arXiv subjects

David McAllester

Publications and source records attributed to David McAllester.

At least 19 recordsLinked to original sources

arXiv2026

Alignment of a Total Automation Economy

We consider economic theory from the perspective of a total automation economy, one with no human involvement in production either in manufacturing or in management. One can naturally ask whether a total automation economy is fundamentally a centrally planned economy or, alternatively, whether efficiency demands decentralization into local decisions by competing agents -- agentic production. A soviet economist, Leonid Kantorovich, developed linear programming as a method companies or governments can use to optimize production. Ironically, he is also generally credited with showing that the most efficient production is achieved through decentralization -- a free market economy with competing agents. Here we review Kantorovich's dualization in detail. We take the objective of the economy to be maximizing production weighted by (human) market price. A fundamental issue is whether an automated pursuit of this objective might have alignment vulnerabilities as the economy evolves. Another question is whether dualization provides insight into the utility of agentic AI systems (multi-agent AI systems) generally.

physics.soc-ph↗

arXiv2026

Training Transformers as a Universal Computer

We demonstrate that a small transformer can learn to execute programs in MicroPy, a simplified yet computationally universal programming language. Given procedure definitions together with an expression to evaluate, the transformer predicts small-step execution using PENCIL scaffolding for space-efficient execution within a bounded context window. After training on randomly generated, meaningless MicroPy programs, the learned transformer generalizes to various human-written programs including bit copying and flipping, binary addition and multiplication, and SAT verification and solving. We note that the trained model can achieve out-of-distribution generalization; i.e., evaluate novel programs from distribution on programs. Since MicroPy can express any computation, our results provide empirical evidence that a standard transformer can be trained to act as a universal computer.

cs.AI↗

arXiv2025

OKBench: Democratizing LLM Evaluation with Fully Automated, On-Demand, Open Knowledge Benchmarking

Knowledge-intensive question answering is central to large language models (LLMs) and is typically assessed using static benchmarks derived from sources like Wikipedia and textbooks. However, these benchmarks fail to capture evolving knowledge in a dynamic world, and centralized curation struggles to keep pace with rapid LLM advancements. To address these drawbacks, we propose Open Knowledge Bench (OKBench), a fully automated framework for generating high-quality, dynamic knowledge benchmarks on demand. Focusing on the news domain where knowledge updates daily, OKBench is an agentic framework that automates the sourcing, creation, validation, and distribution of benchmarks. Our approach democratizes benchmark creation and facilitates thorough evaluation of retrieval-augmented methods by reducing overlap with pretraining data. We evaluate our framework on a wide range open-source and proprietary LLMs of various sizes and configurations, both with and without retrieval over freshly generated knowledge. Our results reveal distinct model behaviors when confronted with new information and highlight how retrieval narrows the performance gap between small and large models. These findings underscore the importance of evaluating LLMs on evolving knowledge benchmarks.

cs.CL↗

arXiv2025

Context-Efficient Retrieval with Factual Decomposition

There has recently been considerable interest in incorporating information retrieval into large language models (LLMs). Retrieval from a dynamically expanding external corpus of text allows a model to incorporate current events and can be viewed as a form of episodic memory. Here we demonstrate that pre-processing the external corpus into semi-structured ''atomic facts'' makes retrieval more efficient. More specifically, we demonstrate that our particular form of atomic facts improves performance on various question answering tasks when the amount of retrieved text is limited. Limiting the amount of retrieval reduces the size of the context and improves inference efficiency.

cs.CL↗

arXiv2025

PENCIL: Long Thoughts with Short Memory

While state-of-the-art LLMs have demonstrated great promise of using long Chains-of-Thought (CoT) to boost reasoning, scaling it up to more challenging problems at test-time is fundamentally limited by suboptimal memory usage -- intermediate computations accumulate indefinitely in context even when no longer needed for future thoughts. We introduce PENCIL, which incorporates a novel reduction mechanism into the autoregressive generation process that recursively cleans up intermediate thoughts based on patterns learned from training. By iteratively generating and erasing thoughts, PENCIL can think deeper to solve harder problems using shorter context and less compute. Empirically, we observe PENCIL is significantly more effective and efficient than CoT. For example, we demonstrate PENCIL with a small 25M-parameter transformer and 2048 context length solves Einstein's puzzle -- a task that challenges much larger models like GPT-4. Theoretically, we prove PENCIL can perform universal efficient computation by simulating any Turing machines with optimal time and space complexity, and thus can solve arbitrary computable tasks that are otherwise intractable for vanilla CoT.

