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Chris Tanner

Publications and source records attributed to Chris Tanner.

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Analyzing Traditional and Neural Approaches to Multilingual Readability Assessment

Transformer-based models excel at Automatic Readability Assessment (ARA), yet feature-based models remain in active use because their predictions tie back to linguistic properties. This matters because readability labels are subjective and rater-dependent, so high accuracy on noisy ground truth may reflect surface patterns rather than the linguistic structure that defines difficulty. We test whether transformers internalize the same features as traditional models across Arabic, English, French, Hindi, and Russian using the ReadMe++ dataset. Shapley Additive Explanations (SHAP) identify the features driving traditional classifiers, which we then use as TCAV concept sets to probe multilingual XLM-R and language-specific encoders. Transformers recover surface-length, syntactic, and lexical-diversity signals, and reflect the ordinal CEFR structure of the traditional models. Alignment varies by model family, language, and layer, with language-specific encoders tracking traditional models more clearly than XLM-R. High linear separability does not always imply directional influence, limiting linear probing for count-based readability features.

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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.

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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.

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Faster Superword Tokenization

Byte Pair Encoding (BPE) is a widely used tokenization algorithm, whose tokens cannot extend across pre-tokenization boundaries, functionally limiting it to representing at most full words. The BoundlessBPE and SuperBPE algorithms extend and improve BPE by relaxing this limitation and allowing the formation of superwords, which are combinations of pretokens that form phrases. However, previous implementations were impractical to train: for example, BoundlessBPE took 4.7 CPU days to train on 1GB of data. We show that supermerge candidates, two or more consecutive pretokens eligible to form a supermerge, can be aggregated by frequency much like regular pretokens. This avoids keeping full documents in memory, as the original implementations of BoundlessBPE and SuperBPE required, leading to a significant training speedup. We present a two-phase formulation of BoundlessBPE that separates first-phase learning of regular merges from second-phase learning of supermerges, producing identical results to the original implementation. We also show a near-equivalence between two-phase BoundlessBPE and SuperBPE, with the difference being that a manually selected hyperparameter used in SuperBPE can be automatically determined in the second phase of BoundlessBPE. These changes enable a much faster implementation, allowing training on that same 1GB of data in 603 and 593 seconds for BoundlessBPE and SuperBPE, respectively, a more than 600x increase in speed. For each of BoundlessBPE, SuperBPE, and BPE, we open-source both a reference Python implementation and a fast Rust implementation.

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Cost-Efficient Estimation of General Abilities Across Benchmarks

Thousands of diverse benchmarks have been developed to measure the quality of large language models (LLMs). Yet prior work has demonstrated that LLM performance is often sufficiently explained by a small set of latent factors, or abilities. This suggests the potential for more efficient and principled benchmarking, but it remains difficult to compare the quality of different methods. Motivated by predictive validity, we argue that the quality of a benchmarking framework should be grounded in how efficiently it enables the prediction of model performance on unseen tasks. To analyze this objective, we collect the "Wide-scale Item Level Dataset" (WILD), a dataset of item-model response pairs, comprising evaluations of 65 models on 109,564 unique items spanning 163 tasks drawn from 27 datasets. This dataset enables the first analysis of how different techniques can predict a model's performance on a large, diverse collection of unseen tasks under different budget constraints. We demonstrate that combining a modified multidimensional item response theory (IRT) model with adaptive item selection driven by optimal experimental design can predict performance on 112 held-out benchmark tasks with a mean absolute error (MAE) of less than 7%, and can do so after observing only 16 items. We further demonstrate that incorporating cost-aware discount factors into our selection criteria can reduce the total tokens needed to reach 7% MAE from 141,000 tokens to only 22,000, an 85% reduction in evaluation cost.

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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.

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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.

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Entropy-Driven Pre-Tokenization for Byte-Pair Encoding

Byte-Pair Encoding (BPE) has become a widely adopted subword tokenization method in modern language models due to its simplicity and strong empirical performance across downstream tasks. However, applying BPE to unsegmented languages such as Chinese presents significant challenges, as its frequency-driven merge operation is agnostic to linguistic boundaries. To address this, we propose two entropy-informed pre-tokenization strategies that guide BPE segmentation using unsupervised information-theoretic cues. The first approach uses pointwise mutual information and left/right entropy to identify coherent character spans, while the second leverages predictive entropy derived from a pretrained GPT-2 model to detect boundary uncertainty. We evaluate both methods on a subset of the PKU dataset and demonstrate substantial improvements in segmentation precision, recall, and F1 score compared to standard BPE. Our results suggest that entropy-guided pre-tokenization not only enhances alignment with gold-standard linguistic units but also offers a promising direction for improving tokenization quality in low-resource and multilingual settings.

