Tokenization with Split Trees

We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed byte n-gram counts, independent of any vocabulary. Given a vocabulary, inference recursively descends each split tree and emits the first in-vocabulary node reached on each path. Vocabulary selection is formulated as an Integer Program (IP) that minimizes the total token count over all split trees under this inference procedure. The Linear Programming (LP) relaxation is near-integral in practice, yielding provably near-optimal vocabularies, with training time empirically scaling quadratically in the number of split trees. On English text, ToaST reduces token counts by more than 11% compared to BPE, WordPiece, and UnigramLM at vocabulary sizes of 40,960 and above, reducing the number of inference tokens for models using this tokenizer, thus extending the effective context length. ToaST also uses common single-byte tokens less frequently than these baselines, leading to a substantial improvement in Renyi efficiency. In experiments training 1.5B parameter language models, ToaST achieves the highest CORE score, outperforming baselines by 2.6%--7.6%, with significance for two of three, and scoring best on 13 of 22 individual tasks.

FrontierFinance: A Long-Horizon Computer-Use Benchmark of Real-World Financial Tasks

As concerns surrounding AI-driven labor displacement intensify in knowledge-intensive sectors, existing benchmarks fail to measure performance on tasks that define practical professional expertise. Finance, in particular, has been identified as a domain with high AI exposure risk, yet lacks robust benchmarks to track real-world developments. This gap is compounded by the absence of clear accountability mechanisms in current Large Language Model (LLM) deployments. To address this, we introduce FrontierFinance, a long-horizon benchmark of 25 complex financial modeling tasks across five core finance models, requiring an average of over 18 hours of skilled human labor per task to complete. Developed with financial professionals, the benchmark reflects industry-standard financial modeling workflows and is paired with detailed rubrics for structured evaluation. We engage human experts to define the tasks, create rubrics, grade LLMs, and perform the tasks themselves as human baselines. We demonstrate that our human experts both receive higher scores on average, and are more likely to provide client-ready outputs than current state-of-the-art systems.

The Effect of Scripts and Formats on LLM Numeracy

Large language models (LLMs) have achieved impressive proficiency in basic arithmetic, rivaling human-level performance on standard numerical tasks. However, little attention has been given to how these models perform when numerical expressions deviate from the prevailing conventions present in their training corpora. In this work, we investigate numerical reasoning across a wide range of numeral scripts and formats. We show that LLM accuracy drops substantially when numerical inputs are rendered in underrepresented scripts or formats, despite the underlying mathematical reasoning being identical. We further demonstrate that targeted prompting strategies, such as few-shot prompting and explicit numeral mapping, can greatly narrow this gap. Our findings highlight an overlooked challenge in multilingual numerical reasoning and provide actionable insights for working with LLMs to reliably interpret, manipulate, and generate numbers across diverse numeral scripts and formatting styles.

On Finding Inconsistencies in Documents

Professionals in academia, law, and finance audit their documents because inconsistencies can result in monetary, reputational, and scientific costs. Language models (LMs) have the potential to dramatically speed up this auditing process. To understand their abilities, we introduce a benchmark, FIND (Finding INconsistencies in Documents), where each example is a document with an inconsistency inserted manually by a domain expert. Despite the documents being long, technical, and complex, the best-performing model (gpt-5) recovered 64% of the inserted inconsistencies. Surprisingly, gpt-5 also found undiscovered inconsistencies present in the original documents. For example, on 50 arXiv papers, we judged 136 out of 196 of the model's suggestions to be legitimate inconsistencies missed by the original authors. However, despite these findings, even the best models miss almost half of the inconsistencies in FIND, demonstrating that inconsistency detection is still a challenging task.

Boundless Byte Pair Encoding: Breaking the Pre-tokenization Barrier

Pre-tokenization, the initial step in many modern tokenization pipelines, segments text into smaller units called pretokens, typically splitting on whitespace and punctuation. While this process encourages having full, individual words as tokens, it introduces a fundamental limitation in most tokenization algorithms such as Byte Pair Encoding (BPE). Specifically, pre-tokenization causes the distribution of tokens in a corpus to heavily skew towards common, full-length words. This skewed distribution limits the benefits of expanding to larger vocabularies, since the additional tokens appear with progressively lower counts. To overcome this barrier, we propose BoundlessBPE, a modified BPE algorithm that relaxes the pretoken boundary constraint. Our approach selectively merges two complete pretokens into a larger unit we term a superword. Superwords are not necessarily semantically cohesive. For example, the pretokens " of" and " the" might be combined to form the superword " of the". This merging strategy results in a substantially more uniform distribution of tokens across a corpus than standard BPE, and compresses text more effectively, with an approximate 20% increase in bytes per token.

