Curriculum Sampling in ML Training

• Curriculum Sampling is a training strategy that adjusts sampling probabilities over time to transition from easy to hard examples.
• It uses explicit schedules, model-based difficulty estimates, and reward proxies to align data exposure with model competence.
• Applied in fields like medical imaging, language pretraining, and reinforcement learning, it improves optimization efficiency and performance.

Curriculum sampling is a training-time strategy that changes the sampling distribution over training units—examples, patches, negatives, timesteps, prompts, or trajectories—so that optimization follows an easy-to-hard or capability-matched progression rather than a fixed or uniformly random distribution. In the recent literature, the technique appears in settings as varied as extreme class imbalance in medical imaging, dense retrieval, sequence prediction, diffusion and flow-based generation, reinforcement learning, and language-model pretraining. Across these settings, the common objective is not merely to reorder data once, but to control which parts of the training distribution are emphasized at each stage of learning, often using explicit schedules, dynamic model-based difficulty estimates, or reward-derived proxies for informativeness (Jesson et al., 2018, Matiisen et al., 2017, Zhang et al., 12 Jun 2025).

1. Conceptual foundations

Curriculum sampling is a specialization of curriculum learning in which the curriculum is implemented through the sampling process itself. Rather than fixing a dataset order offline, the method modifies the probability with which different training units are drawn over time. In the simplest form, this means emphasizing easy items early and harder items later. In stronger formulations, it means continuously adapting the sampling policy to the model’s evolving competence, so that the sampled data remain informative rather than merely difficult.

A recurrent motivation is that uniform sampling can be misaligned with optimization. In lung CT segmentation, naïve random sampling overwhelmingly returns background patches because less than $1\%$ of voxels contain nodules, which makes optimization ineffective for the rare positive class (Jesson et al., 2018). In statutory article retrieval, fixed BM25-mined hard negatives can be “too hard too early” and are also static with respect to the model being trained (Santosh et al., 2024). In RL-based text-to-image generation, uniform prompt sampling wastes updates on prompts that are already mastered or still beyond the model’s reach (Li et al., 18 May 2026). In agentic RAG, uniform rollout sampling ignores heterogeneity in search depth, even though deeper trajectories contain more retrieval decision points (Shen et al., 12 May 2026).

The literature also broadens the notion of “difficulty.” Some papers define difficulty structurally, such as node overlap in paths, proximity in statutory hierarchies, or search depth in trajectories (Yang et al., 2021, Santosh et al., 2024, Shen et al., 12 May 2026). Others define it semantically, using query similarity, model relevance scores, or reward statistics (He et al., 2022, Santosh et al., 2024, Feng et al., 18 Apr 2025). Still others define it in terms of the training distribution itself, such as moving from imbalanced to balanced class exposure, or from middle-biased to uniform timestep coverage (Wang et al., 2019, Sun, 12 Mar 2026).

2. Formal structures of curriculum sampling

One common formal pattern is interpolation between sampling generators. CASED defines a mixture over a nodule-patch generator $g_n$ and a random/background generator $g_r$: $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$ The curriculum is controlled by $p_\tau(g_n)=f_n(\tau)$, with $f_n(\tau)\to 0$ as $\tau\to\infty$, while the background sampler $f_r(\mathcal{L}_\tau(x_i),\tau)$ is required to approach the uniform distribution over patches. The paper explicitly notes that, in the limit, the sampling distribution converges to uniform over training patches, which is why it characterizes the procedure as a valid curriculum learning method (Jesson et al., 2018).

A second pattern is an epoch-dependent target distribution. Dynamic Curriculum Learning for imbalanced classification defines

$D_{target}(l)=D_{train}^{g(l)},$

where $g(l)$ is a monotonically decreasing scheduler from $g_n$0 to $g_n$1. Early in training, the batch distribution stays close to the original imbalanced dataset distribution; later, it approaches a balanced distribution because the elementwise exponent tends toward zero. Within a batch, majority classes can be downselected and minority classes upweighted through class-dependent weights in the Dynamic Selective Learning loss (Wang et al., 2019).

