arXiv subjects

Chris J. Maddison

Publications and source records attributed to Chris J. Maddison.

At least 19 recordsLinked to original sources

arXiv2026

Formally Solving Answer-Construction Problems in Lean

Large language models (LLMs) have achieved remarkable progress in formal mathematical reasoning. Mathematical competition problems fall into two broad types: theorem-proving problems ask for a proof of a fully specified statement, whereas answer-construction problems ask the solver to construct an answer object and prove that it satisfies the stated specification. Existing mathematical reasoning engines mainly target theorem-proving problems, yet answer-construction problems remain less studied. This setting is challenging because model capabilities are misaligned, with general LLMs better suited to answer construction and prover LLMs better suited to proof generation, and because Lean proof checking alone does not rule out inadmissible circular witnesses. To close this gap, we introduce Enumerate-Conjecture-Prove (ECP), a neuro-symbolic framework for solving answer-construction problems in Lean. ECP uses general LLMs to perform bounded enumeration and construct candidate answers, and invokes prover LLMs to produce machine-checked proofs. ECP introduces admissibility checking to ensure that each answer is canonical and does not involve a circular argument. On answer-construction problems from PutnamBench and autoformalized MathArena, ECP formally solves 17/346 PutnamBench instances and 18/75 MathArena instances with admissible answers and proofs, outperforming LLM baselines at aligned inference budgets.

cs.AI↗

arXiv2026

Integral Field Unit Spectroscopy with One Fiber

Integral field unit (IFU) spectroscopy provides spatially resolved spectra across galaxies, offering crucial insights into their evolution. However, its high observational cost limits current IFU datasets to $\sim 10^4$ objects. We present a multi-modal, probabilistic foundation model that predicts high-resolution spectra with calibrated uncertainties at arbitrary spatial locations within a galaxy directly from broadband images. Built on a masked autoencoder framework, our architecture injects fiber positional encodings and redshift aware wavelength encodings, enabling spatially conditioned predictions. Trained on 4.7 million images and single fiber spectroscopic observations from the Dark Energy Spectroscopic Instrument (DESI) survey, our model exploits the natural variance of fiber placements and the morphological self-similarity of galaxies to achieve IFU-like capabilities without any IFU training data. Predicted emission line flux maps match independent IFU observations from the Mapping Nearby Galaxies at APO (MaNGA) survey, with performance comparable to a supervised baseline trained directly on IFU data.

astro-ph.GA↗

arXiv2026

Causal Risk Minimization for High-Dimensional Treatments

Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains. However, classical causal estimators tend to assume that all possible interventions are observed, which is infeasible when interventions vary widely, for instance, in the space of all text strings. We adapt a well-known approach of recasting causal inference as a learning problem, to address high-dimensional treatment spaces. Specifically, under standard assumptions like no unobserved confounding, we show that causal error decomposes into a series of moment-balancing errors of increasing order, and design objectives that directly improve causal estimation. We also show how to project the effect of a high-dimensional treatment onto lower-dimensional treatment attributes, which allows a single model to answer several causal questions without additional attribute-specific training. We empirically evaluate our estimators in settings with high-dimensional continuous, discrete, and text treatments, the last of which used a semi-synthetic dataset of Amazon Reviews. Our experiments demonstrate the benefit of higher-order balance error optimization and competitive performance of projected causal estimates with attribute-specific estimators.

cs.LG↗

arXiv2026

Predicting Large Model Test Losses with a Noisy Quadratic System

We introduce a predictive model that estimates the pre-training loss of large models from model size (N), batch size (B) and number of weight updates (K). This is the first loss prediction model that can handle changing batch size. The model outperforms Chinchilla's loss model, a model of the test loss using the batch size and number of tokens, in terms of projecting the loss at extrapolated compute budgets (up to 1000 folds). A natural use of the model is to find optimal N, B, K configurations under explicit and compound resource constraints like time, memory and compute. In our experiments, the model-selected configurations are close to ground-truth optimal. Our work advocates for loss prediction as a better alternative to heuristic-based laws, which are growing in complexity. The implementation is available on https://github.com/chuningxdy/Noisy-Quadratic-System.

cs.LG↗

arXiv2026

Bayesian Sensitivity of Causal Inference Estimators under Evidence-Based Priors

Causal inference, especially in observational studies, relies on untestable assumptions about the true data-generating process. Sensitivity analysis helps us determine how robust our conclusions are when we alter these underlying assumptions. Existing frameworks for sensitivity analysis are concerned with worst-case changes in assumptions. In this work, we argue that using such pessimistic criteria can often become uninformative or lead to conclusions contradicting our prior knowledge about the world. To demonstrate this claim, we generalize the recent s-value framework (Gupta & Rothenhäusler, 2023) to estimate the sensitivity of three different common assumptions in causal inference. Empirically, we find that, indeed, worst-case conclusions about sensitivity can rely on unrealistic changes in the data-generating process. To overcome this, we extend the s-value framework with a new sensitivity analysis criterion: Bayesian Sensitivity Value (BSV), which computes the expected sensitivity of an estimate to assumption violations under priors constructed from real-world evidence. We use Monte Carlo approximations to estimate this quantity and illustrate its applicability in an observational study on the effect of diabetes treatments on weight loss.

