Entropy-Driven Curriculum Learning

• Entropy-driven curriculum learning is a design pattern that uses entropy signals—such as predictive uncertainty and annotation ambiguity—to order and weight training data.
• It incorporates dynamic strategies like entropy-aware masking, selective dropout, and objective reassignment to adapt training procedures in domains like NLP, RL, and graph clustering.
• Empirical studies show these methods enhance convergence, accuracy, and generalization while highlighting challenges like cold-start issues and the limitations of static entropy estimates.

Entropy-driven curriculum learning denotes a family of training strategies in which an entropy-like signal is used to order, weight, filter, or otherwise modulate training examples, sub-example components, or optimization objectives. In recent work, the relevant entropy can be the predictive entropy of a LLM, the entropy of annotator vote distributions, clustering entropy over pseudo-label assignments, normalized Lempel–Ziv entropy of sequences, or policy-relative entropy in reinforcement learning. The resulting curricula are correspondingly heterogeneous: some emphasize high-entropy tokens, some suppress low-entropy redundant content, some begin with low-entropy examples and progressively admit ambiguous ones, and some adapt online as the model’s own uncertainty changes (Srinivasagan et al., 27 May 2026, Wang et al., 29 Dec 2025, Omidi et al., 25 Jun 2026, Fang et al., 1 Sep 2025).

1. Entropy as a curriculum signal

The central formal object is usually Shannon entropy,

$H(p) = - \sum_i p_i \log p_i,$

but the distribution $p$ differs by task. In masked language modeling, entropy is computed from the model’s token prediction distribution at position $j$,

$$e_{t_j} = - \sum_{v \in \mathcal{V}} \mathbf{P}_{t_j}(v) \log \mathbf{P}_{t_j}(v),$$

so high entropy marks positions where the model is uncertain about the masked token (Srinivasagan et al., 27 May 2026). In speech emotion recognition, entropy is computed over merged primary–secondary annotator vote distributions, often normalized as

$$H_n(p) = - \frac{1}{\log C} \sum_{i=1}^{C} p_i \log p_i,$$

so high entropy denotes perceptual ambiguity rather than model uncertainty (Omidi et al., 25 Jun 2026). In graph clustering, entropy is defined over soft cluster assignments,

$E_i = -\sum_{j=1}^{k} P_{ij} \log P_{ij},$

and is interpreted as low clustering confidence for node $i$ (Zeng et al., 2024).

Other formulations replace predictive entropy with structurally related information measures. Human mobility prediction uses a normalized Lempel–Ziv estimator,

$$H_{LZ} = \frac{\ln N}{\bar{Q} \ln 2}, \qquad H_{\text{norm-LZ}} = \frac{H_{LZ}}{\log_2 N},$$

to quantify the predictability of a trajectory; low normalized entropy indicates highly regular mobility and is treated as easier for forecasting (Fang et al., 1 Sep 2025). Autonomous curriculum design in reinforcement learning uses relative entropy between policies,

$$D_{\mathrm{KL}}(P_{\text{true}} \,\|\, P_{\text{learnt}})(s) = \sum_{a \in A} P_{\text{true}}(s,a)\, \log \frac{P_{\text{true}}(s,a)}{P_{\text{learnt}}(s,a)},$$

as a state-wise uncertainty measure for choosing new start states (Satici et al., 28 Feb 2025).

Across these formulations, entropy serves as a proxy for at least three different quantities. It can denote difficulty in the sense of low predictability, ambiguity in the sense of annotator disagreement, or structural confidence in the sense of how concentrated a model’s internal belief distribution is. This suggests that entropy-driven curricula are not defined by a single semantics of “hardness,” but by a shared mechanism: training allocation is controlled by a scalar uncertainty or information signal derived from data, annotations, or model predictions.

2. Mechanisms by which entropy induces a curriculum

A first mechanism is selection of supervised positions or tokens. In entropy-aware masking for masked language modeling, the mask set $\mathcal{M}$ is no longer sampled uniformly: with high-entropy masking, the model masks the $p$0 positions with the largest entropies in a sequence, concentrating the MLM loss on uncertain tokens rather than random ones (Srinivasagan et al., 27 May 2026). In autoregressive continual pretraining on scarce domain data, EntroDrop does the opposite operation: low-entropy tokens are marked as eligible for dropout,

$p$1

so high-entropy tokens are never dropped and remain fully visible throughout training (Wang et al., 29 Dec 2025).

