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Dan Jurafsky

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21 papers
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21

ICML Conference 2025 Conference Paper

AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders

  • Zhengxuan Wu
  • Aryaman Arora
  • Atticus Geiger
  • Zheng Wang 0078
  • Jing Huang 0014
  • Dan Jurafsky
  • Christopher D. Manning
  • Christopher Potts

Fine-grained steering of language model outputs is essential for safety and reliability. Prompting and finetuning are widely used to achieve these goals, but interpretability researchers have proposed a variety of representation-based techniques as well, including sparse autoencoders (SAEs), linear artificial tomography, supervised steering vectors, linear probes, and representation finetuning. At present, there is no benchmark for making direct comparisons between these proposals. Therefore, we introduce AxBench, a large-scale benchmark for steering and concept detection, and report experiments on Gemma-2-2B and 9B. For steering, we find that prompting outperforms all existing methods, followed by finetuning. For concept detection, representation-based methods such as difference-in-means, perform the best. On both evaluations, SAEs are not competitive. We introduce a novel weakly-supervised representational method (Rank-1 Representation Finetuning; ReFT-r1), which is competitive on both tasks while providing the interpretability advantages that prompting lacks. Along with AxBench, we train and publicly release SAE-scale feature dictionaries for ReFT-r1 and DiffMean.

ICLR Conference 2025 Conference Paper

h4rm3l: A Language for Composable Jailbreak Attack Synthesis

  • Moussa Koulako Bala Doumbouya
  • Ananjan Nandi
  • Gabriel Poesia
  • Davide Ghilardi
  • Anna Goldie
  • Federico Bianchi 0001
  • Dan Jurafsky
  • Christopher D. Manning

Despite their demonstrated valuable capabilities, state-of-the-art (SOTA) widely deployed large language models (LLMs) still have the potential to cause harm to society due to the ineffectiveness of their safety filters, which can be bypassed by prompt transformations called jailbreak attacks. Current approaches to LLM safety assessment, which employ datasets of templated prompts and benchmarking pipelines, fail to cover sufficiently large and diverse sets of jailbreak attacks, leading to the widespread deployment of unsafe LLMs. Recent research showed that novel jailbreak attacks could be derived by composition; however, a formal composable representation for jailbreak attacks, which, among other benefits, could enable the exploration of a large compositional space of jailbreak attacks through program synthesis methods, has not been previously proposed. We introduce h4rm3l, a novel approach that addresses this gap with a human-readable domain-specific language (DSL). Our framework comprises: (1) The h4rm3l DSL, which formally expresses jailbreak attacks as compositions of parameterized string transformation primitives. (2) A synthesizer with bandit algorithms that efficiently generates jailbreak attacks optimized for a target black box LLM. (3) The h4rm3l red-teaming software toolkit that employs the previous two components and an automated harmful LLM behavior classifier that is strongly aligned with human judgment. We demonstrate h4rm3l's efficacy by synthesizing a dataset of 2656 successful novel jailbreak attacks targeting 6 SOTA open-source and proprietary LLMs (GPT-3.5, GPT-4o, Claude-3-Sonnet, Claude-3-Haiku, Llama-3-8B, and Llama-3-70B), and by benchmarking those models against a subset of these synthesized attacks. Our results show that h4rm3l's synthesized attacks are diverse and more successful than existing jailbreak attacks in literature, with success rates exceeding 90% on SOTA LLMs. Warning: This paper and related research artifacts contain offensive and potentially disturbing prompts and model-generated content.

ICML Conference 2025 Conference Paper

What can large language models do for sustainable food?

  • Anna T. Thomas
  • Adam Yee
  • Andrew Mayne
  • Maya B. Mathur
  • Dan Jurafsky
  • Kristina Gligoric

Food systems are responsible for a third of human-caused greenhouse gas emissions. We investigate what Large Language Models (LLMs) can contribute to reducing the environmental impacts of food production. We define a typology of design and prediction tasks based on the sustainable food literature and collaboration with domain experts, and evaluate six LLMs on four tasks in our typology. For example, for a sustainable protein design task, food science experts estimated that collaboration with an LLM can reduce time spent by 45% on average, compared to 22% for collaboration with another expert human food scientist. However, for a sustainable menu design task, LLMs produce suboptimal solutions when instructed to consider both human satisfaction and climate impacts. We propose a general framework for integrating LLMs with combinatorial optimization to improve reasoning capabilities. Our approach decreases emissions of food choices by 79% in a hypothetical restaurant while maintaining participants’ satisfaction with their set of choices. Our results demonstrate LLMs’ potential, supported by optimization techniques, to accelerate sustainable food development and adoption.