cs.LG↗

arXiv2026

MixMin: Finding Data Mixtures via Convex Minimization

Modern machine learning pipelines are increasingly combining and mixing data from diverse and disparate sources, e.g., pre-training large language models. Yet, finding the optimal data mixture is a challenging and open problem. We formalize this data mixing problem as a bi-level objective: the best mixture is the one that would lead to the best model for a downstream objective. Unfortunately, this objective is generally intractable. In this paper, we make the observation that the bi-level data mixing objective becomes convex as our model class becomes larger. We develop and study a gradient-based approach for optimizing this convex objective, which we call MixMin, and test it on language modeling and chemistry tasks. MixMin was the only method that uniformly improved the data mixture in all our experiments. With MixMin, we improved the data mixture using less than 0.2% additional compute for a pythia-410M model trained on 8.2B tokens, resulting between 1-5% relative improvement to negative log likelihood on PIQA, ARC Easy, SciQ, and OpenWebMath. Crucially, we found that MixMin mixtures for smaller models improved training of larger models, suggesting that MixMin mixtures may be scale-invariant. When mixing bioassay data to train an XGBoost model, we saw improvements to average precision scores of 0.03-0.15.

cs.LG↗

arXiv2025

BioReason: Incentivizing Multimodal Biological Reasoning within a DNA-LLM Model

Unlocking deep and interpretable biological reasoning from complex genomic data remains a major AI challenge limiting scientific progress. While current DNA foundation models excel at representing sequences, they struggle with multi-step reasoning and lack transparent, biologically meaningful explanations. BioReason addresses this by tightly integrating a DNA foundation model with a large language model (LLM), enabling the LLM to directly interpret and reason over genomic information. Through supervised fine-tuning and reinforcement learning, BioReason learns to produce logical, biologically coherent deductions. It achieves major performance gains, boosting KEGG-based disease pathway prediction accuracy from 86% to 98% and improving variant effect prediction by an average of 15% over strong baselines. BioReason can reason over unseen biological entities and explain its decisions step by step, offering a transformative framework for interpretable, mechanistic AI in biology. All data, code, and checkpoints are available at https://github.com/bowang-lab/BioReason

cs.LG↗

arXiv2025

Reasoning to Learn from Latent Thoughts

Compute scaling for language model (LM) pretraining has outpaced the growth of human-written texts, leading to concerns that data will become the bottleneck to LM scaling. To continue scaling pretraining in this data-constrained regime, we propose that explicitly modeling and inferring the \emph{latent thoughts} that underlie the text generation process can significantly improve pretraining data efficiency. Intuitively, our approach views web text as the compressed final outcome of a verbose human thought process and that the latent thoughts contain important contextual knowledge and reasoning steps that are critical to data-efficient learning. We empirically demonstrate the effectiveness of our approach through data-constrained continued pretraining for math. We first show that synthetic data approaches to inferring latent thoughts significantly improve data efficiency over training on the same amount of raw data. Furthermore, we demonstrate latent thought inference without a strong teacher, where an LM \emph{bootstraps its own performance} by using an EM algorithm to iteratively improve the capability of the trained LM and the quality of thought-augmented pretraining data. We show that a 1B LM can bootstrap its performance across at least three iterations and significantly outperform baselines trained on raw data, with increasing gains from additional inference compute when performing the E-step. The gains from inference scaling and EM iterations suggest new opportunities for scaling data-constrained pretraining.