A second mechanism is filtering or weighting whole examples. In speech emotion recognition, entropy quantiles over annotation distributions define forward curricula that begin with low-entropy utterances and progressively include higher-entropy ones; weighting-based variants keep all data visible but modulate per-sample loss by entropy (Omidi et al., 25 Jun 2026). In acoustic scene classification under device shift, the entropy of an auxiliary domain classifier is used as a proxy for domain invariance: the top 50% highest-entropy samples form a domain-invariant subset used in Stage 1, and Stage 2 uses mixed batches with 80% domain-invariant and 20% domain-specific samples (Zhang et al., 14 Sep 2025). In mobility prediction, trajectories are sorted by normalized LZ entropy and exposed in three stages, while the prediction horizon is increased from $p$2 to $p$3 to $p$4, making entropy and horizon jointly define task difficulty (Fang et al., 1 Sep 2025).

A third mechanism is dynamic reassignment of training roles or objectives. In CCGL, nodes with lowest clustering entropy are progressively moved from an instance discrimination task into a harder clustering task, with the target number of promoted nodes governed by a pace parameter $p$5 and the update

$p$6

while node assignment is recomputed from current entropies each epoch (Zeng et al., 2024). In entropy-aware on-policy distillation of LLMs, teacher token entropy gates objective composition: $p$7 so high-entropy teacher positions receive an additional forward-KL term to preserve mode coverage (Jin et al., 7 Mar 2026). In supervised diffusion for music generation, the Eisbach barrier computes a normalized entropy over temporal energy, converts it to a log-barrier weight, and uses that weight to modulate gradient magnitude online, yielding what the paper describes as an “online, self-referential data curriculum” (Li et al., 5 Jun 2026).

A fourth mechanism is task generation. In READ-C, curriculum tasks are new MDPs that differ only in start state, and the next task is chosen by selecting the state with maximum KL-based policy uncertainty from a visited-state buffer (Satici et al., 28 Feb 2025). In Variational Curriculum RL, the curriculum itself is the goal distribution $p$8, and the proposed VUVC distribution

$p$9

combines value uncertainty with a density-skew term to accelerate the increase of entropy in the visited-state distribution (Kim et al., 2023).

3. Representative instantiations across domains

The same organizing principle appears in markedly different modalities, but the unit of curriculum and the operational meaning of entropy vary.

Setting	Entropy object	Curriculum action
Encoder MLM (Srinivasagan et al., 27 May 2026)	Token predictive entropy	Select masked positions
Autoregressive CPT (Wang et al., 29 Dec 2025)	Token entropy under base model	Drop low-entropy tokens with a schedule
SER (Omidi et al., 25 Jun 2026)	Annotation entropy of vote distributions	Filter or weight utterances
Mobility prediction (Fang et al., 1 Sep 2025)	Normalized LZ trajectory entropy	Stagewise data ordering and horizon increase
Graph clustering (Zeng et al., 2024)	Entropy of soft cluster assignments	Move nodes between contrastive tasks
RL curriculum design (Satici et al., 28 Feb 2025)	Policy KL / relative entropy at a state	Choose next start state

Earlier work already used entropy explicitly as a curriculum score. In image classification, curriculum scoring functions based on Shannon entropy and standard deviation were used to sort examples and gradually expose larger prefixes of the sorted dataset; entropy-based curricula improved over vanilla training in some settings, although standard deviation was more consistently effective (Sadasivan et al., 2021). In data-driven modeling of dynamical systems, an SVD-based Shannon entropy of time-delay embeddings was used to construct trajectories whose entropy increases from low-entropy neighborhoods of unstable fixed points toward high-entropy chaotic dynamics, creating a simple-to-complex training order for LSTMs (Bucci et al., 2021).

The entropy signal can also be derived from nuisance variables rather than task outputs. In acoustic scene classification, entropy is computed over device posterior probabilities from an auxiliary domain classifier. High entropy there does not mean task ambiguity; it means that device identity is hard to infer, so the sample is treated as more domain-invariant and thus more useful at the beginning of training under domain shift (Zhang et al., 14 Sep 2025). By contrast, in speech emotion recognition, high entropy means that listeners genuinely disagree about the emotional label distribution, so the curriculum addresses ambiguity in supervision rather than invariance across domains (Omidi et al., 25 Jun 2026).

Several recent works blur the boundary between curriculum design and adaptive optimization. HuCurl starts from annotation entropy or loss, groups training examples by difficulty, and then uses generalized logistic weight functions together with dynamic difficulty reassignment to discover high-performing curricula over a parametric curriculum space. The top-performing discovered curricula are often non-monotonic, and the framework encompasses easy-to-hard schedules, data pruning, and other weighting schemes as special cases (Elgaar et al., 2023). This suggests that entropy-driven curricula need not be restricted to sorting once and revealing data gradually; they can be framed as a search problem over schedules, weight functions, and reclassification rules.

