Transformers are effective at inferring the latent task from context via two inference modes: recognizing a task seen during training, and adapting to a novel one. Recent interpretability studies have identified from middle-layer representations task-specific directions, or task vectors, that steer model behavior. However, a lack of rigorous foundations hinders connecting internal representations to external model behavior: existing work fails to explain how task-vector geometry is shaped by the training distribution, and what geometry enables out-of-distribution (OOD) generalization. In this paper, we study these questions in a controlled synthetic setting by training small transformers from scratch on latent-task sequence distributions, which allows a principled mathematical characterization. We show that two inference modes can coexist within a single model. In-distribution behavior is governed by Bayesian task retrieval, implemented internally through convex combinations of learned task vectors. OOD behavior, by contrast, arises through extrapolative task learning, whose representations occupy a subspace nearly orthogonal to the task-vector subspace. Taken together, our results suggest that task-vector geometry, training distributions, and generalization behaviors are closely related.
The transformer's emergent ability to perform in-context learning (ICL) has sparked a wide range of studies designed to understand its underlying mechanisms. Existing works often study how training task diversity, defined either as the number of ICL training task vectors or as the number of function classes from which the task vectors are drawn, shapes both the learning dynamics and generalization capabilities of ICL. While both definitions have uncovered many interesting phenomena, many observations under the latter definition remain theoretically unexplained. This paper presents a minimal analytical model under which these phenomena provably emerge from the properties of the training data. By modeling the training task vectors as a mixture of low-rank Gaussians, we show how training task diversity, defined by the number of non-overlapping columns between subspaces that parameterize the covariance matrices, improves both the generalization and optimization trajectory of ICL with linear attention. In particular, we show that our model can explain (i) why training with task diversity shortens the ICL plateau and (ii) why ICL appears to achieve out-of-distribution generalization. We conclude by empirically demonstrating how our results extend to nonlinear transformers and nonlinear function classes. Overall, our work presents a tractable framework to unify existing observations.
Recent work has promoted task-aware layer pruning as a way to improve model performance on particular tasks, as shown by TALE. In this paper, we investigate when such improvements occur and why. We show first that, across controlled polynomial regression tasks and large language models, such pruning yields no benefit on in-distribution (ID) data but consistently improves out-of-distribution (OOD) accuracy. We further show empirically that OOD inputs induce layerwise norm and pairwise-distance profiles that deviate from the corresponding ID profiles. This leads to a geometric explanation of task-aware pruning: each task induces a task-adapted geometry, characterized empirically by the representation profiles observed on ID inputs. OOD inputs can introduce a distorted version of the task-adapted geometry. Task-aware pruning identifies layers that create or amplify this distortion; by removing them, it shifts OOD representational norms and pairwise distances toward those observed on the adapted distribution. This realigns OOD inputs with the model's task-adapted geometry and improves performance. We provide causal evidence through controlled distribution shifts and residual-scaling interventions, and demonstrate consistent behavior across model scales.
Transformers are remarkably versatile and their design is largely consistent across a variety of applications. But are they optimal for any given task or dataset? The answer may be key for pushing AI beyond merely scaling current designs. Method. We present a method to optimize a transformer architecture for a given dataset, which we use as a tool to study optimal task-specific inductive biases. This method replaces the most important non-linearities (GeLUs,;softmax) with functions learned on held-out data. We then train the resulting architectures on other datasets, as a way to evaluate the compatibility between pairs of tasks. Findings. On algorithmic toy tasks, we identify new architectures with dramatic improvements in learning speed, in- and out-of-distribution generalization, and stability across seeds. The new designs prove very task-specific however, and indicate that these tasks require inductive biases very different from those of standard transformers. On code and language modeling datasets, we also find architectures with consistent, yet smaller improvements. These designs transfer much better across datasets and domains (English & computer code). Implications. Our results show that standard transformers are rarely a local optimum in the space of architectures. Simple alternatives can perform much better but sacrifice universality. This suggests that there may be room for improved architectures that better support multiple capabilities simultaneously, such as fluency and robust reasoning.