Theory-Level Autoformalization: From Isolated Statements to Unified Formal Knowledge Bases

Autoformalization translates informal natural language into formal, machine-verifiable languages. While most work focuses on individual statements, real formalization efforts are inherently theory-level: they require an entire web of axioms, definitions, and lemmas before target theorems can even be stated. In this position paper, we argue for theory-level autoformalization: formalizing complete theories, including all their inter-dependencies, as structured libraries. We examine the significance of this shift, address alternative views, identify open challenges, and propose three promising paths forward. Our survey of autoformalization is available at https://github.com/marcusm117/Awesome-Autoformalization.

Dynamic Tensor Rematerialization

Checkpointing enables training larger models by freeing intermediate activations and recomputing them on demand. Previous checkpointing techniques are difficult to generalize to dynamic models because they statically plan recomputations offline. We present Dynamic Tensor Rematerialization (DTR), a greedy online algorithm for heuristically checkpointing arbitrary models. DTR is extensible and general: it is parameterized by an eviction policy and only collects lightweight metadata on tensors and operators. Though DTR has no advance knowledge of the model or training task, we prove it can train an $N$-layer feedforward network on an $\Omega(\sqrt{N})$ memory budget with only $\mathcal{O}(N)$ tensor operations. Moreover, we identify a general eviction heuristic and show how it allows DTR to automatically provide favorable checkpointing performance across a variety of models and memory budgets.