4. Empirical regularities

In encoder pretraining, entropy-aware masking consistently improves downstream performance over random masking. On GLUE averages, the paper reports BERT base improving from 73.27 under random masking to 75.02 with teacher high-entropy masking and to 76.47 with teacher-initialized self-masking; BERTlet improves from 70.93 to 74.07 and then to 75.15, while adding knowledge distillation yields 77.19 for BERTlet in the best setting (Srinivasagan et al., 27 May 2026). The same study also reports that pure self-masking from random initialization performs poorly, with GLUE averages in the 57–61 range, indicating a strong cold-start effect.

In autoregressive continual pretraining, EntroDrop addresses multi-epoch degradation by suppressing low-entropy tokens rather than emphasizing high-entropy ones directly. On math reasoning, Qwen3-0.6B improves from a baseline math average of 44.52 to 45.54, Qwen3-1.7B from 54.06 to 55.02, and Llama3.1-8B from 50.64 to 51.76; on code generation, Qwen3-0.6B improves from 29.00 to 32.97 average code accuracy. The method also maintains robust performance throughout extended multi-epoch training, and a moderate maximum dropout rate $j$0 performs best in the reported math setting (Wang et al., 29 Dec 2025).

In supervision settings where ambiguity is intrinsic, entropy-aware curricula improve distributional alignment more than hard-decision accuracy alone suggests. For 9-class speech emotion recognition, M90–Filter attains Test1 Macro-F1 of 34.8 with JSD 0.185 and KLD 0.761, improving substantially over Hard–CE, which has JSD 0.322 and KLD 1.672 on the same split (Omidi et al., 25 Jun 2026). High-entropy utterances remain the hardest bin across systems, but distribution-based supervision and entropy-aware curricula improve the mid-entropy regime most consistently.

In data-scarce domain generalization, the gains are largest when labeled data are limited. On DCASE 2024 ASC baselines, the entropy-guided curriculum improves the official baseline from 44.00 to 46.30 at 5% labeled data, Cai_XJTLU from 48.91 to 51.50, and Han_SJTUTHU from 54.35 to 56.60. For Cai_XJTLU at 5%, seen-device accuracy rises from 50.6 to 52.3 while unseen-device accuracy rises from 46.7 to 49.3, indicating that the improvement is concentrated on cross-device generalization rather than merely fitting the training devices better (Zhang et al., 14 Sep 2025).

Outside language and speech, entropy-driven curricula also deliver measurable optimization gains. In human mobility prediction, the entropy-driven curriculum and multi-task framework reaches GEO-BLEU 0.354 and DTW 26.15, with up to 2.92-fold convergence speed relative to training without curriculum learning (Fang et al., 1 Sep 2025). In graph clustering, CCGL achieves 78.66 ACC, 60.24 NMI, and 60.48 ARI on Cora, outperforming its ablations and a range of prior baselines (Zeng et al., 2024). In on-policy language-model distillation, entropy-aware objective mixing yields Pass@8 gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base over baseline on-policy distillation methods (Jin et al., 7 Mar 2026).

Some reported evidence is qualitative rather than metric-centered. In supervised diffusion for music generation, entropy-weighted training produces stronger thematic development, clearer acoustic differentiation, and higher textural diversity than unweighted training, and the paper explicitly describes this as the opposite of mode collapse (Li et al., 5 Jun 2026). In maximum-entropy RL, a thermodynamic analysis argues that curricula minimizing excess work correspond to geodesics in task space, and the MEW algorithm for temperature annealing outperforms SAC’s automatic temperature adjustment on Humanoid-v5 in the reported experiment (Adamczyk et al., 12 Mar 2026).

5. Departure from classical easy-to-hard curricula

A persistent misconception is that curriculum learning is necessarily an easy-to-hard schedule over full examples. The literature surveyed here does not support that restriction. Entropy-aware masking in MLM always prioritizes the hardest tokens in the current sequence, not the easiest ones, and in the self-masking variant the masked set tracks the model’s changing uncertainty frontier rather than following a fixed monotonic progression (Srinivasagan et al., 27 May 2026). EntroDrop, by contrast, improves performance by masking low-entropy tokens and preserving high-entropy ones; the curriculum schedule controls when the regularization becomes strong, but the targeted content is explicitly the easy, redundant portion of the input (Wang et al., 29 Dec 2025).

Another misconception is that entropy-based curricula should always be monotonic. HuCurl shows that top-performing discovered curricula are often non-monotonic, that easy-to-hard and hard-to-easy transition curricula are often at risk of underperforming, and that dynamic reassignment of samples between difficulty groups can outperform fixed monotonic schedules (Elgaar et al., 2023). This is consistent with the graph-clustering setting, where nodes dynamically move from discrimination to clustering as their entropy decreases (Zeng et al., 2024).