ICLR Conference 2024 Conference Paper

A Benchmark for Learning to Translate a New Language from One Grammar Book

  • Garrett Tanzer
  • Mirac Suzgun
  • Eline Visser
  • Dan Jurafsky
  • Luke Melas-Kyriazi

Large language models (LLMs) can perform impressive feats with in-context learning or lightweight finetuning. It is natural to wonder how well these models adapt to genuinely new tasks, but how does one find tasks that are unseen in internet-scale training sets? We turn to a field that is explicitly motivated and bottlenecked by a scarcity of web data: low-resource languages. In this paper, we introduce MTOB (Machine Translation from One Book), a benchmark for learning to translate between English and Kalamang—a language with less than 200 speakers and therefore virtually no presence on the web—using several hundred pages of field linguistics reference materials. This task framing is novel in that it asks a model to learn a language from a single human-readable book of grammar explanations, rather than a large mined corpus of in-domain data, more akin to L2 language learning than L1 language acquisition. We demonstrate that baselines using current LLMs are promising but fall short of human performance, achieving 44.7 chrF on Kalamang to English translation and 45.8 chrF on English to Kalamang translation, compared to 51.6 and 57.0 chrF by a human who learned Kalamang from the same reference materials. We hope that MTOB will help measure LLM capabilities along a new dimension, and that the methods developed to solve it could help expand access to language technology for underserved communities by leveraging qualitatively different kinds of data than traditional machine translation.

ICML Conference 2024 Conference Paper

How Well Can LLMs Negotiate? NegotiationArena Platform and Analysis

  • Federico Bianchi 0001
  • Patrick John Chia
  • Mert Yüksekgönül
  • Jacopo Tagliabue
  • Dan Jurafsky
  • James Y. Zou

Negotiation is the basis of social interactions; humans negotiate everything from the price of cars to how to share common resources. With rapidly growing interest in using large language models (LLMs) to act as agents on behalf of human users, such LLM agents would also need to be able to negotiate. In this paper, we study how well LLMs can negotiate with each other. We develop NegotiationArena: a flexible framework for evaluating and probing the negotiation abilities of LLM agents. We implemented three types of scenarios in NegotiationArena to assess LLM’s behaviors in allocating shared resources (ultimatum games), aggregate resources (trading games) and buy/sell goods (price negotiations). Each scenario allows for multiple turns of flexible dialogues between LLM agents to allow for more complex negotiations. Interestingly, LLM agents can significantly boost their negotiation outcomes by employing certain behavioral tactics. For example, by pretending to be desolate and desperate, LLMs can improve their payoffs by 20% when negotiating against the standard GPT-4. We also quantify irrational negotiation behaviors exhibited by the LLM agents, many of which also appear in humans. Together, NegotiationArena offers a new environment to investigate LLM interactions, enabling new insights into LLM’s theory of mind, irrationality, and reasoning abilities

ICML Conference 2024 Conference Paper

Model Alignment as Prospect Theoretic Optimization

  • Kawin Ethayarajh
  • Winnie Xu
  • Niklas Muennighoff
  • Dan Jurafsky
  • Douwe Kiela

Kahneman & Tversky’s $\textit{prospect theory}$ tells us that humans perceive random variables in a biased but well-defined manner (1992); for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases—the success of these objectives (e. g. , DPO) over cross-entropy minimization can partly be ascribed to them belonging to a family of loss functions that we call $\textit{human-aware losses}$ (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect theory literature. Using a Kahneman-Tversky model of human utility, we propose a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, as current methods do. We call this approach KTO, and it matches or exceeds the performance of preference-based methods at scales from 1B to 30B, despite only learning from a binary signal of whether an output is desirable. More broadly, our work suggests that there is no one HALO that is universally superior; the best loss depends on the inductive biases most appropriate for a given setting, an oft-overlooked consideration.