A third pattern is explicit phase switching. For Flow Matching, Curriculum Sampling defines a two-phase timestep schedule

$g_n$2

Phase 1 uses a middle-biased Logit-Normal distribution for rapid structure learning; Phase 2 switches to Uniform sampling for refinement of the hard boundary regimes near $g_n$3 and $g_n$4 (Sun, 12 Mar 2026).

Other papers instantiate curriculum sampling through discrete buckets or stages. CuSINeS ranks negatives by fused semantic, hierarchical, and sequential difficulty, then partitions them into easy, medium, and difficult buckets whose sampling proportions shift over epochs (Santosh et al., 2024). CAPSTONE sorts pseudo queries by ROUGE-L similarity to the gold query and samples progressively more relevant groups during training (He et al., 2022). PCC ranks paraphrases by BLEURT similarity and maps them to curriculum levels, then revisits those levels cyclically rather than traversing them only once (Lu et al., 2022).

3. Difficulty estimation and informativeness signals

The choice of difficulty signal is central, and the literature shows no single universal definition. In supervised vision, one approach uses a task-independent estimator based on the human time required to decide whether a class is present in an image during a visual search task. That difficulty score is then combined with a diversity term favoring classes that have been sampled less often (Soviany, 2020). In language-model pretraining, six final metrics are retained after Spearman correlation analysis: Compression Ratio, Fertility, Flesch Reading Ease, MTLD, Number of Tokens, and Perplexity (Zhang et al., 12 Jun 2025). In paraphrase-based curriculum data augmentation, higher textual similarity means easier paraphrases and lower similarity means harder paraphrases (Lu et al., 2022).

A second family of signals is model-adaptive. CuSINeS computes semantic difficulty with the model currently being trained: $g_n$5 where higher score means a harder negative because the model currently judges it more relevant (Santosh et al., 2024). Wiki-R1 estimates sample difficulty from observed rewards and then propagates those observations to unobserved samples through a TF-IDF-based label-propagation graph over related Wikipedia articles. The resulting estimated reward becomes the proxy for sample difficulty, and the sampler favors examples near the historical mean training accuracy of $g_n$6, which the paper identifies as the region yielding the strongest gradient signal in RL (Ning et al., 5 Mar 2026).

A third family of signals derives difficulty from reward statistics or trajectory structure. CGPO uses the variance of group rewards for a prompt,

$g_n$7

as an online proxy for prompt inconsistency; high variance indicates that the prompt is partially captured but not yet mastered stably (Li et al., 18 May 2026). ToolSample’s Reward-Based Dynamic Sampling uses mean reward, variance across rollouts, and variance across epochs to separate easy, hard, intermediate, and informative samples, while Task-Based Dynamic Curriculum Learning shifts reward emphasis from format to tool name and keys, then to parameter values (Feng et al., 18 Sep 2025). CuSearch uses search depth as a trajectory-level proxy for retrieval supervision density, formalized through retrieval gradient coverage $g_n$8, and reallocates a fixed update budget toward deeper trajectories (Shen et al., 12 May 2026).

These definitions are not interchangeable. Perplexity can help early in pretraining but may later capture noise rather than constructive difficulty (Zhang et al., 12 Jun 2025). High final reward is not, by itself, a good proxy for informative trajectories in agentic RAG, because a rollout can receive high reward with zero retrieval actions (Shen et al., 12 May 2026). This suggests that curriculum sampling depends as much on the choice of proxy as on the schedule built on top of it.

4. Major application patterns

In class-imbalanced perception problems, curriculum sampling is often used to avoid overwhelming the model with trivial negatives or dominant classes. CASED begins with nodule-containing patches and their local context, then gradually broadens toward the empirical data distribution while emphasizing hard negatives among background patches (Jesson et al., 2018). Diverse curriculum sampling for object detection and instance segmentation combines easy-to-hard sampling with class-visit weighting so that easy dominant classes do not monopolize early training (Soviany, 2020). DCL similarly stages training from the natural imbalanced distribution toward a balanced one while coupling the sampling scheduler to a loss scheduler (Wang et al., 2019).

