Dynamic Sampling & Curriculum Learning

• DSCL is a training strategy that updates sampling policies in real-time based on difficulty, rewards, or learning progress.
• It integrates scoring signals, adaptive sampling rules, and pacing mechanisms to balance early selectivity with broader coverage.
• Empirical results across domains show DSCL accelerates convergence and improves accuracy, as seen in RL tool learning and flow matching.

Dynamic Sampling with Curriculum Learning (DSCL) denotes a class of training procedures in which the sampling distribution over training units is updated during optimization rather than fixed in advance. Across the formulations summarized in recent work, the sampled unit may be a training example, a subtask, a timestep, a token, a clip pair, or a rollout, and the scheduling signal may derive from estimated difficulty, reward statistics, loss decline, learning progress, uncertainty, or competence. In this sense, DSCL extends one-shot easy-to-hard ordering into an online control problem over exposure, emphasis, and coverage, with explicit pacing functions, stage transitions, or adaptive gating rules (Zhang et al., 12 Jun 2025, Feng et al., 18 Sep 2025, Matiisen et al., 2017).

1. Conceptual scope and relation to curriculum learning

In its broadest usage, DSCL is a dynamic variant of curriculum learning in which the learner does not traverse a fixed ordering once, but is repeatedly re-exposed to the training set through a time-varying sampling policy. In large-scale language-model pretraining, DSCL is defined as a strategy that “dynamically” adjusts the probability of sampling training examples according to estimated difficulty; unlike random sampling, it imposes a temporal schedule, and unlike vanilla curriculum learning, it continuously re-samples from all difficulty groups with time-varying proportions (Zhang et al., 12 Jun 2025). In tool learning, DSCL is formulated as a framework with Reward-Based Dynamic Sampling and Task-Based Dynamic Curriculum Learning, explicitly targeting multi-task structure and multi-valued reward functions (Feng et al., 18 Sep 2025).

Earlier dynamic curriculum formulations already contain the same core idea under different names. Teacher-Student Curriculum Learning (TSCL) casts curriculum generation as a teacher policy that chooses subtasks according to observed learning progress or forgetting, using the absolute slope of the student’s learning curve as the priority signal (Matiisen et al., 2017). Dynamic Curriculum Learning for low-resource neural machine translation reorders samples after each phase by relative loss decline and retains only the top fraction allowed by a competence variable derived from development-set BLEU (Xu et al., 2020). Self-Paced Dynamic Curriculum Learning for imbalanced text classification recomputes sample difficulty from both a static linguistic criterion and a dynamic model-capacity criterion, then exposes an increasing fraction of sorted buckets as training proceeds (Zhang et al., 2022).

This literature implies that “curriculum” in DSCL is not limited to a monotone easy-to-hard list. It can mean selective revisitation, delayed activation of hard regions, dynamic widening of visibility, or rebalancing toward under-learned subtasks. A plausible implication is that DSCL is best viewed as an allocation mechanism for finite optimization budget.

2. Recurrent algorithmic structure

Despite substantial domain variation, most DSCL systems instantiate four recurring components: a scoring signal, a sampling rule, a pacing mechanism, and an update rule.

The scoring signal can be loss-based, reward-based, geometry-based, or progress-based. In HaDCL for digital pathology, instantaneous hardness is defined directly by the downstream cross-entropy loss, $s_i(t)\equiv \ell_i(t)$, and the hard portion of a mini-batch is the top-$K$ subset after sorting losses in descending order (Srinidhi et al., 2021). In TSCL, the reward for selecting subtask $i$ is either the change in score since the last visit or a local linear-regression slope, with task priority proportional to the absolute slope so that negative slopes also resurface forgotten tasks (Matiisen et al., 2017). In the gradient-alignment DSCL of Sadasivan and Dasgupta, examples are scored by

$s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$

where $a_t=w^*-w_t$, so examples whose gradients are most aligned with the direction toward the target optimum are treated as easiest (Sadasivan et al., 2021). In Curriculum Consistency Model, difficulty is the PSNR-based knowledge discrepancy

$$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$

which is used online to choose the teacher step size (Liu et al., 2024).

