Coloring clique hypergraphs

Let G = (V, E) be a simple graph. The clique hypergraph of G, denoted as CH( G), has V as its set of vertices, and the maximal cliques as its hyperedges. Let Sk be a set of k colors. A map c : V Sk is a proper k-coloring for CH(G) if any maximal clique of G with at least two vertices receives at least two distinct colors. Let W ⊂ V, and let s ≥ 1. We say that G is (W, s)-extendible if any assignment on W with at most s colors can be extended to a proper s-coloring of CH(G). We prove that the clique hypergraphs of chordal and comparability graphs are bicolorable and that the clique hypergraphs of circular-arc graphs are 3-colorable. Our main result is the characterization of (W, 2)-extendibility for chordal graphs in the case when W=2

Deep Probabilistic Logic: A Unifying Framework for Indirect Supervision

Deep learning has emerged as a versatile tool for a wide range of NLP tasks, due to its superior capacity in representation learning. But its applicability is limited by the reliance on annotated examples, which are difficult to produce at scale. Indirect supervision has emerged as a promising direction to address this bottleneck, either by introducing labeling functions to automatically generate noisy examples from unlabeled text, or by imposing constraints over interdependent label decisions. A plethora of methods have been proposed, each with respective strengths and limitations. Probabilistic logic offers a unifying language to represent indirect supervision, but end-to-end modeling with probabilistic logic is often infeasible due to intractable inference and learning. In this paper, we propose deep probabilistic logic (DPL) as a general framework for indirect supervision, by composing probabilistic logic with deep learning. DPL models label decisions as latent variables, represents prior knowledge on their relations using weighted first-order logical formulas, and alternates between learning a deep neural network for the end task and refining uncertain formula weights for indirect supervision, using variational EM. This framework subsumes prior indirect supervision methods as special cases, and enables novel combination via infusion of rich domain and linguistic knowledge. Experiments on biomedical machine reading demonstrate the promise of this approach.Comment: EMNLP 2018 final versio

Context-faithful Prompting for Large Language Models

Large language models (LLMs) encode parametric knowledge about world facts and have shown remarkable performance in knowledge-driven NLP tasks. However, their reliance on parametric knowledge may cause them to overlook contextual cues, leading to incorrect predictions in context-sensitive NLP tasks (e.g., knowledge acquisition tasks). In this paper, we seek to assess and enhance LLMs' contextual faithfulness in two aspects: knowledge conflict and prediction with abstention. We demonstrate that LLMs' faithfulness can be significantly improved using carefully designed prompting strategies. In particular, we identify opinion-based prompts and counterfactual demonstrations as the most effective methods. Opinion-based prompts reframe the context as a narrator's statement and inquire about the narrator's opinions, while counterfactual demonstrations use instances containing false facts to improve faithfulness in knowledge conflict situations. Neither technique requires additional training. We conduct experiments on three datasets of two standard NLP tasks, machine reading comprehension and relation extraction, and the results demonstrate significant improvement in faithfulness to contexts. Code and data are released at https://github.com/wzhouad/context-faithful-llm.Comment: Accepted at EMNLP 2023 Findings. Code and data are released at https://github.com/wzhouad/context-faithful-ll

BLIAM: Literature-based Data Synthesis for Synergistic Drug Combination Prediction

Language models pre-trained on scientific literature corpora have substantially advanced scientific discovery by offering high-quality feature representations for downstream applications. However, these features are often not interpretable, and thus can reveal limited insights to domain experts. Instead of obtaining features from language models, we propose BLIAM, a literature-based data synthesis approach to directly generate training data points that are interpretable and model-agnostic to downstream applications. The key idea of BLIAM is to create prompts using existing training data and then use these prompts to synthesize new data points. BLIAM performs these two steps iteratively as new data points will define more informative prompts and new prompts will in turn synthesize more accurate data points. Notably, literature-based data augmentation might introduce data leakage since labels of test data points in downstream applications might have already been mentioned in the language model corpus. To prevent such leakage, we introduce GDSC-combo, a large-scale drug combination discovery dataset that was published after the biomedical language model was trained. We found that BLIAM substantially outperforms a non-augmented approach and manual prompting in this rigorous data split setting. BLIAM can be further used to synthesize data points for novel drugs and cell lines that were not even measured in biomedical experiments. In addition to the promising prediction performance, the data points synthesized by BLIAM are interpretable and model-agnostic, enabling in silico augmentation for in vitro experiments

Automatic Calibration and Error Correction for Large Language Models via Pareto Optimal Self-Supervision

Large language models (LLMs) have demonstrated remarkable capabilities out of box for a wide range of applications, yet accuracy still remains a major growth area, especially in mission-critical domains such as biomedicine. An effective method to calibrate the confidence level on LLM responses is essential to automatically detect errors and facilitate human-in-the-loop verification. An important source of calibration signals stems from expert-stipulated programmatic supervision, which is often available at low cost but has its own limitations such as noise and coverage. In this paper, we introduce a Pareto optimal self-supervision framework that can leverage available programmatic supervision to systematically calibrate LLM responses by producing a risk score for every response, without any additional manual efforts. This is accomplished by learning a harmonizer model to align LLM output with other available supervision sources, which would assign higher risk scores to more uncertain LLM responses and facilitate error correction. Experiments on standard relation extraction tasks in biomedical and general domains demonstrate the promise of this approach, with our proposed risk scores highly correlated with the real error rate of LLMs. For the most uncertain test instances, dynamic prompting based on our proposed risk scores results in significant accuracy improvement for off-the-shelf LLMs, boosting GPT-3 results past state-of-the-art (SOTA) weak supervision and GPT-4 results past SOTA supervised results on challenging evaluation datasets