based continual learning algorithms and benchmarks, and that HCTOS-selected orders outperform random orders in its experiments. If these findings hold, transferability scores become practical proxies for comparing continual learning methods and for choosing better task orders when tasks arrive in batches.

What carries the argument

The machinery has three parts. The base component is a pairwise transferability metric $\mathrm{tr}(m, D)$ that estimates how well a model trained on one task transfers to another task's training data; the paper uses LogME for most experiments. On top of it, TFT and TRT average these scores along the task sequence, giving a data-dependent measure of forward transfer and of forgetting, respectively. The third part is the HCTOS greedy rule: train a simple model on each task, compute its transferability score to every other task, then build the order by repeatedly appending the task with the smallest sum of scores to all tasks not yet selected. This rule is designed to make each subsequent step's forward transferability score high, which by the TFT correlation should raise final average accuracy.

What would settle it

Run a replay-based continual learning algorithm (e.g., DER++) on all permutations of a small batch of, say, five tasks from a benchmark such as Split CIFAR-100; compute the algorithm's average accuracy and the TFT score for every permutation. If the rank correlation between TFT and average accuracy is not significantly positive, or if the HCTOS-selected order performs no better than random orders, the paper's central claim would be refuted.

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Extended reading notes

Core claim

The central discovery the authors argue for is that the average accuracy of a continual learning algorithm on a sequence of tasks is well approximated by two simple sequence-level quantities: Total Forward Transferability, $\mathrm{tft}(A, \mathcal{D}) = \frac{1}{T-1}\sum_{t=2}^{T} \mathrm{tr}(m_{t-1}, D_t)$, and Total Reverse Transferability, $\mathrm{trt}(A, \mathcal{D}) = \frac{1}{T-1}\sum_{t=1}^{T-1} \mathrm{tr}(m_T, D_t)$, where $\mathrm{tr}$ is any existing pairwise transferability metric and $m_t$ is the model produced by the continual learning algorithm after seeing task $t$. They show empirically that across replay-based algorithms (A-GEM, ER, DER++, X-DER) and three image-classification benchmarks, higher average accuracy goes with higher TFT and TRT, and that for a fixed algorithm, average accuracy over random task orders correlates with the corresponding TFT and TRT values in the majority of settings. Based on the forward measure, they construct HCTOS, which orders tasks greedily by always placing next the task whose summed transferability to all remaining tasks is smallest, drawing on the empirical observation that transferring from hard to easy tasks yields high transfer scores. The paper reports that HCTOS beats random task ordering in one-batch and multi-batch settings and is stable to the number of samples used to train the scoring models and to the choice of base transferability metric.

Load-bearing premise

The load-bearing premise is that transferability scores computed from simple models trained independently on each task, before any continual learning happens, correctly predict which order of tasks will give the continual learning algorithm the highest average accuracy; specifically, that the greedy min-sum rule raises TFT and hence accuracy.

Editorial extensions

If this is right

  • TFT and TRT can be used to compare continual learning algorithms on a fixed task sequence without running the full training to completion.
  • Given a fixed algorithm, TFT and TRT can rank the hardness of different task sequences, which helps in designing benchmarks and in choosing among candidate orderings.
  • HCTOS offers a practical way to reorder a batch of tasks before feeding them to a continual learning algorithm, improving average accuracy over chronological or random order.
  • HCTOS remains effective when only a few samples per class are used to compute transferability scores and when different base metrics (LEEP, GBC, TransRate) are substituted for LogME.
  • Because TRT is computed with the final model on all previous tasks, it tends to correlate more strongly with average accuracy than TFT does, reflecting the evaluation protocol itself.

Reading between the lines

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

  • If the correlation between TFT and average accuracy holds beyond the benchmarks tested, the same scores could be adapted to class-incremental or online continual learning settings where task boundaries are less clean; the paper itself does not test this.
  • The hard-to-easy ordering principle behind HCTOS suggests a potential link to curriculum learning: HCTOS can be viewed as a data-driven curriculum that arranges tasks by mutual transferability, and its ordering could be compared against standard curriculum heuristics.
  • Because TFT and TRT inherit the behavior of the chosen base metric, a natural extension is to test whether the observed correlations survive when the base metric is replaced by a learned or domain-distance-based estimator rather than the label- and feature-based ones used here.
  • The paper leaves open a model-free version of sequence transferability that predicts TFT and TRT without training any models; such a measure would make task order selection far cheaper for large batches.
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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 two sequence-level measures, Total Forward Transferability (TFT, Eq. 2) and Total Reverse Transferability (TRT, Eq. 3), defined as averages of an existing pairwise transferability metric (LogME) over the transitions of a continual learning (CL) run. It reports that these measures are positively correlated with average accuracy (AA) across four replay-based CL algorithms and three benchmarks (Section 5.1, Table 1, Figure 1), and it uses the TFT intuition to develop HCTOS (Algorithm 1), a heuristic that orders tasks within a batch by iteratively selecting the task with the smallest sum of transferability scores to all remaining tasks. Experiments on Split CIFAR-100 with DER++ and buffer size 360 claim HCTOS outperforms random ordering and is robust to choice of sample size and base transferability metric (Section 5.2, Figures 2-4).