The sampling rule may be hard selection, probabilistic reweighting, or staged replacement. ToolSample assigns each query a priority ratio $R_i\in\{0.0,0.5,1.0\}$ from reward mean and two variance measures, then defines $p_i\propto R_i$ (Feng et al., 18 Sep 2025). D$^3$S in policy optimization first chooses a subset of rollouts that maximizes $\mathrm{Var}(A)$ and then retains only the top $K$0 tokens ranked by $K$1 (Wang et al., 26 Sep 2025). The supervised computer-vision DSCL of Soviany et al. computes continuous weights

$K$2

normalizes them into $K$3, and samples mini-batches accordingly (Soviany, 2020).

Pacing is the mechanism that changes exposure over training. It may be an explicit schedule, such as the competence variable

$K$4

in low-resource NMT (Xu et al., 2020), or a linear interpolation between aggressive and mild retain rates,

$K$5

in D$K$6S (Wang et al., 26 Sep 2025). It may also appear as a fixed switch point, as in curriculum sampling for flow matching, or as a decay toward uniform sampling, as in diversity-aware supervised vision (Sun, 12 Mar 2026, Soviany, 2020).

These repeated design patterns show that DSCL is not tied to a particular model class. The sampled unit and difficulty proxy vary, but the control loop remains recognizable.

3. DSCL for RL-based tool learning

The most explicit use of the term “Dynamic Sampling with Curriculum Learning” appears in “ToolSample: Dual Dynamic Sampling Methods with Curriculum Learning for RL-based Tool Learning” (Feng et al., 18 Sep 2025). Here DSCL is designed for tool learning under GRPO and addresses two properties stated as central: multiple interdependent sub-tasks and multi-valued reward functions.

The framework begins from a dataset $K$7 of user queries. For each sample $K$8 and each RL training epoch $K$9, the policy $i$0 generates $i$1 rollouts with reward vector

$i$2

Tool learning is decomposed into four inter-dependent sub-tasks: format consistency, tool name prediction, parameter key extraction, and parameter value completion. Their reward components are

• $i$3,
• $i$4,
• $i$5,
• $i$6.

The overall rollout reward is

$i$7

Reward-Based Dynamic Sampling (RDS) activates only once the mean reward of seven consecutive batches is at least $i$8. For each sample, it computes the mean reward

$i$9

the sample-level variance

$s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$0

and the epoch-level variance of historical means

$s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$1

Each sample is then classified as “Easy,” “Hard,” or “Intermediate,” and assigned a priority ratio $s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$2:

• $s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$3 if too easy or too hard with low variance,
• $s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$4 if intermediate but only one variance dimension is large,
• $s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$5 if hard with high exploratory variance or intermediate with both variances high.

Task-Based Dynamic Curriculum Learning (TDCL) implements a three-stage curriculum over the four reward components. The stage-specific rewards are

$s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$6

$s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$7

$s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$8

The active stage is chosen by a performance-progress test on sub-task rewards, for example when $s_t(x_i)=\langle a_t,\nabla \ell(w_t;x_i)\rangle,$9 or $a_t=w^*-w_t$0 exceed tuned thresholds.

Algorithmically, DSCL interleaves RDS and TDCL at each GRPO update: sample a batch, generate $a_t=w^*-w_t$1 rollouts, compute the ratio vector by RDS, reweight reward components by TDCL, compute advantage estimates from the adjusted reward, scale advantages by the ratio vector, and update the policy. On BFCL v3, ToolRL achieves $a_t=w^*-w_t$2 overall accuracy, ToolRL+$a_t=w^*-w_t$3 reaches $a_t=w^*-w_t$4, ToolRL+$a_t=w^*-w_t$5 reaches $a_t=w^*-w_t$6, and ToolRL+$a_t=w^*-w_t$7 reaches $a_t=w^*-w_t$8, a $a_t=w^*-w_t$9 improvement over ToolRL. On API-Bank, ToolRL improves from $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$0 to $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$1 under DSCL, a $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$2 gain. An important ablation shows that applying RDS from the very first step causes catastrophic format-errors and reduces overall accuracy to approximately $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$3, whereas delayed activation yields a $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$4 gain by RDS alone.