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BLEUBERI: BLEU is a surprisingly effective reward for instruction following

Reward models are central to aligning LLMs with human preferences, but they are costly to train, requiring large-scale human-labeled preference data and powerful pretrained LLM backbones. Meanwhile, the increasing availability of high-quality synthetic instruction-following datasets raises the question: can simpler, reference-based metrics serve as viable alternatives to reward models during RL-based alignment? In this paper, we show first that BLEU, a basic string-matching metric, surprisingly matches strong reward models in agreement with human preferences on general instruction-following datasets. Based on this insight, we develop BLEUBERI, a method that first identifies challenging instructions and then applies Group Relative Policy Optimization (GRPO) using BLEU directly as the reward function. We demonstrate that BLEUBERI-trained models are competitive with models trained via reward model-guided RL across four challenging instruction-following benchmarks and three different base language models. A human evaluation further supports that the quality of BLEUBERI model outputs is on par with those from reward model-aligned models. Moreover, BLEUBERI models generate outputs that are more factually grounded than competing methods. Overall, we show that given access to high-quality reference outputs (easily obtained via existing instruction-following datasets or synthetic data generation), string matching-based metrics are cheap yet effective proxies for reward models during alignment. We release our code and data at https://github.com/lilakk/BLEUBERI.

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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 up to a 15% increase in bytes per token.

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

Reliable evaluation of large language models (LLMs) is critical as their deployment rapidly expands, particularly in high-stakes domains such as business and finance. The LLM-as-a-Judge framework, which uses prompted LLMs to evaluate response quality, is appealing due to its scalability, low cost, and strong correlations with human stylistic preferences. However, it remains unclear how accurately these methods can assess response quality in domains where correctness matters more than style. To address this gap, we introduce the Business and Finance Fundamentals Benchmark (BFF-Bench), a dataset of 160 challenging questions and long-form responses authored by financial professionals. These experts subsequently evaluated the correctness of 1,200 responses generated by a diverse set of LLMs on both BFF-Bench and a challenging subset of MT-Bench. With this expert-annotated dataset of judgments (VERDICTS), we analyze the agreement between a suite of automated grading methods and human experts. While we observe that LLM Judges are more reliable than other grading methods, our findings reveal a clear pattern in LLM Judge performance: when not provided with a correct reference, judges show high agreement with human experts only on questions the judges were able to correctly answer themselves. We demonstrate that providing the judges with expert-written references largely mitigates this issue, highlighting the limits of using LLM-as-a-Judge without any form of human verification.

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

Tokenization, a crucial initial step in natural language processing, is governed by several key parameters, such as the tokenization algorithm, vocabulary size, pre-tokenization strategy, inference strategy, and training data corpus. This paper investigates the impact of an often-overlooked hyperparameter, tokenizer training data size. We train BPE, UnigramLM, and WordPiece tokenizers across various vocabulary sizes using English training data ranging from 1GB to 900GB. Our findings reveal diminishing returns as training data size increases beyond roughly 150GB, suggesting a practical limit to the improvements in tokenization quality achievable through additional data. We analyze this phenomenon and attribute the saturation effect to constraints introduced by the pre-tokenization stage. We then demonstrate the extent to which these findings can generalize by experimenting on data in Russian, a language typologically distant from English. For Russian text, we observe diminishing returns after training a tokenizer from 200GB of data, which is approximately 33% more than when training on English. These results provide valuable insights for optimizing the tokenization process by reducing the compute required for training on large corpora and suggest promising directions for future research in tokenization algorithms.

