Daily Papers

Before closing venture capital financing rounds, lawyers conduct diligence that includes tying out the capitalization table: verifying that every security (for example, shares, options, warrants) and issuance term (for example, vesting schedules, acceleration triggers, transfer restrictions) is supported by large sets of underlying legal documentation. While LLMs continue to improve on legal benchmarks, specialized legal workflows, such as capitalization tie-out, remain out of reach even for strong agentic systems. The task requires multi-document reasoning, strict evidence traceability, and deterministic outputs that current approaches fail to reliably deliver. We characterize capitalization tie-out as an instance of a real-world benchmark for legal AI, analyze and compare the performance of existing agentic systems, and propose a world model architecture toward tie-out automation-and more broadly as a foundation for applied legal intelligence.

Deep learning practitioners often operate on a computational and monetary budget. Thus, it is critical to design optimization algorithms that perform well under any budget. The linear learning rate schedule is considered the best budget-aware schedule, as it outperforms most other schedules in the low budget regime. On the other hand, learning rate schedules -- such as the 30-60-90 step schedule -- are known to achieve high performance when the model can be trained for many epochs. Yet, it is often not known a priori whether one's budget will be large or small; thus, the optimal choice of learning rate schedule is made on a case-by-case basis. In this paper, we frame the learning rate schedule selection problem as a combination of i) selecting a profile (i.e., the continuous function that models the learning rate schedule), and ii) choosing a sampling rate (i.e., how frequently the learning rate is updated/sampled from this profile). We propose a novel profile and sampling rate combination called the Reflected Exponential (REX) schedule, which we evaluate across seven different experimental settings with both SGD and Adam optimizers. REX outperforms the linear schedule in the low budget regime, while matching or exceeding the performance of several state-of-the-art learning rate schedules (linear, step, exponential, cosine, step decay on plateau, and OneCycle) in both high and low budget regimes. Furthermore, REX requires no added computation, storage, or hyperparameters.