Frequency-Based Curriculum Learning

Updated 9 July 2025

Frequency-based curriculum learning is a set of strategies that dynamically reorders training samples using natural frequency cues across modalities.
These methods initially present high-frequency or simpler samples before progressively incorporating rarer, more complex examples to optimize learning.
Applications in vision, language, and reinforcement tasks demonstrate reduced training time, improved generalization, and enhanced computational efficiency.

Frequency-based curriculum learning is a family of curriculum learning strategies in which the frequency—with which data samples, features, or input characteristics are observed or presented—directly shapes the schedule, order, selection, or weighting of training material. Rather than strictly ordering examples from “easy to hard” by static metrics alone, frequency-based curricula exploit signals derived from natural occurrence statistics (e.g., token or n-gram lexical frequency, spatial frequency in images, or difficulty-weighted presentation frequencies in reinforcement learning tasks). This approach is applicable across modalities, offering computational efficiency, improved convergence, sample efficiency, and in some cases enhanced robustness or generalization. Recent advances in vision, LLMing, and reinforcement learning have demonstrated the practical effectiveness of frequency-based curriculum schedules, both in foundation model pretraining and domain-specific tasks.

1. Conceptual Foundations and Definitions

Frequency-based curriculum learning generalizes classic curriculum learning by incorporating frequency cues as core drivers of example selection or emphasis throughout training. Under the general curriculum learning framework, the training distribution at each stage $t$ is reweighted using a function $W_t(z)$ applied to the base data distribution $P(z)$ :

$Q_t(z) \propto W_t(z) \cdot P(z)$

where $W_t(z)$ may depend on properties such as example frequency, difficulty, or other criteria (2010.13166). Frequency can refer to statistical frequency (e.g., word count in NLP; occurrence of visual motifs in images), spectral frequency (Fourier content), or the scheduling frequency of sample presentation and replay (2010.13166, 2506.11300, 2507.03779).

In practice, high-frequency samples or features may be treated as “easy” and prioritized for early training, or, conversely, rare or underrepresented samples may be upweighted to address data imbalance. Frequency-based strategies are not intrinsically tied to data ordering, but frequently provide a mechanism for dynamic data weighting, schedule pacing, or sample inclusion throughout curriculum design.

2. Frequency-Based Strategies in Vision Systems

Recent work in computer vision leverages the spectral (Fourier) frequency content of images to structure learning curricula that improve training speed and model robustness. EfficientTrain++ (2405.08768) and FastDINOv2 (2507.03779) are exemplary of such approaches:

Low-Frequency First Curriculum: Training images are initially low-pass filtered, retaining only smooth, low-frequency components, typically via Fourier cropping:

$X_{c} = \mathcal{F}^{-1} \circ \mathcal{C}_{B,B} \circ \mathcal{F}(X)$

where $\mathcal{F}$ denotes the 2D DFT, $\mathcal{C}_{B,B}(\cdot)$ is a central crop in the frequency domain, and $X$ is the input image (2405.08768, 2211.09703, 2507.03779).

Curriculum Scheduling: As training progresses, the cropping window $B$ increases, gradually exposing higher-frequency details. Simultaneously, data augmentation intensity is modulated, starting from minimal augmentation to preserve easy (natural) patterns, and increasing to full strength as training matures (2405.08768).
Gaussian Noise Patching: FastDINOv2 complements the low-frequency-first stage with patchwise Gaussian noise injections in the high-frequency phase to enhance robustness, particularly to corruption benchmarks such as ImageNet-C (2507.03779). This hybrid scheme achieves both accelerated convergence (reducing training time by 1.6x–3x) and high robustness.
Empirical Outcomes: These strategies maintain or slightly improve top-1 accuracy on large-scale datasets (ImageNet-1K/22K) while sharply reducing FLOPs and wall-time (2211.09703, 2405.08768, 2507.03779). Additionally, models exhibit improved resistance to corruption and adversarial effects—especially on high-frequency noise perturbations.

A table summarizing core methodological elements is provided:

Study	Frequency Mechanism	Schedule	Application
EfficientTrain++	Fourier cropping (low- $f$ )	Greedy search	Vision transformers, ResNet, MAE
FastDINOv2	Downsample, then full- $f$	2-stage: 75% low- $f$ , 25% full- $f$	DINOv2/ViT-B/16, ImageNet, ImageNet-C
EfficientTrain	Fourier cropping + weak/strong augmentation	Greedy search	General vision backbones

3. Frequency-Based Curriculum in LLMing

In LLMing, frequency-based curriculum learning generally utilizes token, word, or n-gram frequency to order or weight samples, or applies information-theoretic proxies (compression ratio, lexical diversity) that bear strong correlation with observed linguistic frequency.

Key results from large-scale pretraining studies (2506.11300):

Difficulty Metrics: Compression ratio, lexical diversity (MTLD), and Flesch reading ease are used as proxies for textual “easiness” or frequency.
Ordering and Pacing: Models are pretrained by strictly ordering data from low to high difficulty (e.g., by frequency; “vanilla” CL), or via pacing-based curricula where data is chunked into bins of increasing difficulty and mixed according to a pacing schedule. Inverse quadratic pacing functions,

$t_i = \frac{T}{\sum_{j=0}^{N-1} (N-j)^2} \cdot (N-i)^2$

favor earlier exposure to easy/high-frequency data, with gradual transition to lower-frequency (rare, complex) content.