NeurIPS Conference 2024 Conference Paper

ReFT: Representation Finetuning for Language Models

  • Zhengxuan Wu
  • Aryaman Arora
  • Zheng Wang
  • Atticus Geiger
  • Dan Jurafsky
  • Christopher D. Manning
  • Christopher Potts

Parameter-efficient finetuning (PEFT) methods seek to adapt large neural models via updates to a small number of weights. However, much prior interpretability work has shown that representations encode rich semantic information, suggesting that editing representations might be a more powerful alternative. We pursue this hypothesis by developing a family of Representation Finetuning (ReFT) methods. ReFT methods operate on a frozen base model and learn task-specific interventions on hidden representations. We define a strong instance of the ReFT family, Low-rank Linear Subspace ReFT (LoReFT), and we identify an ablation of this method that trades some performance for increased efficiency. Both are drop-in replacements for existing PEFTs and learn interventions that are 15x--65x more parameter-efficient than LoRA. We showcase LoReFT on eight commonsense reasoning tasks, four arithmetic reasoning tasks, instruction-tuning, and GLUE. In all these evaluations, our ReFTs deliver the best balance of efficiency and performance, and almost always outperform state-of-the-art PEFTs. Upon publication, we will publicly release our generic ReFT training library.

ICLR Conference 2024 Conference Paper

Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions

  • Federico Bianchi 0001
  • Mirac Suzgun
  • Giuseppe Attanasio
  • Paul Röttger
  • Dan Jurafsky
  • Tatsunori B. Hashimoto
  • James Y. Zou

Training large language models to follow instructions makes them perform better on a wide range of tasks and generally become more helpful. However, a perfectly helpful model will follow even the most malicious instructions and readily generate harmful content. In this paper, we raise concerns over the safety of models that only emphasize helpfulness, not harmlessness, in their instruction-tuning. We show that several popular instruction-tuned models are highly unsafe. Moreover, we show that adding just 3\% safety examples (a few hundred demonstrations) when fine-tuning a model like LLaMA can substantially improve its safety. Our safety-tuning does not make models significantly less capable or helpful as measured by standard benchmarks. However, we do find exaggerated safety behaviours, where too much safety-tuning makes models refuse perfectly safe prompts if they superficially resemble unsafe ones. As a whole, our results illustrate trade-offs in training LLMs to be helpful and training them to be safe.

NeurIPS Conference 2023 Conference Paper

Ecosystem-level Analysis of Deployed Machine Learning Reveals Homogeneous Outcomes

  • Connor Toups
  • Rishi Bommasani
  • Kathleen Creel
  • Sarah Bana
  • Dan Jurafsky
  • Percy S. Liang

Machine learning is traditionally studied at the model level: researchers measure and improve the accuracy, robustness, bias, efficiency, and other dimensions of specific models. In practice, however, the societal impact of any machine learning model is partially determined by the context into which it is deployed. To capture this, we introduce ecosystem-level analysis: rather than analyzing a single model, we consider the collection of models that are deployed in a given context. For example, ecosystem-level analysis in hiring recognizes that a job candidate’s outcomes are determined not only by a single hiring algorithm or firm but instead by the collective decisions of all the firms to which the candidate applied. Across three modalities (text, images, speech) and 11 datasets, we establish a clear trend: deployed machine learning is prone to systemic failure, meaning some users are exclusively misclassified by all models available. Even when individual models improve at the population level over time, we find these improvements rarely reduce the prevalence of systemic failure. Instead, the benefits of these improvements predominantly accrue to individuals who are already correctly classified by other models. In light of these trends, we analyze medical imaging for dermatology, a setting where the costs of systemic failure are especially high. While traditional analyses reveal that both models and humans exhibit racial performance disparities, ecosystem-level analysis reveals new forms of racial disparity in model predictions that do not present in human predictions. These examples demonstrate that ecosystem-level analysis has unique strengths in characterizing the societal impact of machine learning.

