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Large language models (LLMs) exhibit remarkable performance across various NLP tasks. However, they often generate incorrect or hallucinated information, which hinders their practical applicability in real-world scenarios. Human feedback has been shown to effectively enhance the factuality and quality of generated content, addressing some of these limitations. However, this approach is resource-intensive, involving manual input and supervision, which can be time-consuming and expensive. Moreover, it cannot be provided during inference, further limiting its practical utility in dynamic and interactive applications. In this paper, we introduce ReFeed, a novel pipeline designed to enhance LLMs by providing automatic retrieval feedback in a plug-and-play framework without the need for expensive fine-tuning. ReFeed first generates initial outputs, then utilizes a retrieval model to acquire relevant information from large document collections, and finally incorporates the retrieved information into the in-context demonstration for output refinement, thereby addressing the limitations of LLMs in a more efficient and cost-effective manner. Experiments on four knowledge-intensive benchmark datasets demonstrate our proposed ReFeed could improve over +6.0% under zero-shot setting and +2.5% under few-shot setting, compared to baselines without using retrieval feedback.

The problem of knowledge-based visual question answering involves answering questions that require external knowledge in addition to the content of the image. Such knowledge typically comes in various forms, including visual, textual, and commonsense knowledge. Using more knowledge sources increases the chance of retrieving more irrelevant or noisy facts, making it challenging to comprehend the facts and find the answer. To address this challenge, we propose Multi-modal Answer Validation using External knowledge (MAVEx), where the idea is to validate a set of promising answer candidates based on answer-specific knowledge retrieval. Instead of searching for the answer in a vast collection of often irrelevant facts as most existing approaches do, MAVEx aims to learn how to extract relevant knowledge from noisy sources, which knowledge source to trust for each answer candidate, and how to validate the candidate using that source. Our multi-modal setting is the first to leverage external visual knowledge (images searched using Google), in addition to textual knowledge in the form of Wikipedia sentences and ConceptNet concepts. Our experiments with OK-VQA, a challenging knowledge-based VQA dataset, demonstrate that MAVEx achieves new state-of-the-art results. Our code is available at https://github.com/jialinwu17/MAVEX, Comment: AAAI 2022

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 ($\ge$ 175B) to T5 variants ($\le$ 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We further give comprehensive discussions about important design choices for better generalization, including the tuning data format, the start model checkpoint, and a new model selection method. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs., Preprint

Although counterfactual reasoning is a fundamental aspect of intelligence, the lack of large-scale counterfactual open-domain question-answering (QA) benchmarks makes it difficult to evaluate and improve models on this ability. To address this void, we introduce the first such dataset, named IfQA, where each question is based on a counterfactual presupposition via an "if" clause. For example, if Los Angeles was on the east coast of the U.S., what would be the time difference between Los Angeles and Paris? Such questions require models to go beyond retrieving direct factual knowledge from the Web: they must identify the right information to retrieve and reason about an imagined situation that may even go against the facts built into their parameters. The IfQA dataset contains over 3,800 questions that were annotated annotated by crowdworkers on relevant Wikipedia passages. Empirical analysis reveals that the IfQA dataset is highly challenging for existing open-domain QA methods, including supervised retrieve-then-read pipeline methods (EM score 36.2), as well as recent few-shot approaches such as chain-of-thought prompting with GPT-3 (EM score 27.4). The unique challenges posed by the IfQA benchmark will push open-domain QA research on both retrieval and counterfactual reasoning fronts.

While large language models (LLMs) are proficient at question-answering (QA), the dependencies between their answers and other "beliefs" they may have about the world are typically unstated, and may even be in conflict. Our goal is to uncover such dependencies and reduce inconsistencies among them, so that answers are supported by faithful, system-believed chains of reasoning drawn from a consistent network of beliefs. Our approach, which we call REFLEX, is to add a "rational", self-reflecting layer on top of the LLM. First, given a question, we construct a belief graph using a backward-chaining process to materialize relevant model "beliefs" (including beliefs about answer candidates) and the inferential relationships between them. Second, we identify and minimize contradictions in that graph using a formal constraint reasoner. We find that REFLEX significantly improves consistency (by 8%-11% absolute) without harming overall answer accuracy, resulting in answers supported by faithful chains of reasoning drawn from a more consistent belief system. This suggests a new style of system architecture, in which an LLM extended with a rational layer of self-reflection can repair latent inconsistencies within the LLM alone.