The optimal direction of the curriculum also depends on what entropy measures. When entropy measures annotation ambiguity, forward easy-to-hard curricula are empirically favored: in speech emotion recognition, standard filtering and weighting curricula slightly favor low- and mid-entropy regions, and reverse curricula do not outperform standard ones (Omidi et al., 25 Jun 2026). When entropy measures predictive uncertainty at sub-example level, the best policy may instead be to target current hard positions directly, as in MLM, or to suppress current easy positions, as in EntroDrop (Srinivasagan et al., 27 May 2026, Wang et al., 29 Dec 2025).

A further point concerns granularity. Several successful methods operate over parts of examples rather than whole examples: token positions in MLM, low-entropy tokens in autoregressive language modeling, nodes within a graph, or actions at specific decision points in on-policy distillation (Jin et al., 7 Mar 2026). This suggests that entropy-driven curriculum learning is often better understood as selective allocation of a fixed supervision budget than as global reordering of a dataset.

6. Limitations, computational trade-offs, and open directions

The most immediate limitation is that entropy can be uninformative early in training. In entropy-aware masking, pure self-masking from the beginning fails because a randomly initialized model produces near-uniform token distributions, so entropies are all similar; the successful variant therefore uses a two-phase schedule with teacher masking first and self-masking only after initialization (Srinivasagan et al., 27 May 2026). The same cold-start problem appears in broader form whenever entropy is computed from the learner rather than a stronger reference model.

A second limitation is staleness of static entropy estimates. EntroDrop computes token entropies once using the base model and caches them, which keeps overhead negligible when the target corpus is reused many times, but the paper also notes that the model’s confidence shifts during training and that dynamic training loss could be a better real-time signal at higher cost (Wang et al., 29 Dec 2025). Mobility prediction likewise uses a static LZ-based complexity score and hand-chosen thresholds $j$1 and $j$2, along with fixed horizon stages $j$3; this yields strong results, but the schedule is manually designed and tied to discretized sequence representations (Fang et al., 1 Sep 2025).

A third limitation is quality of the entropy proxy itself. In speech emotion recognition, annotation entropy is estimated from a limited number of annotators and is explicitly described as an imperfect proxy for ambiguity (Omidi et al., 25 Jun 2026). In acoustic scene classification, the method assumes that high entropy of the auxiliary domain classifier corresponds to domain invariance, but the paper notes that high entropy may also arise from noise or weak domain discrimination, and the hard median split is a heuristic (Zhang et al., 14 Sep 2025). In graph clustering, clustering entropy depends on pseudo-labels produced by $j$4-means on current embeddings, so poor initial embeddings or mis-specified $j$5 can make the entropy signal unreliable (Zeng et al., 2024).

Computational trade-offs vary by mechanism. Teacher-masking and teacher-guided distillation require additional forward passes and memory, while self-masking avoids the external model after initialization (Srinivasagan et al., 27 May 2026). Entropy-aware on-policy distillation adds forward-KL only on high-entropy tokens and uses top-$j$6 teacher truncation to control memory cost (Jin et al., 7 Mar 2026). In supervised diffusion, the safety of confidence-based weighting is argued to be specific to supervised diffusion because gradient direction is fixed by ground-truth noise; the paper explicitly cautions that this argument does not transfer to RL or policy optimization (Li et al., 5 Jun 2026). In thermodynamic RL curricula, the geometric framework relies on near-equilibrium and linear-response assumptions, and scalable estimation of the friction tensor beyond one-dimensional schedules remains an open problem (Adamczyk et al., 12 Mar 2026).

Several open directions recur across these papers. Dynamic entropy signals are repeatedly suggested as a natural extension to static ones (Wang et al., 29 Dec 2025). Multiple works are limited in scale, language coverage, or architecture family, including English-only corpora for encoder MLM, BERT-like encoders, and evaluation up to 8B parameters in autoregressive adaptation (Srinivasagan et al., 27 May 2026, Wang et al., 29 Dec 2025). A plausible implication is that future work will increasingly combine entropy with other signals—loss, margin, domain discrepancy, value uncertainty, or thermodynamic friction—rather than treating entropy as a sufficient statistic on its own.

Taken together, the literature portrays entropy-driven curriculum learning less as a single algorithm than as a design pattern. Entropy determines what receives supervision, when difficult or ambiguous content is introduced, and in several settings which objective is applied to that content. The dominant technical question is therefore no longer whether entropy can define a curriculum, but which entropy, at which granularity, and under which update rule, best matches the structure of the learning problem.