Mean Teacher Model

The teacher's weights are not learned via backpropagation. Instead, they are updated as an exponential moving average of the student's weights at each training step: θ′t = αθ′{t-1} + (1-α)θ_t. This temporal ensembling produces a more stable model that acts as a better target generator than the rapidly fluctuating student. The decay rate α is typically set very high (e.g., 0.999) to ensure slow, smooth evolution.

The core loss function combines two terms:

• Supervised classification loss (cross-entropy) on labeled RF samples
• Consistency cost (mean squared error or KL divergence) between the student's prediction and the teacher's prediction for the same unlabeled input under different augmentations

This enforces the model to produce consistent outputs when the input is perturbed by noise, fading, or frequency offset—critical for robust automatic modulation classification in dynamic spectrum environments.

Both the student and teacher receive differently augmented versions of the same unlabeled IQ sample. Typical RF augmentations include:

• Additive white Gaussian noise (AWGN) injection
• Phase rotation and frequency offset simulation
• Time shifting and amplitude scaling

The student must match the teacher's cleaner or differently perturbed prediction, learning representations invariant to channel impairments without requiring labeled data for those conditions.

Unlike contrastive methods such as SimCLR or MoCo, the Mean Teacher framework does not require negative sampling or large memory banks. It relies purely on self-distillation and consistency regularization. This makes it computationally lighter and easier to implement for RF applications where constructing meaningful negative pairs across different modulation schemes or emitters can be ambiguous.

A known failure mode in pseudo-labeling is confirmation bias, where a model reinforces its own mistakes by training on incorrect pseudo-labels. The EMA teacher mitigates this: the slowly evolving teacher provides a temporal ensemble of past student states, averaging out transient errors. The teacher's predictions are more accurate and less noisy than the student's, yielding higher-quality training targets for unlabeled RF data.

In specific emitter identification (SEI) tasks, labeled transmissions from a target device are scarce. Mean Teacher models excel here:

• Pre-train on a large corpus of unlabeled IQ captures from many emitters
• Fine-tune with only 5-10 labeled examples per emitter using prototypical network heads
• The teacher's stable embeddings produce tight, well-separated clusters in the representation space, enabling accurate few-shot classification of previously unseen hardware fingerprints.

The core principle underpinning the Mean Teacher framework. It enforces that a model should produce similar predictions for an unlabeled data point and its perturbed version. In RF contexts, perturbations include additive noise, frequency offset, or time shifts applied to IQ samples. The model learns that these channel-induced variations should not alter the fundamental classification of a signal. This smoothness assumption is critical for generalizing across varying signal-to-noise ratios (SNR) and propagation conditions without requiring labeled data for every scenario.

The weight update mechanism that defines the teacher model. Instead of backpropagation, the teacher's parameters are updated as: θ_t ← αθ_t + (1-α)θ_s, where α is a smoothing coefficient (typically 0.999). This creates a temporal ensemble of student weights, producing a more stable and accurate model over time. In RF applications, this stability is vital because raw IQ data is highly stochastic; the EMA teacher provides consistent target predictions even when individual mini-batches contain noisy or fading signal samples.

A critical distinction in semi-supervised RF learning:

• Pseudo-Labeling: A single model generates hard labels for unlabeled data, which are then used for retraining. Errors in these labels can reinforce confirmation bias.
• Mean Teacher: The teacher model generates soft probability distributions as targets, not hard one-hot labels. The student is trained with a consistency cost (MSE or KL divergence) between its own prediction and the teacher's output. This preserves uncertainty information and is far more robust to the low-SNR ambiguity common in spectrum sensing tasks.

The Mean Teacher is a form of self-distillation where the student and teacher share identical architectures. The student learns by predicting the teacher's outputs on unlabeled data, effectively distilling knowledge from the EMA ensemble into a single model. This differs from traditional knowledge distillation where a larger, pre-trained teacher transfers knowledge to a smaller student. Here, the teacher is co-evolving with the student, making it particularly suited for continual RF adaptation where signal environments change over time.

A crucial architectural safeguard that blocks gradient flow to the teacher network during backpropagation. Without this, the model could collapse to a trivial solution where both networks output identical constant vectors. The stop-gradient ensures the teacher is updated solely via EMA, not by minimizing the consistency loss directly. In RF implementations, this prevents the model from learning to ignore signal content and instead forces it to extract discriminative modulation features from the student pathway while the teacher provides stable regression targets.

A failure mode where the encoder outputs a constant vector for all inputs, achieving perfect consistency but zero utility. Mean Teacher prevents this through:

• Asymmetric update rules: Student learns via gradients; teacher via EMA.
• Input perturbations: Different augmentations applied to student and teacher branches.
• Batch normalization: Maintains activation diversity across mini-batches. In RF domains, additional safeguards like variance regularization on IQ embeddings ensure the model distinguishes between BPSK, QPSK, and QAM signals rather than collapsing to a single uninformative representation.