cs.LG↗

arXiv2023

On the Mathematics of Diffusion Models

This paper gives direct derivations of the differential equations and likelihood formulas of diffusion models assuming only knowledge of Gaussian distributions. A VAE analysis derives both forward and backward stochastic differential equations (SDEs) as well as non-variational integral expressions for likelihood formulas. A score-matching analysis derives the reverse diffusion ordinary differential equation (ODE) and a family of reverse-diffusion SDEs parameterized by noise level. The paper presents the mathematics directly with attributions saved for a final section.

cs.LG↗

arXiv2021

Dependent Type Theory as Related to the Bourbaki Notions of Structure and Isomorphism

This paper develops a version of dependent type theory in which isomorphism is handled through a direct generalization of the 1939 definitions of Bourbaki. More specifically we generalize the Bourbaki definition of structure from simple type signatures to dependent type signatures. Both the original Bourbaki notion of isomorphism and its generalization given here define an isomorphism between two structures $N$ and $N'$ to consist of bijections between their sorts that transport the structure of $N$ to the structure of $N'$. Here transport is defined by commutativity conditions stated with set-theoretic equality. This differs from the dependent type theoretic treatments of isomorphism given in the groupoid model and homotopy type theory where no analogously straightforward set-theoretic definition of transport is specified. The straightforward definition of transport also leads to a straightforward constructive proof (constructive content) for the validity of the substitution of isomorphics -- something that is difficult in the groupoid model or homotopy type theory.

cs.LO↗

arXiv2020

Information-Theoretic Segmentation by Inpainting Error Maximization

We study image segmentation from an information-theoretic perspective, proposing a novel adversarial method that performs unsupervised segmentation by partitioning images into maximally independent sets. More specifically, we group image pixels into foreground and background, with the goal of minimizing predictability of one set from the other. An easily computed loss drives a greedy search process to maximize inpainting error over these partitions. Our method does not involve training deep networks, is computationally cheap, class-agnostic, and even applicable in isolation to a single unlabeled image. Experiments demonstrate that it achieves a new state-of-the-art in unsupervised segmentation quality, while being substantially faster and more general than competing approaches.

cs.CV↗

arXiv2020

On-The-Fly Information Retrieval Augmentation for Language Models

Here we experiment with the use of information retrieval as an augmentation for pre-trained language models. The text corpus used in information retrieval can be viewed as form of episodic memory which grows over time. By augmenting GPT 2.0 with information retrieval we achieve a zero shot 15% relative reduction in perplexity on Gigaword corpus without any re-training. We also validate our IR augmentation on an event co-reference task.

cs.CL↗

arXiv2020

Formal Limitations on the Measurement of Mutual Information

Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual information. More specifically, we show that any distribution-free high-confidence lower bound on mutual information estimated from N samples cannot be larger than O(ln N ).

cs.IT↗

arXiv2020

MathZero, The Classification Problem, and Set-Theoretic Type Theory

AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics -- a MathZero. MathZero would require a formal foundation and an objective. We propose the foundation of set-theoretic dependent type theory and an objective defined in terms of the classification problem -- the problem of classifying concept instances up to isomorphism. The natural numbers arise as the solution to the classification problem for finite sets. Here we generalize classical Bourbaki set-theoretic isomorphism to set-theoretic dependent type theory. To our knowledge we give the first isomorphism inference rules for set-theoretic dependent type theory with propositional set-theoretic equality. The presentation is intended to be accessible to mathematicians with no prior exposure to type theory.

cs.LO↗

arXiv2020

Isomorphism Revisited

Isomorphism is central to the structure of mathematics and has been formalized in various ways within dependent type theory. All previous treatments have done this by replacing quantification over sets with quantification over groupoids of some form --- categories in which every morphism is an isomorphism. Quantification over sets is replaced by quantification over standard groupoids in the groupoid model, by quantification over infinity groupoid in Homotopy type theory, and by quantification over morphoids in the morphoid model. Here we give a treatment of isomorphism based on the intuitive notion of sets as collections without internal structure. Quantification over sets remains as quantification over sets. Isomorphism and groupoid structure then emerge from simple but subtle syntactic restrictions on set-theoretic language. This approach more fully unifies the classical ZFC foundations with a rigorous treatments of isomorphism, symmetry, canonicality, functors, and natural transformations. This is all done without reference to category theory.

