Curriculum learning

Overview

Curriculum learning presents training examples in an order chosen by some complexity measure, so that simpler examples come first. The BabyLM organisers defined it as sorting training steps by one or more complexity metrics 2504.08165 §7.4. The shared invariant of the data-order variants is that the set of examples stays fixed and only their order or schedule changes. Some variants also change the data itself, which matters when comparing results 2504.08165 app. F.

Twelve cards carry this concept, and they do not all change the same thing. Eleven list it under concepts:; the partial multi-label card carries it only as a tag. The BabyLM Challenge findings cover data order, where 13 of 31 teams (41.9%) tried some form of curriculum 2504.08165 §7.4. The paper treats curriculum as its most common approach, and reports that most attempts did not give consistent gains over naive ordering 2504.08165 §7.4. FlexMatch schedules a per-class confidence threshold for pseudo labels, not the order of examples 2110.08263 §3.1. The human-motion model schedules a loss weight 1809.03036 §3.4. The humanoid controller moves through three training stages of rising difficulty, which change the task distribution rather than a list of examples 2408.07295 §4.4. The quadruped locomotion policy ramps obstacle density from sparse to dense over training 2508.11849 §4.4. PredRNN's reverse scheduled sampling changes how often the encoder sees real frames 2103.09504 §4.4. The partial multi-label method recomputes a per-entry loss weight every epoch, and its paper calls that weighted loss a curriculum loss 2610.17635 eq. 1. The DexVLA robot policy lists this concept, though its card describes three training stages that change the data and the trainable parts rather than the order of examples 2502.05855 §3.2. The reinforcement-learning survey gives the most general frame: a curriculum is a directed acyclic graph over experience, and building one has three parts, which are task generation, sequencing and transfer 2003.04960 §3.1 2003.04960 §3.2. It runs no experiments, so it maps methods rather than reporting results. The multilingual translation model NLLB-200 adds groups of language pairs at fixed update counts, so its schedule changes the data mix and not only the order 2207.04672 §8.2.3. The variants below are grouped by what they change.

Variants

Complexity-ranked order

Examples are sorted by a score and presented in that order. The scores the paper lists include sentence length, lexical frequency, syntactic complexity, and surprisal, and whole datasets were sorted by difficulty 2504.08165 §7.4. Card: Findings of the BabyLM Challenge. Several of these submissions found no consistent gain over a random order 2504.08165 app. F.

Staged or two-phase schedule

Training begins with one ordering and then switches. One submission ranked sentences by surprisal, trained on that order, and then trained further on a random-order pass. The random-order phase is what beat its baseline 2504.08165 app. F; see the surprisal entry under Model-selected examples. Another, the Contextualizer, sorted its corpora from easy to hard at the start and end of training and used a noisier arrangement in the middle 2504.08165 app. F. It also built extra samples by combining chunks of text from different contexts. The paper itself calls this a form of data augmentation 2504.08165 §7.4, so its result cannot be credited to the ordering alone 2504.08165 §7.2. Card: Findings of the BabyLM Challenge.

Model-selected examples

A model scores each example and the schedule is built from those scores. One submission ranked sentences by average surprisal from an ensemble of LSTM teachers. It did not beat a random baseline alone, but improved when followed by random-order training 2504.08165 app. F. Another selected training examples by n-gram surprisal and gained on GLUE but lost on MSGS 2504.08165 app. F. Card: Findings of the BabyLM Challenge.

Growing vocabulary or objective

The vocabulary grows during training, or the training objective becomes harder over time 2504.08165 §7.4. Card: Findings of the BabyLM Challenge.

Language-pair buckets added at fixed updates (changes the data mix)

Language pairs are split into four buckets, and each bucket joins training at a fixed update count. The starts are chosen so that pairs that overfit early join late 2207.04672 §8.2.3. The paper's final run enters the buckets at 0, 170k, 230k and 270k of 300k updates. The earliest bucket is the largest, with 822 pairs, and it holds 673 low-resource pairs 2207.04672 §8.2.3. A shorter ablation of 100k updates entered the buckets at 0, 60k and 80k. It gave small gains for vanilla MoE on low-resource directions, and it hurt the MoE variant that uses expert output masking 2207.04672 §6.2.3. Card: No Language Left Behind: Scaling Human-Centered Machine Translation.