cs.LG↗

arXiv2025

LM Agents May Fail to Act on Their Own Risk Knowledge

Language model (LM) agents have demonstrated significant potential for automating real-world tasks, yet they pose a diverse array of potential, severe risks in safety-critical scenarios. In this work, we identify a significant gap between LM agents' risk awareness and safety execution abilities: while they often answer "Yes" to queries like "Is executing `sudo rm -rf /*' dangerous?", they will likely fail to identify such risks in instantiated trajectories or even directly perform these risky actions when acting as agents. To systematically investigate this, we develop a comprehensive evaluation framework to examine agents' safety across three progressive dimensions: 1) their knowledge about potential risks, 2) their ability to identify corresponding risks in execution trajectories, and 3) their actual behaviors to avoid executing these risky actions. Our evaluation reveals two critical performance gaps that resemble the generator-validator gaps observed in LMs: while agents demonstrate near-perfect risk knowledge ($>98\%$ pass rates), they fail to apply this knowledge when identifying risks in actual scenarios (with performance dropping by $>23\%$) and often still execute risky actions ($<26\%$ pass rates). Notably, this trend persists across more capable LMs as well as in specialized reasoning models like DeepSeek-R1, indicating that simply scaling model capabilities or inference compute does not inherently resolve safety concerns. Instead, we take advantage of these observed gaps to develop a risk verifier that independently critiques the proposed actions by agents, with an abstractor that converts specific execution trajectories into abstract descriptions where LMs can more effectively identify the risks. Our overall system achieves a significant reduction of risky action execution by $55.3\%$ over vanilla-prompted agents.

cs.AI↗

arXiv2025

Measuring Scientific Capabilities of Language Models with a Systems Biology Dry Lab

Designing experiments and result interpretations are core scientific competencies, particularly in biology, where researchers perturb complex systems to uncover the underlying systems. Recent efforts to evaluate the scientific capabilities of large language models (LLMs) fail to test these competencies because wet-lab experimentation is prohibitively expensive: in expertise, time and equipment. We introduce SciGym, a first-in-class benchmark that assesses LLMs' iterative experiment design and analysis abilities in open-ended scientific discovery tasks. SciGym overcomes the challenge of wet-lab costs by running a dry lab of biological systems. These models, encoded in Systems Biology Markup Language, are efficient for generating simulated data, making them ideal testbeds for experimentation on realistically complex systems. We evaluated six frontier LLMs on 137 small systems, and released a total of 350 systems. Our evaluation shows that while more capable models demonstrated superior performance, all models' performance declined significantly as system complexity increased, suggesting substantial room for improvement in the scientific capabilities of LLM agents.

cs.AI↗

arXiv2025

Benchmarking Neural Network Training Algorithms

Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.

cs.LG↗

arXiv2025

MixMax: Distributional Robustness in Function Space via Optimal Data Mixtures

Machine learning models are often required to perform well across several pre-defined settings, such as a set of user groups. Worst-case performance is a common metric to capture this requirement, and is the objective of group distributionally robust optimization (group DRO). Unfortunately, these methods struggle when the loss is non-convex in the parameters, or the model class is non-parametric. Here, we make a classical move to address this: we reparameterize group DRO from parameter space to function space, which results in a number of advantages. First, we show that group DRO over the space of bounded functions admits a minimax theorem. Second, for cross-entropy and mean squared error, we show that the minimax optimal mixture distribution is the solution of a simple convex optimization problem. Thus, provided one is working with a model class of universal function approximators, group DRO can be solved by a convex optimization problem followed by a classical risk minimization problem. We call our method MixMax. In our experi ments, we found that MixMax matched or outperformed the standard group DRO baselines, and in particular, MixMax improved the performance of XGBoost over the only baseline, data balancing, for variations of the ACSIncome and CelebA annotations datasets.

cs.LG↗

arXiv2024

On the Efficiency of ERM in Feature Learning

Given a collection of feature maps indexed by a set $\mathcal{T}$, we study the performance of empirical risk minimization (ERM) on regression problems with square loss over the union of the linear classes induced by these feature maps. This setup aims at capturing the simplest instance of feature learning, where the model is expected to jointly learn from the data an appropriate feature map and a linear predictor. We start by studying the asymptotic quantiles of the excess risk of sequences of empirical risk minimizers. Remarkably, we show that when the set $\mathcal{T}$ is not too large and when there is a unique optimal feature map, these quantiles coincide, up to a factor of two, with those of the excess risk of the oracle procedure, which knows a priori this optimal feature map and deterministically outputs an empirical risk minimizer from the associated optimal linear class. We complement this asymptotic result with a non-asymptotic analysis that quantifies the decaying effect of the global complexity of the set $\mathcal{T}$ on the excess risk of ERM, and relates it to the size of the sublevel sets of the suboptimality of the feature maps. As an application of our results, we obtain new guarantees on the performance of the best subset selection procedure in sparse linear regression under general assumptions.