When large language models (LMs) are applied in zero- or few-shot settings to discriminative tasks such as multiple-choice questions, their attentiveness (i.e., probability mass) is spread across many vocabulary tokens that are not valid choices. Such a spread across multiple surface forms with identical meaning is thought to cause an underestimation of a model's true performance, referred to as the "surface form competition" (SFC) hypothesis. This has motivated the introduction of various probability normalization methods. However, many core questions remain unanswered. How do we measure SFC or attentiveness? Are there direct ways of increasing attentiveness on valid choices? Does increasing attentiveness always improve task accuracy? We propose a mathematical formalism for studying this phenomenon, provide a metric for quantifying attentiveness, and identify a simple method for increasing it -- namely, in-context learning with even just one example containing answer choices. The formalism allows us to quantify SFC and bound its impact. Our experiments on three diverse datasets and six LMs reveal several surprising findings. For example, encouraging models to generate a valid answer choice can, in fact, be detrimental to task performance for some LMs, and prior probability normalization methods are less effective (sometimes even detrimental) to instruction-tuned LMs. We conclude with practical insights for effectively using prompted LMs for multiple-choice tasks.

Models trained with counterfactually augmented data learn representations of the causal structure of tasks, enabling robust generalization. However, high-quality counterfactual data is scarce for most tasks and not easily generated at scale. When crowdsourced, such data is typically limited in scale and diversity; when generated using supervised methods, it is computationally expensive to extend to new counterfactual dimensions. In this work, we introduce DISCO (DIStilled COunterfactual Data), a new method for automatically generating high quality counterfactual data at scale. DISCO engineers prompts to generate phrasal perturbations with a large general language model. Then, a task-specific teacher model filters these generations to distill high-quality counterfactual data. While task-agnostic, we apply our pipeline to the task of natural language inference (NLI) and find that on challenging evaluations such as the NLI stress test, comparatively smaller student models trained with DISCO generated counterfactuals are more robust (6% absolute) and generalize better across distributions (2%) compared to models trained without data augmentation. Furthermore, DISCO augmented models are 10% more consistent between counterfactual pairs on three evaluation sets, demonstrating that DISCO augmentation enables models to more reliably learn causal representations. Our repository is available at: https://github.com/eric11eca/disco, ACL 2023 camera ready, final title change

Can we teach natural language understanding models to track their beliefs through intermediate points in text? We propose a representation learning framework called breakpoint modeling that allows for learning of this type. Given any text encoder and data marked with intermediate states (breakpoints) along with corresponding textual queries viewed as true/false propositions (i.e., the candidate beliefs of a model, consisting of information changing through time) our approach trains models in an efficient and end-to-end fashion to build intermediate representations that facilitate teaching and direct querying of beliefs at arbitrary points alongside solving other end tasks. To show the benefit of our approach, we experiment with a diverse set of NLU tasks including relational reasoning on CLUTRR and narrative understanding on bAbI. Using novel belief prediction tasks for both tasks, we show the benefit of our main breakpoint transformer, based on T5, over conventional representation learning approaches in terms of processing efficiency, prediction accuracy and prediction consistency, all with minimal to no effect on corresponding QA end tasks. To show the feasibility of incorporating our belief tracker into more complex reasoning pipelines, we also obtain SOTA performance on the three-tiered reasoning challenge for the TRIP benchmark (around 23-32% absolute improvement on Tasks 2-3)., EMNLP 2022

Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified mathematical reasoning benchmark consisting of 23 diverse tasks along four dimensions: (i) mathematical abilities e.g., arithmetic, calculus (ii) language format e.g., question-answering, fill-in-the-blanks (iii) language diversity e.g., no language, simple language (iv) external knowledge e.g., commonsense, physics. We construct our benchmark by extending 20 datasets benchmark by collecting task instructions and solutions in the form of Python programs, thereby obtaining explainable solutions in addition to the correct answer. We additionally introduce two evaluation datasets to measure out-of-distribution performance and robustness to language perturbation. Finally, we introduce BHASKARA, a general-purpose mathematical reasoning model trained on LILA. Importantly, we find that multi-tasking leads to significant improvements (average relative improvement of 21.83% F1 score vs. single-task models), while the best performing model only obtains 60.40%, indicating the room for improvement in general mathematical reasoning and understanding., EMNLP 2022

One way to interpret the reasoning power of transformer-based language models is to describe the types of logical rules they can resolve over some input text. Recently, Chiang et al. (2023) showed that finite-precision transformers can be equivalently expressed in a generalization of first-order logic. However, finite-precision transformers are a weak transformer variant because, as we show, a single head can only attend to a constant number of tokens and, in particular, cannot represent uniform attention. Since attending broadly is a core capability for transformers, we ask whether a minimally more expressive model that can attend universally can also be characterized in logic. To this end, we analyze transformers whose forward pass is computed in $\log n$ precision on contexts of length $n$. We prove that any log-precision transformer can be equivalently expressed as a first-order logic sentence that, in addition to standard universal and existential quantifiers, may also contain majority-vote quantifiers. This is the tightest known upper bound and first logical characterization of log-precision transformers., May 24, 2023: Restructured version of old preprint

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting., 27 pages, 17 figures + references and appendices, repo: https://github.com/google/BIG-bench

Despite their omnipresence in modern NLP, characterizing the computational power of transformer neural nets remains an interesting open question. We prove that transformers whose arithmetic precision is logarithmic in the number of input tokens (and whose feedforward nets are computable using space linear in their input) can be simulated by constant-depth logspace-uniform threshold circuits. This provides insight on the power of transformers using known results in complexity theory. For example, if $\mathsf L \neq \mathsf P$ (i.e., not all poly-time problems can be solved using logarithmic space), then transformers cannot even accurately solve linear equalities or check membership in an arbitrary context-free grammar with empty productions. Our result intuitively emerges from the transformer architecture's high parallelizability. We thus speculatively introduce the idea of a fundamental parallelism tradeoff: any model architecture as parallelizable as the transformer will obey limitations similar to it. Since parallelism is key to training models at massive scale, this suggests a potential inherent weakness of the scaling paradigm., Comment: Accepted at TACL. Formerly entitled "Log-Precision Transformers are Constant-Depth Threshold Circuits". Updated with minor corrections in Section 2 (Implications) on March 6, 2023. Update with minor edits to the proof of Lemma 3 on April 26, 2023

Fine-tuning continuous prompts for target tasks has recently emerged as a compact alternative to full model fine-tuning. Motivated by these promising results, we investigate the feasibility of extracting a discrete (textual) interpretation of continuous prompts that is faithful to the problem they solve. In practice, we observe a "wayward" behavior between the task solved by continuous prompts and their nearest neighbor discrete projections: We can find continuous prompts that solve a task while being projected to an arbitrary text (e.g., definition of a different or even a contradictory task), while being within a very small (2%) margin of the best continuous prompt of the same size for the task. We provide intuitions behind this odd and surprising behavior, as well as extensive empirical analyses quantifying the effect of various parameters. For instance, for larger model sizes we observe higher waywardness, i.e, we can find prompts that more closely map to any arbitrary text with a smaller drop in accuracy. These findings have important implications relating to the difficulty of faithfully interpreting continuous prompts and their generalization across models and tasks, providing guidance for future progress in prompting language models., Comment: NAACL 2022

Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves are hard to learn, especially when embedded in more complex tasks. To address this, we propose Decomposed Prompting, a new approach to solve complex tasks by decomposing them (via prompting) into simpler sub-tasks that can be delegated to a library of prompting-based LLMs dedicated to these sub-tasks. This modular structure allows each prompt to be optimized for its specific sub-task, further decomposed if necessary, and even easily replaced with more effective prompts, trained models, or symbolic functions if desired. We show that the flexibility and modularity of Decomposed Prompting allows it to outperform prior work on few-shot prompting using GPT3. On symbolic reasoning tasks, we can further decompose sub-tasks that are hard for LLMs into even simpler solvable sub-tasks. When the complexity comes from the input length, we can recursively decompose the task into the same task but with smaller inputs. We also evaluate our approach on textual multi-step reasoning tasks: on long-context multi-hop QA task, we can more effectively teach the sub-tasks via our separate sub-tasks prompts; and on open-domain multi-hop QA, we can incorporate a symbolic information retrieval within our decomposition framework, leading to improved performance on both tasks. Datasets, Code and Prompts available at https://github.com/allenai/DecomP., Comment: ICLR'23 Camera Ready

Prompting-based large language models (LLMs) are surprisingly powerful at generating natural language reasoning steps or Chains-of-Thoughts (CoT) for multi-step question answering (QA). They struggle, however, when the necessary knowledge is either unavailable to the LLM or not up-to-date within its parameters. While using the question to retrieve relevant text from an external knowledge source helps LLMs, we observe that this one-step retrieve-and-read approach is insufficient for multi-step QA. Here, \textit{what to retrieve} depends on \textit{what has already been derived}, which in turn may depend on \textit{what was previously retrieved}. To address this, we propose IRCoT, a new approach for multi-step QA that interleaves retrieval with steps (sentences) in a CoT, guiding the retrieval with CoT and in turn using retrieved results to improve CoT. Using IRCoT with GPT3 substantially improves retrieval (up to 21 points) as well as downstream QA (up to 15 points) on four datasets: HotpotQA, 2WikiMultihopQA, MuSiQue, and IIRC. We observe similar substantial gains in out-of-distribution (OOD) settings as well as with much smaller models such as Flan-T5-large without additional training. IRCoT reduces model hallucination, resulting in factually more accurate CoT reasoning. Code, data, and prompts are available at \url{https://github.com/stonybrooknlp/ircot}, Comment: ACL'23 Camera Ready

Considerable progress has been made recently in open-domain question answering (QA) problems, which require Information Retrieval (IR) and Reading Comprehension (RC). A popular approach to improve the system's performance is to improve the quality of the retrieved context from the IR stage. In this work we show that for StrategyQA, a challenging open-domain QA dataset that requires multi-hop reasoning, this common approach is surprisingly ineffective -- improving the quality of the retrieved context hardly improves the system's performance. We further analyze the system's behavior to identify potential reasons., Comment: 10 pages

The instruction learning paradigm -- where a model learns to perform new tasks from task descriptions alone -- has become popular in general-purpose model research. The capabilities of large transformer models as instruction learners, however, remain poorly understood. We use a controlled synthetic environment to characterize such capabilities. Specifically, we use the task of deciding whether a given string matches a regular expression (viewed as an instruction) to identify properties of tasks, instructions, and instances that make instruction learning challenging. For instance, we find that our model, a fine-tuned T5-based text2text transformer, struggles with large regular languages, suggesting that less precise instructions are challenging for models. Additionally, instruction executions that require tracking longer contexts of prior steps are also more difficult. We use our findings to systematically construct a challenging instruction learning dataset, which we call Hard RegSet. Fine-tuning on Hard RegSet, our large transformer learns to correctly interpret only 65.6% of test instructions (with at least 90% accuracy), and 11%-24% of the instructions in out-of-distribution generalization settings. We propose Hard RegSet as a challenging instruction learning task, and a controlled environment for studying instruction learning., Comment: Typos corrected, rewordings

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift., Comment: Preprint

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms., Accepted to AAAI-2022, AAAI preprint