Sample and task sequencing in reinforcement learning (survey)

The survey orders methods by how far they change the task, from reordering experience of the final task to defining new intermediate tasks 2003.04960 §4.2. At the narrow end, sample sequencing reorders experience from the target task without changing the MDP, with prioritised and hindsight replay as examples 2003.04960 §4.2.1. Co-learning lets a curriculum emerge from agents that interact or self-play in one environment 2003.04960 §4.2.2. Reward and initial or terminal state changes make intermediate tasks differ only in those properties 2003.04960 §4.2.3. Other methods allow any difference from the target, and human-in-the-loop methods have people sequence the tasks by hand 2003.04960 §4.2.4 2003.04960 §4.2.5. Intermediate tasks can also be generated automatically from a parameterised domain 2003.04960 §4.1.

Transferred knowledge is classed as low level (policies, value functions, task models, training instances) or high level (partial policies, options, skills, shaping rewards) 2003.04960 §4.3. Its tables place each listed paper on the seven dimensions, and every sample-sequencing row uses only the target task, with no transfer 2003.04960 tab. 2. Card: Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey.

Stage-wise task difficulty in reinforcement learning (not a data order)

A humanoid controller that follows masked motion directives is trained in three stages 2408.07295 §4.4. Stage 1 uses locomotion directives only, with single torso pushes. Stage 2 adds continuous pushes and grows the episodes to 800 policy steps (16 s). Stage 3 uses whole-body directives, which may be fully specified or partially masked 2408.07295 §4.4. The stages change episode length, disturbances and the mix of task types. They do not reorder a fixed dataset.

Against a variant trained without the stages, the authors report lower simulated mimicry failure (4.875% against 0.450%) and lower walking root drift at 1 m/s (1.346 m against 0.413 m) 2408.07295 tab. 5. The same table shows the opposite for standing under a push: root drift of 0.189 m against 0.256 m at 50 N, and 0.234 m against 0.311 m at 100 N 2408.07295 tab. 5. The comparison is not compute-matched. The variant without the stages trained until its loss plateaued, for longer than the full model 2408.07295 §5.5. Card: Learning Multi-Modal Whole-Body Control for Real-World Humanoid Robots.

Obstacle density ramp in RL (not a data order)

A quadruped locomotion policy is trained with PPO in simulation. The density of obstacles rises linearly from sparse to dense over training, and each iteration samples a curriculum density 2508.11849 §4.4 2508.11849 alg. 1. The paper does not state the start and end densities or the length of the ramp 2508.11849 tab. 3. The ramp runs alongside per-episode physics randomisation, which is a separate technique 2508.11849 tab. 3. The card's results compare architectures and token counts, not the ramp on and off 2508.11849 tab. 4 2508.11849 tab. 7, so the ramp's own effect is not isolated in the paper. Card: LocoMamba: Vision-Driven Locomotion via End-to-End Deep Reinforcement Learning with Mamba.

Attack-strength threshold in adversarial training (the paper calls it a curriculum)

In PGD adversarial training the inner attack usually runs for a fixed number of steps on every batch. This variant stops each example's attack once a stationarity score, FOSC, falls to or below a threshold. The threshold falls linearly from c_max to zero over the first T′ epochs, so early epochs train on attacks that are solved less fully and later epochs on attacks that are solved more fully 2112.08304 §4.1 2112.08304 alg. 1. The paper treats FOSC as a difficulty measure, so it calls the method a curriculum. It contrasts this with a curriculum that uses the PGD step count as difficulty, and argues that more steps can overshoot 2112.08304 §4.3. The clean inputs stay the same, but the adversarial inputs change every epoch, so this is a schedule on difficulty rather than a reordering of examples. In an earlier observation, replacing the first 20 epochs of PGD with one-step FGSM gave higher final robustness 2112.08304 §3.2 fig. 3.

The authors report, for CIFAR-10 with an 8-layer CNN, 48.06% under PGD-10 against 44.39% for standard PGD training and 45.54% for the step-count curriculum 2112.08304 tab. 1. The same run is also higher on CIFAR-10 under FGSM, PGD-20 and C&W∞ than both baselines 2112.08304 tab. 1. On MNIST it has the highest PGD-10, PGD-20 and C&W∞ values, while the step-count curriculum is higher on FGSM and on clean accuracy 2112.08304 tab. 1. Under black-box attacks on CIFAR-10, the paper reports 72.15% against 65.80% for standard training under PGD-10 2112.08304 tab. 2. These are author-reported numbers. The step-count curriculum's CIFAR-10 C&W∞ value (35.77%) is below standard training's (36.33%) 2112.08304 tab. 1.