stat.ML↗

arXiv2024

End-To-End Causal Effect Estimation from Unstructured Natural Language Data

Knowing the effect of an intervention is critical for human decision-making, but current approaches for causal effect estimation rely on manual data collection and structuring, regardless of the causal assumptions. This increases both the cost and time-to-completion for studies. We show how large, diverse observational text data can be mined with large language models (LLMs) to produce inexpensive causal effect estimates under appropriate causal assumptions. We introduce NATURAL, a novel family of causal effect estimators built with LLMs that operate over datasets of unstructured text. Our estimators use LLM conditional distributions (over variables of interest, given the text data) to assist in the computation of classical estimators of causal effect. We overcome a number of technical challenges to realize this idea, such as automating data curation and using LLMs to impute missing information. We prepare six (two synthetic and four real) observational datasets, paired with corresponding ground truth in the form of randomized trials, which we used to systematically evaluate each step of our pipeline. NATURAL estimators demonstrate remarkable performance, yielding causal effect estimates that fall within 3 percentage points of their ground truth counterparts, including on real-world Phase 3/4 clinical trials. Our results suggest that unstructured text data is a rich source of causal effect information, and NATURAL is a first step towards an automated pipeline to tap this resource.

cs.LG↗

arXiv2024

Test-Time Fairness and Robustness in Large Language Models

Frontier Large Language Models (LLMs) can be socially discriminatory or sensitive to spurious features of their inputs. Because only well-resourced corporations can train frontier LLMs, we need robust test-time strategies to control such biases. Existing solutions, which instruct the LLM to be fair or robust, rely on the model's implicit understanding of bias. Causality provides a rich formalism through which we can be explicit about our debiasing requirements. Yet, as we show, a naive application of the standard causal debiasing strategy, counterfactual data augmentation, fails under standard assumptions to debias predictions at an individual level at test time. To address this, we develop a stratified notion of debiasing called stratified invariance, which can capture a range of debiasing requirements from population level to individual level through an additional measurement that stratifies the predictions. We present a complete observational test for stratified invariance. Finally, we introduce a data augmentation strategy that guarantees stratified invariance at test time under suitable assumptions, together with a prompting strategy that encourages stratified invariance in LLMs. We show that our prompting strategy, unlike implicit instructions, consistently reduces the bias of frontier LLMs across a suite of synthetic and real-world benchmarks without requiring additional data, finetuning or pre-training.

cs.CL↗

arXiv2024

Observational Scaling Laws and the Predictability of Language Model Performance

Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different scales has limited their use. We propose an alternative, observational approach that bypasses model training and instead builds scaling laws from ~100 publically available models. Building a single scaling law from multiple model families is challenging due to large variations in their training compute efficiencies and capabilities. However, we show that these variations are consistent with a simple, generalized scaling law where language model performance is a function of a low-dimensional capability space, and model families only vary in their efficiency in converting training compute to capabilities. Using this approach, we show the surprising predictability of complex scaling phenomena: we show that several emergent phenomena follow a smooth, sigmoidal behavior and are predictable from small models; we show that the agent performance of models such as GPT-4 can be precisely predicted from simpler non-agentic benchmarks; and we show how to predict the impact of post-training interventions like Chain-of-Thought and Self-Consistency as language model capabilities continue to improve.

cs.LG↗

arXiv2024

APPL: A Prompt Programming Language for Harmonious Integration of Programs and Large Language Model Prompts

Large Language Models (LLMs) have become increasingly capable of handling diverse tasks with the aid of well-crafted prompts and integration of external tools, but as task complexity rises, the workflow involving LLMs can be complicated and thus challenging to implement and maintain. To address this challenge, we propose APPL, A Prompt Programming Language that acts as a bridge between computer programs and LLMs, allowing seamless embedding of prompts into Python functions, and vice versa. APPL provides an intuitive and Python-native syntax, an efficient parallelized runtime with asynchronous semantics, and a tracing module supporting effective failure diagnosis and replaying without extra costs. We demonstrate that APPL programs are intuitive, concise, and efficient through three representative scenarios: Chain-of-Thought with self-consistency (CoT-SC), ReAct tool use agent, and multi-agent chat. Experiments on three parallelizable workflows further show that APPL can effectively parallelize independent LLM calls, with a significant speedup ratio that almost matches the estimation.

cs.AI↗

arXiv2024

Minimax Linear Regression under the Quantile Risk

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs, we obtain the exact minimax quantile risk for a rich family of error functions and establish the minimaxity of OLS. This improves on the known lower bounds for the special case of square error, and provides us with a lower bound on the minimax quantile risk over larger sets of distributions. Under the square error and a fourth moment assumption on the distribution of inputs, we show that this lower bound is tight over a larger class of problems. Specifically, we prove a matching upper bound on the worst-case quantile risk of a variant of the recently proposed min-max regression procedure, thereby establishing its minimaxity, up to absolute constants. We illustrate the usefulness of our approach by extending this result to all $p$-th power error functions for $p \in (2, \infty)$. Along the way, we develop a generic analogue to the classical Bayesian method for lower bounding the minimax risk when working with the quantile risk, as well as a tight characterization of the quantiles of the smallest eigenvalue of the sample covariance matrix.

math.ST↗