4. Representative DSCL variants across model families

A prominent continuous-time variant is “Curriculum Sampling” for flow matching (Sun, 12 Mar 2026). The paper identifies a U-shaped per-timestep loss profile,

$$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$5

with persistent difficulty near both $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$6 and $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$7. The proposed two-phase schedule uses a middle-biased Logit-Normal distribution during a Structure Phase and switches to Uniform sampling during a Refinement Phase: $$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$8 On CIFAR-10, the schedule LN$$KDC_t^u = 100-\mathrm{PSNR}(x_{\mathrm{est}},x_{\mathrm{target}}),$$9 Uniform with $R_i\in\{0.0,0.5,1.0\}$0k attains best FID $R_i\in\{0.0,0.5,1.0\}$1 at $R_i\in\{0.0,0.5,1.0\}$2k steps, compared with Uniform baseline best FID $R_i\in\{0.0,0.5,1.0\}$3 at $R_i\in\{0.0,0.5,1.0\}$4k steps.

In RL for reasoning models, D$R_i\in\{0.0,0.5,1.0\}$5S also exhibits a dual-level DSCL structure (Wang et al., 26 Sep 2025). At the sample level, it selects a subset of rollouts that maximizes the variance of normalized advantages; at the token level, it ranks tokens by $R_i\in\{0.0,0.5,1.0\}$6 and keeps only the top $R_i\in\{0.0,0.5,1.0\}$7. The retain rates are then relaxed over training by linear interpolation from aggressive initial values to milder final values. On Qwen2.5-7B with a GRPO backbone, D$R_i\in\{0.0,0.5,1.0\}$8S uses fewer than $R_i\in\{0.0,0.5,1.0\}$9 of tokens relative to GRPO baseline, produces gradient norms approximately $p_i\propto R_i$0 higher in early training, and improves average Pass@1 from $p_i\propto R_i$1 to $p_i\propto R_i$2 and Pass@8 from $p_i\propto R_i$3 to $p_i\propto R_i$4 over seven benchmarks.

Other DSCL instantiations differ mainly in their difficulty proxies. HaDCL for digital pathology emphasizes hard examples in two stages, easy-to-hard and hard-to-very-hard, by thresholding top-loss subsets within each mini-batch (Srinidhi et al., 2021). ConCur for self-supervised video learning measures positive-pair difficulty by temporal distance and enlarges the temporal span $p_i\propto R_i$5 linearly over curriculum epochs, thereby shifting from temporally close to temporally distant positives (Roy et al., 2022). Low-resource NMT sorts sentences by relative loss decline and admits only the top $p_i\propto R_i$6 easiest samples permitted by competence (Xu et al., 2020). Language-model pretraining DSCL partitions corpora into difficulty groups under metrics such as compression ratio, lexical diversity, readability, fertility, sequence length, and perplexity, then samples from those groups according to pacing or interleaving schedules (Zhang et al., 12 Jun 2025).

These examples show that DSCL is compatible with supervised, self-supervised, generative, and reinforcement-learning settings. What changes is the object of scheduling, not the basic principle of time-varying information allocation.

5. Empirical regularities and common misconceptions

Several recurrent empirical patterns emerge across DSCL studies. First, dynamic curricula frequently accelerate early or mid-training convergence. Curriculum Sampling reaches peak FID at $p_i\propto R_i$7k rather than $p_i\propto R_i$8k steps in flow matching (Sun, 12 Mar 2026). D$p_i\propto R_i$9S is reported as $^3$0 faster than GRPO to reach the same performance on Qwen2.5-7B and $^3$1 faster than GSPO (Wang et al., 26 Sep 2025). In low-resource NMT, the decline-plus-dynamic-competence variant improves En–De $^3$2K from $^3$3 to $^3$4 BLEU (Xu et al., 2020). In language-model pretraining, curriculum warmup can yield up to $^3$5 improvement, and interleaved compression-ratio pacing reaches the baseline peak in $^3$6 fewer steps (Zhang et al., 12 Jun 2025).