The convergence bound uses constants (smoothness, strong concavity, gradient variance and the inner-solve error) that the experiments do not estimate, and the paper says Danskin's theorem does not strictly hold for ReLU networks 2112.08304 §4.2. The bound therefore does not predict the reported gains. The paper suggests estimating c_max from FGSM examples, but uses 0.5 in every run 2112.08304 §4.1 2112.08304 §5.1. Card: On the Convergence and Robustness of Adversarial Training.

Scheduled input source in recurrent video prediction (not a data order)

During encoder steps, reverse scheduled sampling feeds the cell the true frame with a probability ε, and otherwise the model's own previous prediction. ε rises from a start value to an end value over training 2103.09504 §4.4 eq. 9. The paper's best run uses an exponential rise from 0.5 to 1.0 2103.09504 tab. 6. The paper does not state the step counts of the schedule 2103.09504 §4.4. The schedule changes the inputs, not the order of training examples, so it is a schedule in the broader sense only.

In one ablation without the decoupling loss, the exponential schedule lowers fixed Moving MNIST MSE from 57.3 to 50.6 against the model alone 2103.09504 tab. 6. The same schedule on a convolutional LSTM lowers MSE from 103.3 to 64.2 2103.09504 tab. 5. Both results are one dataset family, and the authors report them themselves. Card: PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning.

Per-class pseudo-label threshold (not a data order)

In semi-supervised image classification, the model labels unlabeled images itself and keeps only the labels it is confident about. A single cut-off is usually used for all classes. FlexMatch gives each class its own cut-off and moves it with how many unlabeled samples are currently assigned to that class. Classes the model has not learned well get a lower cut-off and admit more pseudo labels. The authors call this Curriculum Pseudo Labeling 2110.08263 §3.1 2110.08263 eq. 12. It keeps one stored class mark per unlabeled sample and adds no parameters or extra forward passes 2110.08263 §3.1.

The authors report lower error than FixMatch in 8 of 11 cells of their main table, with large gains on CIFAR-100 with 400 labels (39.94% against 46.42%) and STL-10 with 40 labels (29.15% against 35.97%) 2110.08263 tab. 1. It is not uniformly better. FixMatch is equal or better on CIFAR-10 with 250 labels and on SVHN 2110.08263 tab. 1 2110.08263 §4.1. These are author-reported results. Card: FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling.

Loss-weight schedule (not a data order)

The closed-loop term of the training loss is multiplied by a weight that starts at zero and rises in steps. The model first learns one-step prediction from real data, then learns to predict from its own outputs 1809.03036 §3.4 eq. 6. The paper does not call this curriculum learning. It changes the loss, not the examples or their order, so it is a schedule in the broader sense only. The paper gives no step values for the weight 1809.03036 §3.4. The card's source gives no number that isolates the schedule's effect; the ablations are referred to supplementary material 1809.03036 §5. Card: A Neural Temporal Model for Human Motion Prediction.

Calibrated per-entry weight, recomputed each epoch (not a data order)

Each training image in partial multi-label learning carries candidate tags, and some are wrong. Each candidate positive is weighted by a calibrator, which maps a histogram of the model's confidences to the probability that the candidate is correct 2610.17635 §4.1 eq. 7. Each epoch, the confidences on the training set are collected and the weights are recomputed 2610.17635 alg. 1. Negative entries keep weight 1 in the algorithm 2610.17635 alg. 1.

The calibrator is pre-trained on VOC 2007 and then used unchanged on other datasets and noise rates 2610.17635 §4.1 2610.17635 §5.2. The authors report the best mAP in 15 of 16 noise settings against nine baselines, with LL-R ahead at VOC with 20% noise 2610.17635 tab. 1 2610.17635 §5.2. On COCO at 80% noise, at epoch 1, the pre-trained calibrator reaches 61.48 mAP. Fixed hard, soft and identity weightings reach 59.79, 60.08 and 59.93, and weights from true labels reach 66.42 2610.17635 tab. 2. The last row uses ground truth and is an upper bound, not a method. The paper does not state how many runs stand behind each cell, and gives no variance 2610.17635 §5.1. Card: Calibrated Disambiguation for Partial Multi-label Learning.

Staged pre-training, alignment and adaptation (not a data order)

A vision-language-action policy for robots is trained in three runs, each on a different data set and with different parts trainable 2502.05855 §3.2. Stage 1 trains only the action expert on cross-embodiment data, about 100 hours over 91 tasks and four robot bodies 2502.05855 app. C.4. Stage 2 keeps one embodiment and trains the language model, the projection and the expert together. Stage 3 fine-tunes on demonstrations for one task, and the authors skip it for simpler tasks 2502.05855 §3.2. The card does not describe these stages as a curriculum. The card lists the paper under this concept, and the stages move from broad to specific data, so this is a schedule in the broader sense only.