In retrieval and representation learning, curriculum sampling frequently appears as negative sampling. CuSINeS orders statutory negatives from easy to hard using semantic relevance, hierarchical proximity, and sequential proximity, then fuses those rankings with Reciprocal Rank Fusion (Santosh et al., 2024). Path InfoMax generates random negative paths first, then harder same-source/same-destination alternatives using the top-$g_n$9 diversified shortest path algorithm, so that both the path-path and path-node mutual-information objectives receive progressively stronger contrast (Yang et al., 2021). CAPSTONE applies curriculum sampling to pseudo-query expansion: documents are first expanded with weakly related generated queries and later with more query-like pseudo queries, thereby reducing the train-test mismatch between gold-query expansion at training time and generated-query expansion at inference (He et al., 2022).

In sequence modeling and augmentation, curriculum sampling is often used to bridge train-test mismatch rather than class imbalance. Nearest-Neighbor Replacement Sampling replaces teacher-forced tokens with sampled nearest neighbors from a truncated top-$g_r$0 cosine-similarity distribution, thereby creating an intermediate regime between exact targets and model predictions (Neill et al., 2021). PCC uses bottom-$g_r$1 sampling in paraphrase generation to create “super-hard” instances for later curricula and uses cyclic learning to revisit earlier levels, explicitly framing repeated passes as a mitigation for catastrophic forgetting (Lu et al., 2022).

In generative modeling and RL, curriculum sampling increasingly targets capability matching. Flow Matching uses a middle-biased structure phase followed by Uniform refinement (Sun, 12 Mar 2026). ACS for diffusion-based dataset distillation partitions the distilled set into curricula and uses adversarial guidance so that later curricula are difficult for a discriminator trained on earlier ones, thereby reducing redundancy among diffusion samples (Zou et al., 2 Aug 2025). In KB-VQA, Wiki-R1 couples curriculum sampling with controllable curriculum data generation over retrieval noise levels (Ning et al., 5 Mar 2026). In intent detection, Reward-based Curriculum Sampling first trains GRPO on the full dataset, scores examples by accumulated reward, and then continues training on the challenging subset (Feng et al., 18 Apr 2025). In text-to-image generation, CGPO increases prompt sampling probabilities for prompts with high reward variance and calibrates category imbalance through proportional fairness optimization (Li et al., 18 May 2026). In agentic RAG, CuSearch reallocates update budget toward deeper-search trajectories, either implicitly through SDGA-Auto or explicitly through SDGA-Phase (Shen et al., 12 May 2026).

Large-scale language-model pretraining supplies a final application pattern: curriculum as data-order control under realistic token budgets. The pretraining study distinguishes vanilla easy-to-hard ordering, pacing-based sampling across difficulty groups, interleaved curricula, and curriculum warmup followed by shuffled continuation (Zhang et al., 12 Jun 2025).

5. Empirical behavior and reported effects

Reported improvements differ substantially by domain, metric, and schedule, but several papers show that curriculum sampling changes both optimization speed and the final operating point rather than merely smoothing early training.

Paper	Setting	Reported outcome
CASED (Jesson et al., 2018)	LUNA16 lung nodule detection	average sensitivity $g_r$2
Curriculum Sampling for Flow Matching (Sun, 12 Mar 2026)	CIFAR-10	best FID $g_r$3 vs $g_r$4 for Uniform
Wiki-R1 (Ning et al., 5 Mar 2026)	KB-VQA	Encyclopedic VQA $g_r$5; InfoSeek $g_r$6
ACS (Zou et al., 2 Aug 2025)	Dataset distillation	$g_r$7 on Imagewoof and $g_r$8 on ImageNet-1k
CuSearch (Shen et al., 12 May 2026)	Agentic RAG	up to $g_r$9 exact-match points over standard GRPO
ToolSample / DSCL (Feng et al., 18 Sep 2025)	RL-based tool learning	$$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$0 improvement on BFCLv3

The medical-imaging and retrieval papers emphasize optimization under skewed sampling. CASED reports that accurate segmentation plus connected-component analysis can top the LUNA16 leaderboard without a separate detection stage, and that comparable results can be obtained when only a point and radius are provided for each ground-truth nodule during training (Jesson et al., 2018). CuSINeS reports consistent improvements over BM25-based fixed negative sampling across four dense retrievers, and its ablations indicate that performance improves when increasing buckets up to $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$1, but then declines if too many buckets are used (Santosh et al., 2024).