Significance. If the correlations and the HCTOS advantage were well supported, TFT and TRT would be inexpensive, data-dependent descriptors of task sequences that could aid benchmark design and task-order selection. The correlation analysis covers several algorithms, buffer sizes, and datasets, and the paper is transparent that computing TFT/TRT requires running a CL algorithm (Section 3.3). However, the central task-ordering claim currently rests on a single narrow experiment with no error bars or significance tests, and, more importantly, the greedy rule in Algorithm 1 is not aligned with the TFT objective it is motivated by. These issues need to be resolved before the contributions can be assessed.

major comments (4)
  1. [3.2, Eqs. (2)-(3), Table 1] The definition of a transferability measure in Section 3.2 makes tr(m, D_target) monotone with the target accuracy after transfer learning. Consequently, TRT in Eq. (3), an average of tr(m_T, D_t) with the final CL model m_T, is by construction an average of proxies for the per-task accuracy of m_T after fine-tuning, while AA in Eq. (1) is the per-task accuracy of m_T without fine-tuning. The reported AA-TRT correlations are therefore partly expected and do not independently validate TRT as a new sequence-level characterization. The authors should either demonstrate that the correlations remain high when the base metric is not calibrated to predict post-transfer accuracy, or provide a formal argument that the relationship is not a near-tautology.
  2. [4.1, Algorithm 1] The motivation in Section 4.1 says the sequence should be constructed by maximizing the TFT step tr(m_{t_{i-1}}, D_{t_i}) in Eq. (4), citing hard-to-easy transfer as a reason to choose harder tasks first. However, Algorithm 1 lines 7-8 compute L_t = sum_{j not in S ∪ {t}} a_{t,j}, the sum of pairwise transferability scores from candidate task t to all remaining tasks, and select argmin_t L_t. This criterion depends on the candidate as source, not on the current CL model m_{t_{i-1}} as source, so it is not a greedy maximizer of the TFT term. Moreover, if hard-to-easy transfers yield high scores, a hard-first rule would prefer candidates with high outgoing scores to the remaining easy tasks, i.e., argmax, not argmin, of the row sum. No experiment in Section 5.2 measures whether HCTOS orders actually have high TFT or isolates the hard-to-easy mechanism. The authors should either align Algorithm 1 with the TFT objective, or provide direct evidence that the row-sum argmin rule raises TFT and final accuracy.
  3. [5.2, Figures 2-4] The central HCTOS claim is supported by experiments on a single benchmark (Split CIFAR-100), a single CL algorithm (DER++), and a single buffer size (360). Figures 2-4 do not report error bars, the number of random-order runs used for the baseline, or any significance test. Since the reported advantage over random is likely small relative to order-to-order variance, this is insufficient to support the abstract claim that the method 'can be shown to offer a better performance' than random selection. Please provide means and standard deviations over multiple seeds/order samples and statistical tests, across additional benchmarks, algorithms, and buffer sizes.
  4. [Table 1] The claim that TFT and TRT are 'well-correlated' with AA is stronger than Table 1 warrants. For example, the AA-TFT correlations on Split tiny-ImageNet for DER++ are 0.44, 0.37, 0.41, and 0.53, several of which are not statistically significant at p < 0.05, and many other entries across the table are moderate or non-significant. The statement that 'more than 70% of settings' show moderate to very high correlations is a post hoc summary that counts coefficients in the moderate range as support. The authors should report confidence intervals or rank correlations, specify exactly which settings violate the claim, and temper the wording of Result 2 and the abstract accordingly.
minor comments (5)
  1. [3.2] The definition of a transferability measure uses an 'if and only if' condition that is acknowledged to 'rarely hold' in practice. This is better presented as a desideratum or an idealization, rather than a definition, to avoid the impression of a circular construction.
  2. [5.1] The phrase 'more than 70% of the settings' is imprecise; please provide the exact number of settings and the thresholds used for 'moderate' and 'very high' categories.
  3. [Figure 2] The caption does not specify how many random orderings were averaged, whether error bars are omitted, or whether the difference is statistically significant; please add this information.
  4. [Algorithm 1] The 'simple model' trained in lines 1-4 is not fully specified: the main text says ResNet18 with 20 samples per class for Section 5.2, but the optimizer, epochs, and feature-extraction details for the simple models should be stated in the algorithm description or experimental setup.
  5. [5.1, Benchmarks] The 'Split mutual-CIFAR-10' benchmark is non-standard and its construction is only briefly described; please clarify how the overlapping class is assigned across the five tasks and how the mutual class affects evaluation.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: TFT/TRT are empirical aggregates of an existing transferability metric, and HCTOS is an evaluated heuristic; self-citations are background only.