Second, many DSCL systems combine early selectivity with later broadening. In flow matching, a static middle-biased distribution accelerates early convergence but has worse asymptotic fidelity than Uniform sampling, so the proposed solution explicitly switches from middle-biased sampling to Uniform refinement (Sun, 12 Mar 2026). In D$^3$7S, static down-sampling variants accelerate early training but overfit later; only the dynamic schedule sustains gains throughout training (Wang et al., 26 Sep 2025). In supervised computer vision, the exponential factor $^3$8 drives the sampler back toward uniform sampling as training proceeds (Soviany, 2020).

Third, a common misconception is that DSCL always means “sample hard examples as early as possible.” Multiple results contradict this. In flow matching, Uniform sampling allocates too much early effort to endpoint regimes and slows global structure learning (Sun, 12 Mar 2026). In tool learning, applying RDS from the first step causes catastrophic format-errors (Feng et al., 18 Sep 2025). In HaDCL, hard-example emphasis is guarded by an adaptive threshold and a fallback to the full batch when the hard subset does not satisfy the threshold condition (Srinidhi et al., 2021). These results suggest that DSCL is often most effective when hard-example focus is gated by readiness, stability, or warm-up.

A second misconception is that DSCL is equivalent to fixed easy-to-hard sorting. The pretraining formulation explicitly distinguishes DSCL from vanilla curriculum learning because DSCL continuously re-samples from all groups with time-varying proportions rather than imposing a single strict ordering (Zhang et al., 12 Jun 2025). Teacher-driven and competence-driven systems reinforce the same distinction.

6. Limitations, sensitivities, and open questions

The literature also identifies several constraints. Some DSCL variants depend on expensive or impractical signals. The gradient-alignment formulation requires an approximate optimum $^3$9 and per-example gradients over the entire dataset every epoch, which the authors identify as costly (Sadasivan et al., 2021). Low-resource NMT DCL adds approximately $\mathrm{Var}(A)$0 overhead from loss evaluation and sorting (Xu et al., 2020). Tool-learning DSCL requires tuned thresholds such as $\mathrm{Var}(A)$1, $\mathrm{Var}(A)$2, and stage-advance conditions (Feng et al., 18 Sep 2025).

Performance is also domain- and scale-dependent. HaDCL yields substantial slide-level gains on Camelyon16 but only a marginal AUC increase from $\mathrm{Var}(A)$3 to $\mathrm{Var}(A)$4 on MHIST patch-level colorectal classification (Srinidhi et al., 2021). In low-resource NMT, gains shrink with data scale, reaching only $\mathrm{Var}(A)$5 BLEU on En–De $\mathrm{Var}(A)$6M (Xu et al., 2020). This suggests that DSCL is especially consequential when signal is sparse, reward is heterogeneous, or optimization is bottlenecked by uninformative samples.

Hyperparameter sensitivity remains central. Curriculum Sampling reports that switching at approximately $\mathrm{Var}(A)$7–$\mathrm{Var}(A)$8 of the budget balances structure and refinement best, while switching too early loses mid-$\mathrm{Var}(A)$9 coverage and switching too late starves endpoints (Sun, 12 Mar 2026). Diversity-aware supervised vision recommends tuning $K$00, $K$01, and $K$02 so that the curriculum lasts roughly the first one-third to one-half of training (Soviany, 2020). SPDCL similarly depends on the bucket count, pacing exponent, and the decay of the static-versus-dynamic difficulty mixture (Zhang et al., 2022).

Finally, theory remains incomplete. The curriculum-scoring work of Sadasivan and Dasgupta notes that a complete theory for deep nonconvex networks is open (Sadasivan et al., 2021). Curriculum Consistency Model explicitly states that it does not provide a formal convergence proof or explicit error-bound theorem (Liu et al., 2024). What is established instead are localized arguments: upper bounds that increase with selected advantage variance in D$K$03S, empirical U-shaped timestep difficulty in flow matching, and empirical monotonicity of PSNR-based discrepancy across timesteps in consistency distillation (Wang et al., 26 Sep 2025, Sun, 12 Mar 2026, Liu et al., 2024).

Taken together, these results place DSCL at the intersection of sampling theory, optimization control, and curriculum design. The common claim across domains is not that one universal curriculum exists, but that the sampling policy itself is a trainable or schedulable object, and that treating it as such can materially change both convergence dynamics and final model quality.