Transformers have become a standard neural network architecture for many NLP problems, motivating theoretical analysis of their power in terms of formal languages. Recent work has shown that transformers with hard attention are quite limited in power (Hahn, 2020), as they can be simulated by constant-depth AND/OR circuits (Hao et al. 2021). However, hard attention is a strong assumption, which may complicate the relevance of these results in practice. In this work, we analyze the circuit complexity of transformers with saturated attention: a generalization of hard attention that more closely captures the attention patterns learnable in practical transformers. We first show that saturated transformers transcend the known limitations of hard-attention transformers. We then prove saturated transformers with floating-point values can be simulated by constant-depth threshold circuits, giving the class $\mathsf{TC}^0$ as an upper bound on the formal languages they recognize., To appear in TACL

While day-to-day questions come with a variety of answer types, the current question-answering (QA) literature has failed to adequately address the answer diversity of questions. To this end, we present GooAQ, a large-scale dataset with a variety of answer types. This dataset contains over 5 million questions and 3 million answers collected from Google. GooAQ questions are collected semi-automatically from the Google search engine using its autocomplete feature. This results in naturalistic questions of practical interest that are nonetheless short and expressed using simple language. GooAQ answers are mined from Google's responses to our collected questions, specifically from the answer boxes in the search results. This yields a rich space of answer types, containing both textual answers (short and long) as well as more structured ones such as collections. We benchmarkT5 models on GooAQ and observe that: (a) in line with recent work, LM's strong performance on GooAQ's short-answer questions heavily benefit from annotated data; however, (b) their quality in generating coherent and accurate responses for questions requiring long responses (such as 'how' and 'why' questions) is less reliant on observing annotated data and mainly supported by their pre-training. We release GooAQ to facilitate further research on improving QA with diverse response types., EMNLP-Findings 2021

Large neural models have demonstrated human-level performance on language and vision benchmarks, while their performance degrades considerably on adversarial or out-of-distribution samples. This raises the question of whether these models have learned to solve a dataset rather than the underlying task by overfitting to spurious dataset biases. We investigate one recently proposed approach, AFLite, which adversarially filters such dataset biases, as a means to mitigate the prevalent overestimation of machine performance. We provide a theoretical understanding for AFLite, by situating it in the generalized framework for optimum bias reduction. We present extensive supporting evidence that AFLite is broadly applicable for reduction of measurable dataset biases, and that models trained on the filtered datasets yield better generalization to out-of-distribution tasks. Finally, filtering results in a large drop in model performance (e.g., from 92% to 62% for SNLI), while human performance still remains high. Our work thus shows that such filtered datasets can pose new research challenges for robust generalization by serving as upgraded benchmarks., Comment: Accepted to ICML 2020

Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap, we introduce belief propagation neural networks (BPNNs), a class of parameterized operators that operate on factor graphs and generalize Belief Propagation (BP). In its strictest form, a BPNN layer (BPNN-D) is a learned iterative operator that provably maintains many of the desirable properties of BP for any choice of the parameters. Empirically, we show that by training BPNN-D learns to perform the task better than the original BP: it converges 1.7x faster on Ising models while providing tighter bounds. On challenging model counting problems, BPNNs compute estimates 100's of times faster than state-of-the-art handcrafted methods, while returning an estimate of comparable quality.

Computing the permanent of a non-negative matrix is a core problem with practical applications ranging from target tracking to statistical thermodynamics. However, this problem is also #P-complete, which leaves little hope for finding an exact solution that can be computed efficiently. While the problem admits a fully polynomial randomized approximation scheme, this method has seen little use because it is both inefficient in practice and difficult to implement. We present AdaPart, a simple and efficient method for drawing exact samples from an unnormalized distribution. Using AdaPart, we show how to construct tight bounds on the permanent which hold with high probability, with guaranteed polynomial runtime for dense matrices. We find that AdaPart can provide empirical speedups exceeding 25x over prior sampling methods on matrices that are challenging for variational based approaches. Finally, in the context of multi-target tracking, exact sampling from the distribution defined by the matrix permanent allows us to use the optimal proposal distribution during particle filtering. Using AdaPart, we show that this leads to improved tracking performance using an order of magnitude fewer samples., 19 pages

