Curriculum Learning

Curriculum learning changes the order or weighting of training examples so the model sees easier, cleaner, shorter, or more reliable examples before harder ones.

Instead of optimizing over a fixed data distribution, training uses a time-dependent sampling distribution:

$$\underset{\theta }{\min }{\mathbb{E}}_{(x,y)\sim q_t(x,y)}\left[\mathcal{L}(f_{\theta }(x),y)\right]$$

where $q_t$ changes with training step $t$.

An example-weighted objective is:

$${\mathcal{L}}_t(\theta )=\frac{1}{n}\sum _{i=1}^n{w}_i(t)\mathcal{L}(f_{\theta }(x_i),y_i)$$

where $w_i(t)$ controls when and how strongly example $i$ contributes.

Curriculum Contract

Curriculum learning needs an explicit policy for ordering or weighting examples:

$$w_i(t)={\pi }_{\mathrm{cur}}(x_i,y_i,t;s_i)$$

where $s_i$ is a difficulty, quality, source, or confidence signal.

Contract field	Question
difficulty signal	what makes an example easy or hard?
schedule	how does sampling change with training step?
coverage	when does the model see the full target distribution?
adaptation	is the curriculum fixed or based on model performance?
evaluation	is the final test distribution unchanged?

Curriculum is a training intervention, not a reason to evaluate only on easy examples.

Schedule Types

Type	Example	Risk
fixed schedule	short sequences before long sequences	hand-designed difficulty may be wrong
source schedule	synthetic or curated data before noisy real data	source bias can persist
confidence schedule	high-confidence labels first	rare/ambiguous cases delayed
self-paced	model selects examples it can learn	confirmation bias
anti-curriculum	hard examples first	instability if model lacks basics

Evaluation Boundary

The claim should distinguish faster training from better final generalization.

Claim	Evidence
stabilizes optimization	fewer divergences, smoother learning curves
improves sample efficiency	same metric with fewer examples/steps
improves final quality	better metric on full target distribution
improves robustness	better hard-slice or OOD performance
only filters bad data	compare against data cleaning baseline

Curriculum Signals

• Sequence length or context length.
• Label confidence or annotation quality.
• Data source reliability.
• Task difficulty or synthetic-to-real transition.
• Coarse-to-fine resolution.
• Simple-to-complex tool or reasoning traces.

Why It Matters

• Can stabilize training on noisy or heterogeneous data.
• Makes data ordering a modeling decision, not just an implementation detail.
• Can bias the model if difficult or rare examples are under-sampled.
• In agent and scientific workflows, curriculum can separate basic format learning from hard verification tasks.

Checks

• What defines easy and hard examples?
• Is the curriculum fixed, learned, or performance-adaptive?
• Are rare but important examples delayed too long?
• Does the final evaluation cover the full difficulty distribution?
• Is improvement from curriculum or simply from data filtering?
• Is the curriculum schedule documented enough to reproduce?
• Are easy/hard slices reported separately?

Related

• Sampling strategy
• Label noise
• Learning curve
• Fine-tuning
• Training loop
• Robustness