Kai J. Sandbrink | Searcharxiv

arXiv2026

Teacher Geometry Shapes Learnability in Teacher-Student Networks

Teacher-student systems, in which a teacher neural network generates training labels so that a student neural network can learn to implement the same function, are widely used as an abstract setting to study learning. However, the structure of the teachers is often overlooked by assuming randomly-generated, normally-distributed parameters. This hides substantial variation in how learnable different teachers are. We formalize learnability as the success rate of converging to the global minimum, as a function of overparameterization, learning algorithm, student initialization distribution, and teacher geometry. We both identify an easy distribution that maximizes node dissimilarity and a hard distribution that minimizes it, and show that these two distributions induce markedly different success rates across a large range of settings and for different activation functions. To explain the gap, we study the loss landscape of small neural networks that contain two distinct kinds of suboptimal local minima, out-of-bounds (OOB) minima at the edge of the data distribution and interior minima within. Assuming infinite data and a fast readout layer, we analytically reduce the loss landscape of small networks to two dimensions, showing that the region of attraction of interior minima changes as a function of teacher structure. In larger networks, maximally dissimilar teachers induce more interior minima, while minimally dissimilar teachers induce more OOB minima. Motivated by these analyses, we show that differentially increasing the learning rate of the readout layer and decreasing the learning rate of the inner biases increases success rates. These findings provide an important step in narrowing the gap between the study of teacher-student networks and more structured functions that arise in practice.

cs.LG↗

arXiv2026

Pretraining Curricula Enable Selective Fine-tuning

Transformers follow implicit curricula whereby some tasks are learned before others. However, how explicit pretraining curricula influence learning, generalization, and the selectivity of fine-tuning is unclear. This is important for AI safety, where fine-tuning is used to selectively suppress misaligned behaviors. Here, we compare curricula that pretrain tasks in a balanced (sampled uniformly) or an imbalanced (one task early, the other late) fashion. We show that imbalanced learning of two conflicting copy tasks promotes in-context learning and improves the selectivity of refusal fine-tuning. Ablations and activation patching show that this occurs because imbalanced pretraining encourages tasks to be disentangled in separable neural circuits, whereas balanced training routes both tasks through a common pathway. We extend these findings to a synthetic language learning task involving rule-consistent and rule-violating data, where imbalanced curricula similarly lead to more localized, less entangled rule representations, resulting in more robust rule-following behavior. Together, these results suggest that imbalanced pretraining curricula may be an important tool for promoting disentangled representations, with direct consequences for the precision and reliability of safety fine-tuning.

cs.LG↗