In the authors' stage ablation, runs without stage 1 or without stage 2 score 0.0 on both shirt and laundry folding. Without stage 3, laundry folding scores 0.0 against 0.4 with it, and shirt folding is 0.92 in both 2502.05855 §4.4. The card notes that the paper's explanation for the stage-1 result (that stage 1 warms up a large expert) is a hypothesis the paper does not test 2502.05855 §4.4. These are author-reported results on the authors' own robots, with 10 trials per task and no variance given 2502.05855 §4.1 2502.05855 §4.3. Card: DexVLA: Vision-Language Model with Plug-In Diffusion Expert for General Robot Control.

Scale-stage growth in NeRF (adds data and a network block per stage; not a data order)

A neural radiance field for city scenes seen from satellite to street level is trained in four stages 2112.05504 §3.3. Stage 1 uses only the most distant image scale and a four-layer base block. Each later stage adds the next closer scale to the training rays and appends one two-layer residual block with its own output head 2112.05504 §3.3. Head L is trained on every scale up to L, so each head gives one level of detail 2112.05504 eq. 3. The stages change the training set and the network together. The set grows rather than being reordered, so this is a schedule in the broader sense only. The paper's reason is that training all scales at once biases a plain NeRF toward low frequencies 2112.05504 §3.2.

The paper gives 100,000 iterations per stage 2112.05504 §4. Its main comparison uses a row labelled "same iter as baselines", which the paper says uses the baselines' budget but does not give as a number. Its "until convergence" row trains longer 2112.05504 tab. 2. On average PSNR, the same-iteration row gives 23.48 on 56 Leonard and 23.61 on Transamerica, against 22.31 and 22.83 for the strongest Mip-NeRF baseline 2112.05504 tab. 2. In the ablation, dropping the data-feeding scheme gives 22.34 on 56 Leonard and 23.02 on Transamerica, and dropping model growing gives 22.14 and 23.06 2112.05504 tab. 3. On the averages, the no-feeding variant is only just above the strongest baseline on both scenes, which contradicts the text's wording 2112.05504 §4.2. The tables cover two scenes, and the authors report them themselves. Card: BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering.

When to use which

The data-order evidence rests on one paper, so the first five rows do not rank methods on general grounds. Any choice should be checked against a random-order run on your own data. The per-class threshold, attack-strength threshold, stage-wise, obstacle-ramp, scale-stage, input-schedule, calibrated-weight, staged-pipeline and bucket rows each rest on one paper's own experiments, so check them against a fixed-schedule baseline on your data. The loss-weight schedule has no comparison in the card to base a choice on, so it is not in this table. The last two rows are classifications of published work, not measured comparisons, so they say where a method sits and do not say which one wins.

Implementation sketch

Language-agnostic pseudocode of the common core. Variants differ in the score and in how many phases they use.

# Curriculum over a fixed corpus  [§7.4] [app. F]
# Input:  corpus (list of examples), score(example) -> complexity
# Output: one training order over the same examples

def curriculum_order(corpus, score, phase_two_random=True):
    # Rank every example by one complexity measure (length, frequency,
    # surprisal, parse depth) [§7.4]
    ranked = sorted(corpus, key=score)
    # Easy-to-hard first phase
    if not phase_two_random:
        return ranked
    # Second phase: a random permutation of the same examples [app. F]
    return ranked + random_permutation(corpus)

Notes: the sort key is the only part that changes across variants. The two-phase tail is one reported pattern, not the only one 2504.08165 app. F. Surprisal ranking needs a scoring model, an LSTM ensemble or an n-gram model, run over the whole corpus before training starts 2504.08165 app. F. The loss-weight schedule is a different operation (a per-step weight on the loss term) and is not covered by this sketch 1809.03036 §3.4. The per-class threshold is also a different operation (a class-dependent mask on pseudo labels) 2110.08263 §3.1. The bucket schedule adds whole groups of examples at fixed update counts, which this sketch does not cover 2207.04672 §8.2.3. Scale-stage NeRF training also grows the network at each stage, adding a block and an output head, so it does not fit this sketch either 2112.05504 §3.3. The stage-wise RL curriculum changes the episode length, the disturbances and the directive sampler, not a list of examples 2408.07295 §4.4. Reverse scheduled sampling is a per-step choice of input, made with probability ε 2103.09504 eq. 9. The calibrated weight is a per-entry loss weight set from confidence bins, recomputed every epoch 2610.17635 alg. 1. The DexVLA stages are separate training runs over different data and trainable parts, so they are not a sort of one corpus 2502.05855 §3.2. The obstacle ramp changes the simulated terrain, not a list of examples 2508.11849 §4.4. The attack-strength threshold stops each example's inner attack on a per-example score inside the adversarial loop; the example set is unchanged 2112.08304 alg. 1.