JMLR Journal 2023 Journal Article

Foundation Models and Fair Use

  • Peter Henderson
  • Xuechen Li
  • Dan Jurafsky
  • Tatsunori Hashimoto
  • Mark A. Lemley
  • Percy Liang

Existing foundation models are trained on copyrighted material. Deploying these models can pose both legal and ethical risks when data creators fail to receive appropriate attribution or compensation. In the United States and several other countries, copyrighted content may be used to build foundation models without incurring liability due to the fair use doctrine. However, there is a caveat: If the model produces output that is similar to copyrighted data, particularly in scenarios that affect the market of that data, fair use may no longer apply to the output of the model. In this work, we emphasize that fair use is not guaranteed, and additional work may be necessary to keep model development and deployment squarely in the realm of fair use. First, we survey the potential risks of developing and deploying foundation models based on copyrighted content. We review relevant U.S. case law, drawing parallels to existing and potential applications for generating text, source code, and visual art. Experiments confirm that popular foundation models can generate content considerably similar to copyrighted material. Second, we discuss technical mitigations that can help foundation models stay in line with fair use. We argue that more research is needed to align mitigation strategies with the current state of the law. Third, we suggest that the law and technical mitigations should co-evolve. For example, coupled with other policy mechanisms, the law could more explicitly consider safe harbors when strong technical tools are used to mitigate infringement harms. This co-evolution may help strike a balance between intellectual property and innovation, which speaks to the original goal of fair use. But we emphasize that the strategies we describe here are not a panacea and more work is needed to develop policies that address the potential harms of foundation models. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

ICLR Conference 2023 Conference Paper

When and Why Vision-Language Models Behave like Bags-Of-Words, and What to Do About It?

  • Mert Yüksekgönül
  • Federico Bianchi 0001
  • Pratyusha Kalluri
  • Dan Jurafsky
  • James Y. Zou

Despite the success of large vision and language models (VLMs) in many downstream applications, it is unclear how well they encode the compositional relationships between objects and attributes. Here, we create the Attribution, Relation, and Order (ARO) benchmark to systematically evaluate the ability of VLMs to understand different types of relationships, attributes, and order information. ARO consists of \emph{Visual Genome Attribution}, to test the understanding of objects' properties; \emph{Visual Genome Relation}, to test for relational understanding; and \emph{COCO-Order \& Flickr30k-Order}, to test for order sensitivity in VLMs. ARO is orders of magnitude larger than previous benchmarks of compositionality, with more than 50,000 test cases. We present the settings where state-of-the-art VLMs behave like bags-of-words---i.e. when they have poor relational understanding, can blunder when linking objects to their attributes, and demonstrate a severe lack of order sensitivity. VLMs are predominantly trained and evaluated on large scale datasets with rich compositional structure in the images and captions. Yet, training on these datasets has not been enough to address the lack of compositional understanding, and evaluating on these datasets has failed to surface this deficiency. To understand why these limitations emerge and are not represented in the standard tests, we zoom into the evaluation and training procedures. We demonstrate that it is possible to perform well on image-text retrieval over existing datasets without using the composition and order information. This further motivates the value of using ARO to benchmark VLMs. Given that contrastive pretraining optimizes for retrieval on large datasets with similar shortcuts, we hypothesize that this can explain why the models do not need to learn to represent compositional information. This finding suggests a natural solution: composition-aware hard negative mining. We show that a simple-to-implement modification of contrastive learning significantly improves the performance on tasks requiring understanding of order and compositionality.

NeurIPS Conference 2022 Conference Paper

Picking on the Same Person: Does Algorithmic Monoculture lead to Outcome Homogenization?

  • Rishi Bommasani
  • Kathleen A. Creel
  • Ananya Kumar
  • Dan Jurafsky
  • Percy S. Liang

As the scope of machine learning broadens, we observe a recurring theme of algorithmic monoculture: the same systems, or systems that share components (e. g. datasets, models), are deployed by multiple decision-makers. While sharing offers advantages like amortizing effort, it also has risks. We introduce and formalize one such risk, outcome homogenization: the extent to which particular individuals or groups experience the same outcomes across different deployments. If the same individuals or groups exclusively experience undesirable outcomes, this may institutionalize systemic exclusion and reinscribe social hierarchy. We relate algorithmic monoculture and outcome homogenization by proposing the component sharing hypothesis: if algorithmic systems are increasingly built on the same data or models, then they will increasingly homogenize outcomes. We test this hypothesis on algorithmic fairness benchmarks, demonstrating that increased data-sharing reliably exacerbates homogenization and individual-level effects generally exceed group-level effects. Further, given the current regime in AI of foundation models, i. e. pretrained models that can be adapted to myriad downstream tasks, we test whether model-sharing homogenizes outcomes across tasks. We observe mixed results: we find that for both vision and language settings, the specific methods for adapting a foundation model significantly influence the degree of outcome homogenization. We also identify societal challenges that inhibit the measurement, diagnosis, and rectification of outcome homogenization in deployed machine learning systems.