No Free Labels: Limitations of LLM-as-a-Judge Without Human Grounding

LLM-as-a-Judge is a framework that uses an LLM (large language model) to evaluate the quality of natural language text - typically text that is also generated by an LLM. This framework holds great promise due to its relative low-cost, ease of use, and strong correlations with human stylistic preferences. However, LLM Judges have been shown to exhibit biases that can distort their judgments. We evaluate how well LLM Judges can grade whether a given response to a conversational question is correct, an ability crucial to soundly estimating the overall response quality. To do so, we create and publicly release a human-annotated dataset with labels of correctness for 1,200 LLM responses. We source questions from a combination of existing datasets and a novel, challenging benchmark (BFF-Bench) created for this analysis. We demonstrate a strong connection between an LLM's ability to correctly answer a question and grade responses to that question. Although aggregate level statistics might imply a judge has high agreement with human annotators, it will struggle on the subset of questions it could not answer. To address this issue, we recommend a simple solution: provide the judge with a correct, human-written reference answer. We perform an in-depth analysis on how reference quality can affect the performance of an LLM Judge. We show that providing a weaker judge (e.g. Qwen 2.5 7B) with higher quality references reaches better agreement with human annotators than a stronger judge (e.g. GPT-4o) with synthetic references.

How Much is Enough? The Diminishing Returns of Tokenization Training Data

Tokenization, a crucial initial step in natural language processing, is often assumed to benefit from larger training datasets. This paper investigates the impact of tokenizer training data sizes ranging from 1GB to 900GB. Our findings reveal diminishing returns as the data size increases, highlighting a practical limit on how much further scaling the training data can improve tokenization quality. We analyze this phenomenon and attribute the saturation effect to the constraints imposed by the pre-tokenization stage of tokenization. These results offer valuable insights for optimizing the tokenization process and highlight potential avenues for future research in tokenization algorithms.

Are Language Model Logits Calibrated?

Some information is factual (e.g., "Paris is in France"), whereas other information is probabilistic (e.g., "the coin flip will be a [Heads/Tails]."). We believe that good Language Models (LMs) should understand and reflect this nuance. Our work investigates this by testing if LMs' output probabilities are calibrated to their textual contexts. We define model "calibration" as the degree to which the output probabilities of candidate tokens are aligned with the relative likelihood that should be inferred from the given context. For example, if the context concerns two equally likely options (e.g., heads or tails for a fair coin), the output probabilities should reflect this. Likewise, context that concerns non-uniformly likely events (e.g., rolling a six with a die) should also be appropriately captured with proportionate output probabilities. We find that even in simple settings the best LMs (1) are poorly calibrated, and (2) have systematic biases (e.g., preferred colors and sensitivities to word orderings). For example, gpt-4o-mini often picks the first of two options presented in the prompt regardless of the options' implied likelihood, whereas Llama-3.1-8B picks the second. Our other consistent finding is mode-collapse: Instruction-tuned models often over-allocate probability mass on a single option. These systematic biases introduce non-intuitive model behavior, making models harder for users to understand.

SEC-QA: A Systematic Evaluation Corpus for Financial QA

The financial domain frequently deals with large numbers of long documents that are essential for daily operations. Significant effort is put towards automating financial data analysis. However, a persistent challenge, not limited to the finance domain, is the scarcity of datasets that accurately reflect real-world tasks for model evaluation. Existing datasets are often constrained by size, context, or relevance to practical applications. Moreover, LLMs are currently trained on trillions of tokens of text, limiting access to novel data or documents that models have not encountered during training for unbiased evaluation. We propose SEC-QA, a continuous dataset generation framework with two key features: 1) the semi-automatic generation of Question-Answer (QA) pairs spanning multiple long context financial documents, which better represent real-world financial scenarios; 2) the ability to continually refresh the dataset using the most recent public document collections, not yet ingested by LLMs. Our experiments show that current retrieval augmented generation methods systematically fail to answer these challenging multi-document questions. In response, we introduce a QA system based on program-of-thought that improves the ability to perform complex information retrieval and quantitative reasoning pipelines, thereby increasing QA accuracy.

An Analysis of Multilingual FActScore

FActScore has gained popularity as a metric to estimate the factuality of long-form texts generated by Large Language Models (LLMs) in English. However, there has not been any work in studying the behavior of FActScore in other languages. This paper studies the limitations of each component in the four-component pipeline of FActScore in the multilingual setting. We introduce a new dataset for FActScore on texts generated by strong multilingual LLMs. Our evaluation shows that LLMs exhibit distinct behaviors in both fact extraction and fact scoring tasks. No LLM produces consistent and reliable FActScore across languages with varying levels of resources. We also find that the knowledge source plays an important role in the quality of the estimated FActScore. Using Wikipedia as the knowledge source may hinder the true FActScore of long-form text due to its limited coverage in medium- and low-resource languages. We also incorporate three mitigations to our knowledge source that ultimately improve FActScore estimation across all languages.