cs.LO↗

arXiv2020

Domain-independent Dominance of Adaptive Methods

From a simplified analysis of adaptive methods, we derive AvaGrad, a new optimizer which outperforms SGD on vision tasks when its adaptability is properly tuned. We observe that the power of our method is partially explained by a decoupling of learning rate and adaptability, greatly simplifying hyperparameter search. In light of this observation, we demonstrate that, against conventional wisdom, Adam can also outperform SGD on vision tasks, as long as the coupling between its learning rate and adaptability is taken into account. In practice, AvaGrad matches the best results, as measured by generalization accuracy, delivered by any existing optimizer (SGD or adaptive) across image classification (CIFAR, ImageNet) and character-level language modelling (Penn Treebank) tasks.

cs.LG↗

arXiv2019

Evidence Sentence Extraction for Machine Reading Comprehension

Remarkable success has been achieved in the last few years on some limited machine reading comprehension (MRC) tasks. However, it is still difficult to interpret the predictions of existing MRC models. In this paper, we focus on extracting evidence sentences that can explain or support the answers of multiple-choice MRC tasks, where the majority of answer options cannot be directly extracted from reference documents. Due to the lack of ground truth evidence sentence labels in most cases, we apply distant supervision to generate imperfect labels and then use them to train an evidence sentence extractor. To denoise the noisy labels, we apply a recently proposed deep probabilistic logic learning framework to incorporate both sentence-level and cross-sentence linguistic indicators for indirect supervision. We feed the extracted evidence sentences into existing MRC models and evaluate the end-to-end performance on three challenging multiple-choice MRC datasets: MultiRC, RACE, and DREAM, achieving comparable or better performance than the same models that take as input the full reference document. To the best of our knowledge, this is the first work extracting evidence sentences for multiple-choice MRC.

cs.CL↗

arXiv2018

Information Theoretic Co-Training

This paper introduces an information theoretic co-training objective for unsupervised learning. We consider the problem of predicting the future. Rather than predict future sensations (image pixels or sound waves) we predict "hypotheses" to be confirmed by future sensations. More formally, we assume a population distribution on pairs $(x,y)$ where we can think of $x$ as a past sensation and $y$ as a future sensation. We train both a predictor model $P_Φ(z|x)$ and a confirmation model $P_Ψ(z|y)$ where we view $z$ as hypotheses (when predicted) or facts (when confirmed). For a population distribution on pairs $(x,y)$ we focus on the problem of measuring the mutual information between $x$ and $y$. By the data processing inequality this mutual information is at least as large as the mutual information between $x$ and $z$ under the distribution on triples $(x,z,y)$ defined by the confirmation model $P_Ψ(z|y)$. The information theoretic training objective for $P_Φ(z|x)$ and $P_Ψ(z|y)$ can be viewed as a form of co-training where we want the prediction from $x$ to match the confirmation from $y$.

cs.LG↗

arXiv2018

Isomorphism within Naive Type Theory

We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and proper classes respectively. Each proper class, such as "group" or "topological space", has an associated notion of isomorphism in correspondence with standard definitions. Isomorphism is handled by definging a groupoid structure on the space of all definable values. The values are simultaneously objects (oids) and morphism --- they are "morphoids". Soundness can then be proved for simple and natural inference rules deriving isomorphisms and for the substitution of isomorphics.

cs.LO↗

arXiv2017

Exploring Generalization in Deep Learning

With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization, highlighting the importance of scale normalization, and making a connection between sharpness and PAC-Bayes theory. We then investigate how well the measures explain different observed phenomena.

cs.LG↗

arXiv2017

Emergent Predication Structure in Hidden State Vectors of Neural Readers

A significant number of neural architectures for reading comprehension have recently been developed and evaluated on large cloze-style datasets. We present experiments supporting the emergence of "predication structure" in the hidden state vectors of these readers. More specifically, we provide evidence that the hidden state vectors represent atomic formulas $Φ[c]$ where $Φ$ is a semantic property (predicate) and $c$ is a constant symbol entity identifier.

cs.CL↗