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Language Model Probabilities are Not Calibrated in Numeric Contexts

Some statements have one well-defined continuation (e.g., "the Eiffel Tower is in [Paris]"), whereas others have a natural distribution over multiple options (e.g., "the weighted coin flip was [Heads/Tails].") We argue that language model (LM) outputs should capture these natural distributions. Our work specifically tests whether LM output probabilities are calibrated to numeric information within their textual contexts. For example, if the context (the prompt) concerns two equally likely options (e.g., heads or tails for a fair coin), the LM output probabilities should also be equal. Likewise, in a context with nonuniformly likely events (e.g., rolling a pair with two dice) an LM should output proportionate probabilities. However, we find that even in simple settings, the best LMs (1) are poorly calibrated and (2) have systematic biases: artifacts like word identity, word order, and word frequency all impact calibration. For example, gpt-4o-mini often picks the first of two options presented in the prompt regardless of the options' implied likelihoods, whereas Llama-3.1-8B picks the second. Models do not allocate probability mass among valid options in a calibrated manner.

cs.AI

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.

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Greed is All You Need: An Evaluation of Tokenizer Inference Methods

While subword tokenizers such as BPE and WordPiece are typically used to build vocabularies for NLP models, the method of decoding text into a sequence of tokens from these vocabularies is often left unspecified, or ill-suited to the method in which they were constructed. We provide a controlled analysis of seven tokenizer inference methods across four different algorithms and three vocabulary sizes, performed on a novel intrinsic evaluation suite we curated for English, combining measures rooted in morphology, cognition, and information theory. We show that for the most commonly used tokenizers, greedy inference performs surprisingly well; and that SaGe, a recently-introduced contextually-informed tokenizer, outperforms all others on morphological alignment.

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Tokenization Is More Than Compression

Tokenization is a foundational step in natural language processing (NLP) tasks, bridging raw text and language models. Existing tokenization approaches like Byte-Pair Encoding (BPE) originate from the field of data compression, and it has been suggested that the effectiveness of BPE stems from its ability to condense text into a relatively small number of tokens. We test the hypothesis that fewer tokens lead to better downstream performance by introducing PathPiece, a new tokenizer that segments a document's text into the minimum number of tokens for a given vocabulary. Through extensive experimentation we find this hypothesis not to be the case, casting doubt on the understanding of the reasons for effective tokenization. To examine which other factors play a role, we evaluate design decisions across all three phases of tokenization: pre-tokenization, vocabulary construction, and segmentation, offering new insights into the design of effective tokenizers. Specifically, we illustrate the importance of pre-tokenization and the benefits of using BPE to initialize vocabulary construction. We train 64 language models with varying tokenization, ranging in size from 350M to 2.4B parameters, all of which are made publicly available.

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DocFinQA: A Long-Context Financial Reasoning Dataset

For large language models (LLMs) to be effective in the financial domain -- where each decision can have a significant impact -- it is necessary to investigate realistic tasks and data. Financial professionals often interact with documents that are hundreds of pages long, but most financial research datasets only deal with short excerpts from these documents. To address this, we introduce a long-document financial QA task. We augment 7,437 questions from the existing FinQA dataset with the full-document context, extending the average context length from under 700 words in FinQA to 123k words in DocFinQA. We conduct extensive experiments over retrieval-based QA pipelines and long-context language models. DocFinQA proves a significant challenge for even state-of-the-art systems. We also provide a case-study on the longest documents in DocFinQA and find that models particularly struggle on these documents. Addressing these challenges may have a wide reaching impact across applications where specificity and long-range contexts are critical, like gene sequences and legal document contract analysis.

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BizBench: A Quantitative Reasoning Benchmark for Business and Finance

Answering questions within business and finance requires reasoning, precision, and a wide-breadth of technical knowledge. Together, these requirements make this domain difficult for large language models (LLMs). We introduce BizBench, a benchmark for evaluating models' ability to reason about realistic financial problems. BizBench comprises eight quantitative reasoning tasks, focusing on question-answering (QA) over financial data via program synthesis. We include three financially-themed code-generation tasks from newly collected and augmented QA data. Additionally, we isolate the reasoning capabilities required for financial QA: reading comprehension of financial text and tables for extracting intermediate values, and understanding financial concepts and formulas needed to calculate complex solutions. Collectively, these tasks evaluate a model's financial background knowledge, ability to parse financial documents, and capacity to solve problems with code. We conduct an in-depth evaluation of open-source and commercial LLMs, comparing and contrasting the behavior of code-focused and language-focused models. We demonstrate that the current bottleneck in performance is due to LLMs' limited business and financial understanding, highlighting the value of a challenging benchmark for quantitative reasoning within this domain.

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