The generative-modeling papers emphasize a speed-quality trade-off. In Flow Matching, static middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling; the two-phase schedule improves the best FID from $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$2 to $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$3 and reaches peak performance at $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$4k rather than $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$5k training steps (Sun, 12 Mar 2026). In LLM pretraining, curriculum learning consistently improves convergence in early and mid-training phases, and warmup curricula can yield lasting gains, with up to $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$6 improvement reported in continual-training settings (Zhang et al., 12 Jun 2025).

RL-based systems show an especially strong dependence on capability matching. Wiki-R1 reports that, in preliminary DAPO experiments, over $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$7 of samples had zero advantage, and that curriculum sampling becomes effective only when paired with observation propagation from sparse rewards (Ning et al., 5 Mar 2026). RCS for intent detection shows that the first stage alone is not stronger than the baseline, but the second stage focused on challenging examples yields an average of $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$8 on MultiWOZ, above both SFT and plain GRPO (Feng et al., 18 Apr 2025). In tool learning, the ablation “RDS w/o CL” performs worse than ToolRL, while full RDS improves over it, indicating that dynamic sampling without curriculum or warmup can be harmful in this setting (Feng et al., 18 Sep 2025).

6. Limitations, boundary cases, and adjacent concepts

Curriculum sampling is often described as “easy-to-hard,” but the literature shows that the phrase is too narrow. Some methods decay back to uniform or empirical sampling, as in CASED and Flow Matching (Jesson et al., 2018, Sun, 12 Mar 2026). Some methods repeatedly revisit earlier material, as in cyclic learning for PCC and forgetting-aware teacher selection in TSCL (Lu et al., 2022, Matiisen et al., 2017). Others maintain mixed difficulty throughout training, as in interleaved curricula for language-model pretraining (Zhang et al., 12 Jun 2025). The common denominator is therefore controlled exposure, not monotonic hardness alone.

The design is also sensitive to schedule granularity and gating. CuSINeS reports that too many buckets can hurt performance (Santosh et al., 2024). ACS shows that moderate adversarial guidance improves performance, but too much guidance hurts because the samples become too hard, too rare, or drift away from the data manifold (Zou et al., 2 Aug 2025). Sequence-prediction work reports that high sampling too early destabilizes learning, whereas later increases improve robustness (Neill et al., 2021). In tool learning, dynamic sampling is delayed until the mean reward of seven consecutive batches exceeds $$p_\tau(x_i)=p_\tau(x_i\mid g_r)(1-p_\tau(g_n))+p(x_i\mid g_n)p_\tau(g_n).$$9, because early rewards are too unstable under strict output formatting (Feng et al., 18 Sep 2025).

A related misconception is that curriculum sampling is synonymous with hard-negative mining. Hard negatives are important in several methods, including CASED and CuSINeS, but the curriculum contribution lies in when and how such examples are introduced, not merely in their presence (Jesson et al., 2018, Santosh et al., 2024). Another misconception is that any difficulty proxy will suffice. The empirical record is more selective: reward variance outperforms alternative prompt-level indicators in CGPO; search depth is stronger than reward-only selection in CuSearch; and Perplexity is less reliable than Compression Ratio, MTLD, and Flesch Reading Ease in pretraining (Li et al., 18 May 2026, Shen et al., 12 May 2026, Zhang et al., 12 Jun 2025).

Finally, the term should be distinguished from broader-terms curriculum mapping, which is an educational-program planning method based on classification of learning objectives, NLP, and visualization, rather than a machine-learning sampling strategy (Duarte et al., 2021). In machine learning, curriculum sampling refers specifically to changing the training-time sampling distribution.

Taken together, these works suggest that curriculum sampling is best understood as a mechanism for allocating optimization effort: it decides which parts of the training distribution should absorb gradient budget at which stage of learning. The exact implementation varies—from mixture distributions and phased schedules to reward-variance updates and search-depth allocation—but the central technical claim is stable across domains: fixed uniform sampling often misallocates training effort, and a capability-matched sampling policy can improve convergence, final performance, or both (Matiisen et al., 2017, Zhang et al., 12 Jun 2025).