Empirical Findings: Frequency-based ordering accelerates convergence (requiring up to 27.5% fewer steps to reach peak performance with “number of tokens” ordering) and can yield lasting improvements if used as a warmup phase. Gains of up to 3.5% in benchmark scores over random orderings are reported, with benefits persisting across multiple metrics and tasks (2506.11300).
Interpretation: Frequent tokens or simpler, more redundant constructions build core representations efficiently; gradually shifting to rare or complex tokens fosters broader generalization and coverage, mirroring pedagogical strategies in human language acquisition.

4. Curriculum Scheduling, Optimization, and Search

Frequency-based curricula may be constructed manually or discovered via metaheuristic or continuous optimization. In reinforcement learning, the curriculum is often parameterized as a multiset of task presentations, allowing tasks to repeat according to a frequency vector $f(m)$ (1901.11478):

$\text{Curriculum } c = \langle m_1, m_2, \ldots, m_L \rangle, \quad f(m) = \text{frequency of } m.$

Search methods such as greedy search, genetic algorithms, and ant colony optimization operate over frequency assignments, optimizing for performance objectives (e.g., jumpstart, regret, max-return) that are frequency-sensitive (1901.11478).

In computer vision, tailored greedy or computational-constrained search algorithms are developed to choose frequency-cropping window parameters that trade off between computation and accuracy, validated on held-out sets (2405.08768).

In supervised learning and RL, dynamic sample weighting (e.g., via ScreenerNet) provides soft frequency adjustments according to model error, enabling frequency-based reweighting without hard thresholds (1801.00904).

5. Theoretical Insights and Challenges

Analytical frameworks reveal that curriculum effects—when measured via frequency or difficulty ordering—are strongly regime-dependent:

Online Learning: Presenting frequent/easy examples first speeds up learning but may not improve asymptotic generalization unless explicit consolidation mechanisms (e.g., Gaussian priors or elastic coupling in the loss function) are imposed at curriculum boundaries (2106.08068).
Batch Learning: Without intervention, the benefits of curriculum ordering may dissipate in convex (well-posed) learning scenarios; explicit loss modifications are needed to achieve robust gains (2106.08068).
Hybrid and Adaptive Approaches: Theory and experiments show that curricula which adapt frequency to learning progress or learner state—either via sample difficulty estimates, performance feedback, or pacing functions—yield the greatest efficiency and generalization benefits (2004.11812, 2010.13166, 2106.08569).
Trade-offs: Over-emphasizing frequent/easy examples can suppress diversity; curriculum must balance the ease of early learning with coverage and robustness (2010.13166, 2101.10382). Defining appropriate frequency metrics, pacing rates, and blending strategies remains an open challenge in some domains.

6. Applications and Empirical Impact

Frequency-based curriculum learning has demonstrated broad applicability:

Efficient Vision Model Pretraining: Significant reductions in compute (1.5–3x), accelerated convergence, and maintained or improved corruption robustness are established for visual backbone models including ViT, ResNet, MAE, and DINOv2 (2211.09703, 2405.08768, 2507.03779).
LLM Pretraining: Systematic ordering by frequency-aligned metrics yields faster convergence and superior or equivalent task performance across a wide range of NLP benchmarks (2506.11300).
Continual and Incremental Learning: Automated curriculum scheduling based on inter-class feature similarities (measured via pretrained representations) can inform optimal frequency and temporal spacing between similar tasks to reduce forgetting and boost transfer—demonstrated to benefit both machine learning models and human learning in psychophysical experiments (2211.15470).
Reinforcement Learning Task Sequencing: Frequency-controlled presentation of sub-tasks, combined with performance-based search, optimizes policy transfer and sample efficiency while reducing suboptimal actions in critical domains (1901.11478, 1906.06178).

7. Future Research Directions

Open problems and next steps in frequency-based curriculum learning include:

Theory and Boundaries: Clarifying the conditions under which frequency-based or “easy-to-hard” curricula yield persistent generalization gains versus transient acceleration (2106.08068).
Dynamic and Hybrid Scheduling: Further development of hybrid approaches combining frequency-based signals with difficulty, loss, or performance feedback—potentially using learning-to-teach or meta-learning methods (2010.13166, 2004.11812).
Domain-Specific Frequency Cues: Extending frequency-based strategies to modalities beyond vision and language, such as graph data, medical imaging, and unsupervised or self-supervised settings (2010.13166, 2101.10382).
Diversity and Fairness: Designing curricula that leverage frequency while ensuring sufficient diversity and mitigating bias in the presence of class imbalance or skewed data distributions (2010.13166).
Automated Curriculum Discovery: Scaling up continuous optimization, autoencoder-based scheduling, and reinforcement learning strategies to discover efficient frequency-based curricula in large, heterogeneous datasets (2106.08569, 2405.08768).

In summary, frequency-based curriculum learning represents a flexible and empirically validated paradigm for structuring learning schedules according to natural or task-induced frequency statistics. By adaptively controlling the occurrence and temporal spacing of data, features, or sub-tasks, these curricula yield accelerated convergence, computational efficiency, enhanced robustness, and generalization, with continued theoretical and practical innovation forecast across modalities and domains.