full rationale

The paper's central claims are empirical rather than derivational. TFT and TRT (Eqs. 2-3) are defined as averages of a base transferability metric tr, which Section 3.2 explicitly says only approximates an ideal monotonic relation to transfer accuracy ('the above condition rarely holds and existing transferability measures only try to approximate this ideal condition'). Therefore the observed correlations with average accuracy in Table 1 and Figure 1 are empirical findings about LogME, not logical consequences of the definitions. The paper also acknowledges that computing TFT/TRT requires running the CL algorithm and that model-free measures are future work, which is a limitation rather than a disguised fit. HCTOS (Algorithm 1) is a heuristic that computes pairwise transferability scores on cheap simple models and greedily orders tasks; it is compared directly against a random baseline in Section 5.2, with no parameter fitted to the target accuracy. The fact that the greedy rule (minimizing outgoing row sums) may not align with the stated TFT-maximization motivation is a correctness/consistency concern, not circularity. Self-citations (Nguyen et al. 2019, 2020, 2023; Tran et al. 2019) are used as background, definitions, or empirical observations; none is an unverified uniqueness theorem invoked to force the paper's choices. Overall, the derivation chain does not reduce to its own inputs.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

No parameter fitting is used; the only hand-chosen number is the sample size for the cheap models in Algorithm 1. The central assumptions are domain assumptions about transferability metrics remaining faithful inside a continual learning model and the hard-to-easy ordering premise for HCTOS; both are empirical and untested outside the paper's benchmarks. No invented entities are introduced.

free parameters (1)
  • sample size for simple models in Algorithm 1 = 20 random samples per class
    Section 5.2 states simple models are trained with 20 random samples per class; robustness to other sample sizes is tested, so the default is a hand-chosen number rather than a fitted constant.
assumptions (4)
  • domain assumption The base transferability metric tr(m, D_target) is monotonically related to the target task accuracy after transfer learning.
    Section 3.2 defines tr through this ideal condition and then relies on LogME's approximation; if LogME is not a faithful proxy on a task pair, TFT, TRT, and HCTOS all degrade.
  • domain assumption All tasks are task-incremental classification tasks sharing one input space with task-specific label spaces.
    Section 3.1 assumes X_t in X and Y_t in Y_t, so average accuracy is evaluated with task identity known; results may not carry to class-incremental or mixed-domain settings.
  • domain assumption Hard-to-easy task transitions produce higher transferability and learning harder tasks first benefits later transfer.
    Section 4.1 grounds the HCTOS rule in Tran et al. 2019 and Mahdisoltani et al. 2018; this prior empirical observation is assumed rather than derived or validated here.
  • ad hoc to paper Greedy selection of the task with the smallest sum of pairwise transferability scores to all remaining tasks approximates maximizing TFT and final accuracy.
    Algorithm 1 lines 5-10 implement this rule, but the paper provides no proof or bound connecting the rule to TFT or AA; it is a heuristic.

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Cite this review

Pith. "Pith review of Sequence Transferability and Task Order Selection in Continual Learning." pith.science (2026). https://pith.science/paper/HBAKSWXA

@misc{pith2026250206544,
  author       = {Pith},
  title        = {Pith review of: Sequence Transferability and Task Order Selection in Continual Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HBAKSWXA}},
  note         = {Machine review of arXiv:2502.06544}
}
read the original abstract

In continual learning, understanding the properties of task sequences and their relationships to model performance is important for developing advanced algorithms with better accuracy. However, efforts in this direction remain underdeveloped despite encouraging progress in methodology development. In this work, we investigate the impacts of sequence transferability on continual learning and propose two novel measures that capture the total transferability of a task sequence, either in the forward or backward direction. Based on the empirical properties of these measures, we then develop a new method for the task order selection problem in continual learning. Our method can be shown to offer a better performance than the conventional strategy of random task selection.

Figures

Figures reproduced from arXiv: 2502.06544 by the authors.

Figure 1
Figure 1. The AA, TFT, and TRT of different replay-based CL algorithms over three benchmarks. Given a buffer size, TFT and TRT show [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Effects of sample size when training simple models on the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Average accuracy of HCTOS with respect to four different [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: The AA, TFT, and TRT of different CL algorithms on Split mutual-CIFAR-10 and Split CIFAR-100. Error bars are the standard [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry add.period write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence '...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.