Discrete integration in a high dimensional space of n variables poses fundamental challenges. The WISH algorithm reduces the intractable discrete integration problem into n optimization queries subject to randomized constraints, obtaining a constant approximation guarantee. The optimization queries are expensive, which limits the applicability of WISH. We propose AdaWISH, which is able to obtain the same guarantee but accesses only a small subset of queries of WISH. For example, when the number of function values is bounded by a constant, AdaWISH issues only O(log n) queries. The key idea is to query adaptively, taking advantage of the shape of the weight function being integrated. In general, we prove that AdaWISH has a regret of only O(log n) relative to an idealistic oracle that issues queries at data-dependent optimal points. Experimentally, AdaWISH gives precise estimates for discrete integration problems, of the same quality as that of WISH and better than several competing approaches, on a variety of probabilistic inference benchmarks. At the same time, it saves substantially on the number of optimization queries compared to WISH. On a suite of UAI inference challenge benchmarks, it saves 81.5% of WISH queries while retaining the quality of results.

Multi-hop textual question answering requires combining information from multiple sentences. We focus on a natural setting where, unlike typical reading comprehension, only partial information is provided with each question. The model must retrieve and use additional knowledge to correctly answer the question. To tackle this challenge, we develop a novel approach that explicitly identifies the knowledge gap between a key span in the provided knowledge and the answer choices. The model, GapQA, learns to fill this gap by determining the relationship between the span and an answer choice, based on retrieved knowledge targeting this gap. We propose jointly training a model to simultaneously fill this knowledge gap and compose it with the provided partial knowledge. On the OpenBookQA dataset, given partial knowledge, explicitly identifying what's missing substantially outperforms previous approaches., Comment: EMNLP 2019

Systems for language understanding have become remarkably strong at overcoming linguistic imperfections in tasks involving phrase matching or simple reasoning. Yet, their accuracy drops dramatically as the number of reasoning steps increases. We present the first formal framework to study such empirical observations. It allows one to quantify the amount and effect of ambiguity, redundancy, incompleteness, and inaccuracy that the use of language introduces when representing a hidden conceptual space. The idea is to consider two interrelated spaces: a conceptual meaning space that is unambiguous and complete but hidden, and a linguistic space that captures a noisy grounding of the meaning space in the words of a language---the level at which all systems, whether neural or symbolic, operate. Applying this framework to a special class of multi-hop reasoning, namely the connectivity problem in graphs of relationships between concepts, we derive rigorous intuitions and impossibility results even under this simplified setting. For instance, if a query requires a moderately large (logarithmic) number of hops in the meaning graph, no reasoning system operating over a noisy graph grounded in language is likely to correctly answer it. This highlights a fundamental barrier that extends to a broader class of reasoning problems and systems, and suggests an alternative path forward: focusing on aligning the two spaces via richer representations, before investing in reasoning with many hops.

We present a new question set, text corpus, and baselines assembled to encourage AI research in advanced question answering. Together, these constitute the AI2 Reasoning Challenge (ARC), which requires far more powerful knowledge and reasoning than previous challenges such as SQuAD or SNLI. The ARC question set is partitioned into a Challenge Set and an Easy Set, where the Challenge Set contains only questions answered incorrectly by both a retrieval-based algorithm and a word co-occurence algorithm. The dataset contains only natural, grade-school science questions (authored for human tests), and is the largest public-domain set of this kind (7,787 questions). We test several baselines on the Challenge Set, including leading neural models from the SQuAD and SNLI tasks, and find that none are able to significantly outperform a random baseline, reflecting the difficult nature of this task. We are also releasing the ARC Corpus, a corpus of 14M science sentences relevant to the task, and implementations of the three neural baseline models tested. Can your model perform better? We pose ARC as a challenge to the community., 10 pages, 7 tables, 2 figures

