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Systems for making determinations on socially-constructed and complex concepts at scale are increasingly being deployed. To make such fuzzy concepts tractable for training and evaluating AI, aligning model outputs, or human-in-the-loop workflows, the prevailing strategy involves developing `constitutions' in the form of rules, policies, or principles. However, high-level rules often fail to capture situational nuances or have differing interpretations, resulting in inconsistent decisions. In this work, we introduce case law grounding (CLG), a hybrid workflow inspired by case law in the legal realm where past judgments on specific cases inform new decisions. Evaluating on two task domains, we find that CLG can improve alignment of decisions (+9.6% and +10.9% accuracy) and consistency ($\Delta\bar{\kappa}$ of +0.263 and +0.433) of human decision-makers, while also providing auditable rationales. We also find similarly substantial alignment improvements for an LLM decision-maker (+25% and +23% accuracy).

There is growing evidence that pretraining on high quality, carefully thought-out tokens such as code or mathematics plays an important role in improving the reasoning abilities of large language models. For example, Minerva, a PaLM model finetuned on billions of tokens of mathematical documents from arXiv and the web, reported dramatically improved performance on problems that require quantitative reasoning. However, because all known open source web datasets employ preprocessing that does not faithfully preserve mathematical notation, the benefits of large scale training on quantitive web documents are unavailable to the research community. We introduce OpenWebMath, an open dataset inspired by these works containing 14.7B tokens of mathematical webpages from Common Crawl. We describe in detail our method for extracting text and LaTeX content and removing boilerplate from HTML documents, as well as our methods for quality filtering and deduplication. Additionally, we run small-scale experiments by training 1.4B parameter language models on OpenWebMath, showing that models trained on 14.7B tokens of our dataset surpass the performance of models trained on over 20x the amount of general language data. We hope that our dataset, openly released on the Hugging Face Hub, will help spur advances in the reasoning abilities of large language models.

Question answering over hybrid contexts is a complex task, which requires the combination of information extracted from unstructured texts and structured tables in various ways. Recently, In-Context Learning demonstrated significant performance advances for reasoning tasks. In this paradigm, a large language model performs predictions based on a small set of supporting exemplars. The performance of In-Context Learning depends heavily on the selection procedure of the supporting exemplars, particularly in the case of HybridQA, where considering the diversity of reasoning chains and the large size of the hybrid contexts becomes crucial. In this work, we present Selection of ExEmplars for hybrid Reasoning (SEER), a novel method for selecting a set of exemplars that is both representative and diverse. The key novelty of SEER is that it formulates exemplar selection as a Knapsack Integer Linear Program. The Knapsack framework provides the flexibility to incorporate diversity constraints that prioritize exemplars with desirable attributes, and capacity constraints that ensure that the prompt size respects the provided capacity budgets. The effectiveness of SEER is demonstrated on FinQA and TAT-QA, two real-world benchmarks for HybridQA, where it outperforms previous exemplar selection methods.

Fine-tuning diffusion models through personalized datasets is an acknowledged method for improving generation quality across downstream tasks, which, however, often inadvertently generates unintended concepts such as watermarks and QR codes, attributed to the limitations in image sources and collecting methods within specific downstream tasks. Existing solutions suffer from eliminating these unintentionally learned implicit concepts, primarily due to the dependency on the model's ability to recognize concepts that it actually cannot discern. In this work, we introduce Geom-Erasing, a novel approach that successfully removes the implicit concepts with either an additional accessible classifier or detector model to encode geometric information of these concepts into text domain. Moreover, we propose Implicit Concept, a novel image-text dataset imbued with three implicit concepts (i.e., watermarks, QR codes, and text) for training and evaluation. Experimental results demonstrate that Geom-Erasing not only identifies but also proficiently eradicates implicit concepts, revealing a significant improvement over the existing methods. The integration of geometric information marks a substantial progression in the precise removal of implicit concepts in diffusion models.

Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV originates from the study of series-parallel orders, cographs, and proof systems. Both logics enjoy a cut-admissibility result, but for neither logic can this be done in the sequent calculus. Provability in pomset logic can be checked via a proof net correctness criterion and in BV via a deep inference proof system. It has long been conjectured that these two logics are the same. In this paper we show that this conjecture is false. We also investigate the complexity of the two logics, exhibiting a huge gap between the two. Whereas provability in BV is NP-complete, provability in pomset logic is $\Sigma_2^p$-complete. We also make some observations with respect to possible sequent systems for the two logics.

The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently encountered in practice, the chain graph model has been largely under investigated in literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this paper, we first establish a set of novel identifiability conditions for the Gaussian chain graph model, exploiting a low rank plus sparse decomposition of the precision matrix. Further, an efficient learning algorithm is built upon the identifiability conditions to fully recover the chain graph structure. Theoretical analysis on the proposed method is conducted, assuring its asymptotic consistency in recovering the exact chain graph structure. The advantage of the proposed method is also supported by numerical experiments on both simulated examples and a real application on the Standard & Poor 500 index data.

Large Language Models (LLMs) have the ability to solve a variety of tasks, such as text summarization and mathematical questions, just out of the box, but they are often trained with a single task in mind. Due to high computational costs, the current trend is to use prompt instruction tuning to better adjust monolithic, pretrained LLMs for new -- but often individual -- downstream tasks. Thus, how one would expand prompt tuning to handle -- concomitantly -- heterogeneous tasks and data distributions is a widely open question. To address this gap, we suggest the use of \emph{Mixture of Prompts}, or MoPs, associated with smart gating functionality: the latter -- whose design is one of the contributions of this paper -- can identify relevant skills embedded in different groups of prompts and dynamically assign combined experts (i.e., collection of prompts), based on the target task. Additionally, MoPs are empirically agnostic to any model compression technique applied -- for efficiency reasons -- as well as instruction data source and task composition. In practice, MoPs can simultaneously mitigate prompt training "interference" in multi-task, multi-source scenarios (e.g., task and data heterogeneity across sources), as well as possible implications from model approximations. As a highlight, MoPs manage to decrease final perplexity from $\sim20\%$ up to $\sim70\%$, as compared to baselines, in the federated scenario, and from $\sim 3\%$ up to $\sim30\%$ in the centralized scenario.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.