arXiv subjects

Grigory Sapunov

Publications and source records attributed to Grigory Sapunov.

2 recordsLinked to original sources

arXiv2026

Universal Transformers Need Memory: Depth-State Trade-offs in Adaptive Recursive Reasoning

We study learned memory tokens as a computational scratchpad for a single-block Universal Transformer with Adaptive Computation Time (ACT) on Sudoku-Extreme, a combinatorial reasoning benchmark. Memory tokens are empirically necessary: no configuration without them reaches non-trivial performance. The optimal count has a sharp lower threshold (T=0 always fails, T=8 reliably succeeds) followed by a stable plateau (T=8-32, 57.4% +/- 0.7% exact-match) and a dilution boundary at T=64. Under halt-side pressure (lambda warmup), mean halt drops monotonically with memory size across the plateau (from 11.6 at T=8 to 8.3 at T=64), showing that memory tokens and ponder depth substitute as resources at fixed accuracy. We also identify a router initialization trap that causes the majority of training runs to fail: both default zero-bias and Graves' recommended positive bias settle into a shallow halt equilibrium the model cannot escape. Inverting the bias to -3 ("deep start") eliminates the failure mode, and ablation shows the trap is inherent to ACT initialization rather than an artifact of our architecture. With reliable training, ACT yields an order of magnitude lower seed variance than fixed-depth processing (+/-0.7 vs +/-9.3 pp); lambda warmup recovers 34% of compute at matched accuracy; and attention heads specialize into memory readers, constraint propagators, and integrators across recursive depth. Code: https://github.com/che-shr-cat/utm-jax.

cs.LG↗

arXiv2026

Theory of Code Space: Do Code Agents Understand Software Architecture?

AI code agents excel at isolated tasks yet struggle with multi-file software engineering requiring architectural understanding. We introduce Theory of Code Space (ToCS), a benchmark that evaluates whether agents can construct, maintain, and update coherent architectural beliefs during codebase exploration. Agents explore procedurally generated codebases under partial observability -- opening files under a budget -- and periodically externalize their belief state as structured JSON, producing a time-series of architectural understanding. Three findings emerge from experiments with four baselines and six frontier LLMs. First, the Active-Passive Gap is model-dependent: one model builds better maps through active exploration than from seeing all files at once, while another shows the opposite -- revealing that active exploration is itself a non-trivial capability absent from some models. Second, retaining structured belief maps in context acts as self-scaffolding for some models but not others, showing that the mechanism is model-dependent. Third, belief state maintenance varies dramatically: a smaller model maintains perfectly stable beliefs across probes while its larger sibling suffers catastrophic belief collapse -- forgetting previously-discovered components between probes. We release ToCS as open-source software. Code: https://github.com/che-shr-cat/tocs

cs.SE↗