Answering science questions posed in natural language is an important AI challenge. Answering such questions often requires non-trivial inference and knowledge that goes beyond factoid retrieval. Yet, most systems for this task are based on relatively shallow Information Retrieval (IR) and statistical correlation techniques operating on large unstructured corpora. We propose a structured inference system for this task, formulated as an Integer Linear Program (ILP), that answers natural language questions using a semi-structured knowledge base derived from text, including questions requiring multi-step inference and a combination of multiple facts. On a dataset of real, unseen science questions, our system significantly outperforms (+14%) the best previous attempt at structured reasoning for this task, which used Markov Logic Networks (MLNs). It also improves upon a previous ILP formulation by 17.7%. When combined with unstructured inference methods, the ILP system significantly boosts overall performance (+10%). Finally, we show our approach is substantially more robust to a simple answer perturbation compared to statistical correlation methods., Extended version of the paper accepted to IJCAI'16

Our goal is to answer elementary-level science questions using knowledge extracted automatically from science textbooks, expressed in a subset of first-order logic. Given the incomplete and noisy nature of these automatically extracted rules, Markov Logic Networks (MLNs) seem a natural model to use, but the exact way of leveraging MLNs is by no means obvious. We investigate three ways of applying MLNs to our task. In the first, we simply use the extracted science rules directly as MLN clauses. Unlike typical MLN applications, our domain has long and complex rules, leading to an unmanageable number of groundings. We exploit the structure present in hard constraints to improve tractability, but the formulation remains ineffective. In the second approach, we instead interpret science rules as describing prototypical entities, thus mapping rules directly to grounded MLN assertions, whose constants are then clustered using existing entity resolution methods. This drastically simplifies the network, but still suffers from brittleness. Finally, our third approach, called Praline, uses MLNs to align the lexical elements as well as define and control how inference should be performed in this task. Our experiments, demonstrating a 15\% accuracy boost and a 10x reduction in runtime, suggest that the flexibility and different inference semantics of Praline are a better fit for the natural language question answering task., Comment: 7 pages, 1 figure, StarAI workshop at UAI'15

Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly generated parity constraints. By exploiting a connection with max-likelihood decoding of binary codes, we show that these optimizations are computationally hard. Inspired by iterative message passing decoding algorithms, we propose an Integer Linear Programming (ILP) formulation for the problem, enhanced with new sparsification techniques to improve decoding performance. By solving the ILP through a sequence of LP relaxations, we get both lower and upper bounds on the partition function, which hold with high probability and are much tighter than those obtained with variational methods., Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013)

Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a general discrete integral defined over an exponentially large set. This algorithm relies on solving only a small number of instances of a discrete combinatorial optimization problem subject to randomly generated parity constraints used as a hash function. As an application, we demonstrate that with a small number of MAP queries we can efficiently approximate the partition function of discrete graphical models, which can in turn be used, for instance, for marginal computation or model selection.

Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding the success of SP, it was recently shown that SP can be viewed as a form of belief propagation, computing marginal probabilities over certain objects called covers of a formula. This explanation was, however, shortly dismissed by experiments suggesting that non-trivial covers simply do not exist for large formulas. In this paper, we show that these experiments were misleading: not only do covers exist for large hard random formulas, SP is surprisingly accurate at computing marginals over these covers despite the existence of many cycles in the formulas. This re-opens a potentially simpler line of reasoning for understanding SP, in contrast to some alternative lines of explanation that have been proposed assuming covers do not exist., Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007)

UCT has recently emerged as an exciting new adversarial reasoning technique based on cleverly balancing exploration and exploitation in a Monte-Carlo sampling setting. It has been particularly successful in the game of Go but the reasons for its success are not well understood and attempts to replicate its success in other domains such as Chess have failed. We provide an in-depth analysis of the potential of UCT in domain-independent settings, in cases where heuristic values are available, and the effect of enhancing random playouts to more informed playouts between two weak minimax players. To provide further insights, we develop synthetic game tree instances and discuss interesting properties of UCT, both empirically and analytically., Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010)