NeurIPS Conference 2022 Conference Paper

Pile of Law: Learning Responsible Data Filtering from the Law and a 256GB Open-Source Legal Dataset

  • Peter Henderson
  • Mark Krass
  • Lucia Zheng
  • Neel Guha
  • Christopher D Manning
  • Dan Jurafsky
  • Daniel Ho

One concern with the rise of large language models lies with their potential for significant harm, particularly from pretraining on biased, obscene, copyrighted, and private information. Emerging ethical approaches have attempted to filter pretraining material, but such approaches have been ad hoc and failed to take context into account. We offer an approach to filtering grounded in law, which has directly addressed the tradeoffs in filtering material. First, we gather and make available the Pile of Law, a ~256GB (and growing) dataset of open-source English-language legal and administrative data, covering court opinions, contracts, administrative rules, and legislative records. Pretraining on the Pile of Law may help with legal tasks that have the promise to improve access to justice. Second, we distill the legal norms that governments have developed to constrain the inclusion of toxic or private content into actionable lessons for researchers and discuss how our dataset reflects these norms. Third, we show how the Pile of Law offers researchers the opportunity to learn such filtering rules directly from the data, providing an exciting new research direction in model-based processing.

ICLR Conference 2021 Conference Paper

Nearest Neighbor Machine Translation

  • Urvashi Khandelwal
  • Angela Fan
  • Dan Jurafsky
  • Luke Zettlemoyer
  • Mike Lewis

We introduce $k$-nearest-neighbor machine translation ($k$NN-MT), which predicts tokens with a nearest-neighbor classifier over a large datastore of cached examples, using representations from a neural translation model for similarity search. This approach requires no additional training and scales to give the decoder direct access to billions of examples at test time, resulting in a highly expressive model that consistently improves performance across many settings. Simply adding nearest-neighbor search improves a state-of-the-art German-English translation model by 1.5 BLEU. $k$NN-MT allows a single model to be adapted to diverse domains by using a domain-specific datastore, improving results by an average of 9.2 BLEU over zero-shot transfer, and achieving new state-of-the-art results---without training on these domains. A massively multilingual model can also be specialized for particular language pairs, with improvements of 3 BLEU for translating from English into German and Chinese. Qualitatively, $k$NN-MT is easily interpretable; it combines source and target context to retrieve highly relevant examples.

AAAI Conference 2020 Conference Paper

Automatically Neutralizing Subjective Bias in Text

  • Reid Pryzant
  • Richard Diehl Martinez
  • Nathan Dass
  • Sadao Kurohashi
  • Dan Jurafsky
  • Diyi Yang

Texts like news, encyclopedias, and some social media strive for objectivity. Yet bias in the form of inappropriate subjectivity — introducing attitudes via framing, presupposing truth, and casting doubt — remains ubiquitous. This kind of bias erodes our collective trust and fuels social conflict. To address this issue, we introduce a novel testbed for natural language generation: automatically bringing inappropriately subjective text into a neutral point of view (“neutralizing” biased text). We also offer the first parallel corpus of biased language. The corpus contains 180, 000 sentence pairs and originates from Wikipedia edits that removed various framings, presuppositions, and attitudes from biased sentences. Last, we propose two strong encoder-decoder baselines for the task. A straightforward yet opaque CONCURRENT system uses a BERT encoder to identify subjective words as part of the generation process. An interpretable and controllable MODULAR algorithm separates these steps, using (1) a BERT-based classifier to identify problematic words and (2) a novel join embedding through which the classifier can edit the hidden states of the encoder. Large-scale human evaluation across four domains (encyclopedias, news headlines, books, and political speeches) suggests that these algorithms are a first step towards the automatic identification and reduction of bias.