Contradictions

• Majority negative vs. positive summaries. The paper says most curriculum attempts did not improve consistently 2504.08165 §7.4, but also says one curriculum method gave significant gains 2504.08165 §9 and that curricula can beat a naive ordering on GLUE 2504.08165 app. D.
• Linguistic ordering. One team reported that six linguistic complexity metrics beat a random order on the 10M-word track 2504.08165 app. F. Another found dependency-based ranking best among its curricula, yet all of them underperformed a random baseline 2504.08165 app. F.
• Surprisal ordering. The LSTM-teacher version did not beat a random baseline on its own, but did when followed by random-order training 2504.08165 app. F. The n-gram version improved GLUE but not MSGS 2504.08165 app. F.
• Curriculum with output masking. The final NLLB model combines the four-phase bucket schedule with expert output masking 2207.04672 §8.2.4. The authors' shorter ablation found the curriculum helped vanilla MoE on low-resource directions but hurt MoE with output masking 2207.04672 §6.2.3. The two runs differ in length (100k against 300k updates), so the paper does not settle the question.
• MSGS. The paper says principled curriculum approaches can improve the MSGS score 2504.08165 app. D, while its main summary says most curricula did not help 2504.08165 §7.4.
• Scale-stage NeRF, text against table. The paper says that without progressive data feeding the results are "even inferior than baselines" 2112.05504 §4.2. Its averages in tab. 3 show the variant slightly above the strongest baseline on both scenes 2112.05504 tab. 2 2112.05504 tab. 3.
• Stage-wise RL, by setting. The same ablation favours the staged curriculum on walking and mimicry, and the no-stage variant on standing under push 2408.07295 tab. 5. The authors' text calls the standing performance on par with the baseline, while the baseline comparison table shows a larger drift for the controller under a 50 N push 2408.07295 §5.3 2408.07295 tab. 2.

Papers

• Findings of the BabyLM Challenge: Sample-Efficient Pretraining on Developmentally Plausible Corpora: the first BabyLM shared task, with 31 submissions and a meta-analysis that reports most curriculum attempts did not improve consistently.
• FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling: applies a per-class, learning-status-dependent threshold to FixMatch-style pseudo labels. The name refers to curriculum learning, but the schedule acts on the pseudo-label threshold, not on the order of examples.
• A Neural Temporal Model for Human Motion Prediction: listed under this concept for its closed-loop loss-weight schedule. The paper does not describe that schedule as curriculum learning.
• Learning Multi-Modal Whole-Body Control for Real-World Humanoid Robots: a three-stage difficulty curriculum for one humanoid controller, with an ablation against a variant trained without it. The comparison is author-reported and not compute-matched.
• BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering: a NeRF that adds one closer image scale and one residual block per stage, with an output head per level of detail. Its ablations are author-reported and cover two city scenes.
• PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning: uses reverse scheduled sampling, a schedule on the input source rather than on the examples. Listed under this concept by the card.
• No Language Left Behind: Scaling Human-Centered Machine Translation: a four-phase schedule that adds language-pair buckets at fixed updates for a 54.5B-parameter MoE translation model. Its own ablations are author-reported and use the dev set.
• Calibrated Disambiguation for Partial Multi-label Learning: a calibrated per-entry weight recomputed each epoch, which the paper calls a curriculum loss. Its weights are not a data order.
• Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey: a survey that defines curriculum learning for RL as task generation, sequencing and transfer, and classifies published methods on seven dimensions. It has no experiments of its own.
• DexVLA: Vision-Language Model with Plug-In Diffusion Expert for General Robot Control: a three-stage training pipeline (cross-embodiment pretraining, embodiment alignment, task adaptation) for a robot policy. Listed under this concept by the card. Its results are author-reported on the authors' own robots.
• LocoMamba: Vision-Driven Locomotion via End-to-End Deep Reinforcement Learning with Mamba: a PPO locomotion policy in PyBullet that ramps obstacle density over training. The paper's comparisons are architecture comparisons, and the ramp is not isolated. Results are author-reported.
• On the Convergence and Robustness of Adversarial Training: a FOSC threshold that falls linearly over training, which stops each PGD example once its inner solve is good enough. The paper calls this a curriculum, but the threshold sets attack strength, not example order. Results are author-reported.