ICLR Conference 2020 Conference Paper

Generalization through Memorization: Nearest Neighbor Language Models

  • Urvashi Khandelwal
  • Omer Levy
  • Dan Jurafsky
  • Luke Zettlemoyer
  • Mike Lewis

We introduce $k$NN-LMs, which extend a pre-trained neural language model (LM) by linearly interpolating it with a $k$-nearest neighbors ($k$NN) model. The nearest neighbors are computed according to distance in the pre-trained LM embedding space, and can be drawn from any text collection, including the original LM training data. Applying this transformation to a strong Wikitext-103 LM, with neighbors drawn from the original training set, our $k$NN-LM achieves a new state-of-the-art perplexity of 15.79 -- a 2.9 point improvement with no additional training. We also show that this approach has implications for efficiently scaling up to larger training sets and allows for effective domain adaptation, by simply varying the nearest neighbor datastore, again without further training. Qualitatively, the model is particularly helpful in predicting rare patterns, such as factual knowledge. Together, these results strongly suggest that learning similarity between sequences of text is easier than predicting the next word, and that nearest neighbor search is an effective approach for language modeling in the long tail.

NeurIPS Conference 2020 Conference Paper

Language Through a Prism: A Spectral Approach for Multiscale Language Representations

  • Alex Tamkin
  • Dan Jurafsky
  • Noah Goodman

Language exhibits structure at a wide range of scales, from subwords to words, sentences, paragraphs, and documents. We propose building models that isolate scale-specific information in deep representations, and develop methods for encouraging models during training to learn more about particular scales of interest. Our method for creating scale-specific neurons in deep NLP models constrains how the activation of a neuron can change across the tokens of an input by interpreting those activations as a digital signal and filtering out parts of its frequency spectrum. This technique enables us to extract scale-specific information from BERT representations: by filtering out different frequencies we can produce new representations that perform well on part of speech tagging (word-level), dialog speech acts classification (utterance-level), or topic classification (document-level), while performing poorly on the other tasks. We also present a prism layer for use during training, which constrains different neurons of a BERT model to different parts of the frequency spectrum. Our proposed BERT + Prism model is better able to predict masked tokens using long-range context, and produces individual multiscale representations that perform with comparable or improved performance across all three tasks. Our methods are general and readily applicable to other domains besides language, such as images, audio, and video.

JMLR Journal 2020 Journal Article

Towards the Systematic Reporting of the Energy and Carbon Footprints of Machine Learning

  • Peter Henderson
  • Jieru Hu
  • Joshua Romoff
  • Emma Brunskill
  • Dan Jurafsky
  • Joelle Pineau

Accurate reporting of energy and carbon usage is essential for understanding the potential climate impacts of machine learning research. We introduce a framework that makes this easier by providing a simple interface for tracking realtime energy consumption and carbon emissions, as well as generating standardized online appendices. Utilizing this framework, we create a leaderboard for energy efficient reinforcement learning algorithms to incentivize responsible research in this area as an example for other areas of machine learning. Finally, based on case studies using our framework, we propose strategies for mitigation of carbon emissions and reduction of energy consumption. By making accounting easier, we hope to further the sustainable development of machine learning experiments and spur more research into energy efficient algorithms. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

NeurIPS Conference 2018 Conference Paper

Embedding Logical Queries on Knowledge Graphs

  • Will Hamilton
  • Payal Bajaj
  • Marinka Zitnik
  • Dan Jurafsky
  • Jure Leskovec

Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict "em what drugs are likely to target proteins involved with both diseases X and Y? " -- a query that requires reasoning about all possible proteins that might interact with diseases X and Y. Here we introduce a framework to efficiently make predictions about conjunctive logical queries -- a flexible but tractable subset of first-order logic -- on incomplete knowledge graphs. In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e. g. , translation, rotation) in this embedding space. By performing logical operations within a low-dimensional embedding space, our approach achieves a time complexity that is linear in the number of query variables, compared to the exponential complexity required by a naive enumeration-based approach. We demonstrate the utility of this framework in two application studies on real-world datasets with millions of relations: predicting logical relationships in a network of drug-gene-disease interactions and in a graph-based representation of social interactions derived from a popular web forum.

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