Abstract Automated agents, powered by large language models (LLMs), are emerging as the go-to tool for querying information. However, evaluation benchmarks for LLM agents rarely feature natural questions that are both information-seeking and genuinely time-consuming for humans. To address this gap we introduce MoNaCo, a benchmark of 1,315 natural and time-consuming questions that require dozens, and at times hundreds, of intermediate steps to solve— far more than any existing QA benchmark. To build MoNaCo, we developed a decomposed annotation pipeline to elicit and manually answer real-world time-consuming questions at scale. Frontier LLMs evaluated on MoNaCo achieve at most 61.2% F1, hampered by low recall and hallucinations. Our results underscore the limitations of LLM-powered agents in handling the complexity and sheer breadth of real-world information-seeking tasks—with MoNaCo providing an effective resource for tracking such progress. The MoNaCo benchmark, codebase, prompts, and models predictions are all publicly available at: https://tomerwolgithub.github.io/monaco.

Can the rapid advances in code generation, function calling, and data analysis using large language models (LLMs) help automate the search and verification of hypotheses purely from a set of provided datasets? To evaluate this question, we present DiscoveryBench, the first comprehensive benchmark that formalizes the multi-step process of data-driven discovery. The benchmark is designed to systematically assess current model capabilities in discovery tasks and provide a useful resource for improving them. Our benchmark contains 264 tasks collected across 6 diverse domains, such as sociology and engineering, by manually deriving discovery workflows from published papers to approximate the real-world challenges faced by researchers, where each task is defined by a dataset, its metadata, and a discovery goal in natural language. We additionally provide 903 synthetic tasks to conduct controlled evaluations on data-driven workflows that are not covered in the manually collected split. Furthermore, our structured formalism of data-driven discovery enables a facet-based evaluation that provides useful insights into different failure modes. We evaluate several popular LLM-based reasoning frameworks using both open and closed LLMs as baselines on DiscoveryBench and find that even the best system scores only 25%. Our benchmark, thus, illustrates the challenges in autonomous data-driven discovery and serves as a valuable resource for the community to make progress.

Multiple-choice question answering (MCQA) is a key competence of performant transformer language models that is tested by mainstream benchmarks. However, recent evidence shows that models can have quite a range of performance, particularly when the task format is diversified slightly (such as by shuffling answer choice order). In this work we ask: how do successful models perform formatted MCQA? We employ vocabulary projection and activation patching methods to localize key hidden states that encode relevant information for predicting the correct answer. We find that prediction of a specific answer symbol is causally attributed to a few middle layers, and specifically their multi-head self-attention mechanisms. We show that subsequent layers increase the probability of the predicted answer symbol in vocabulary space, and that this probability increase is associated with a sparse set of attention heads with unique roles. We additionally uncover differences in how different models adjust to alternative symbols. Finally, we demonstrate that a synthetic task can disentangle sources of model error to pinpoint when a model has learned formatted MCQA, and show that logit differences between answer choice tokens continue to grow over the course of training.

Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss, understanding the differences between these recent proposals, as well as developing new DPA loss functions, remains difficult given the lack of a technical and conceptual framework for reasoning about the underlying semantics of these algorithms. In this paper, we attempt to remedy this by formalizing DPA losses in terms of discrete reasoning problems. Specifically, we ask: Given an existing DPA loss, can we systematically derive a symbolic program that characterizes its semantics? We propose a novel formalism for characterizing preference losses for single model and reference model based approaches, and identify symbolic forms for a number of commonly used DPA variants. Further, we show how this formal view of preference learning sheds new light on both the size and structure of the DPA loss landscape, making it possible to not only rigorously characterize the relationships between recent loss proposals but also to systematically explore the landscape and derive new loss functions from first principles. We hope our framework and findings will help provide useful guidance to those working on human AI alignment.

We investigate the logical reasoning capabilities of Large Language Models (LLMs) and their scalability across complex deductive tasks. Using ZebraLogic, a newly developed benchmark dataset of logic grid puzzles derived from constraint satisfaction problems (CSPs), we systematically evaluate LLM performance. ZebraLogic spans a broad range of search space complexities and incorporates diverse logical constraints, providing a controlled environment to assess reasoning abilities. Our results reveal a significant decline in accuracy as problem complexity increases—a phenomenon we term the “curse of complexity.” Notably, this limitation persists even with scaling model size and inference-time computation, suggesting fundamental constraints in current LLM reasoning capabilities. Additionally, we explore strategies such as Best-of-N sampling, backtracking mechanisms, and self-verification prompts to enhance logical reasoning performance. Our findings provide critical insights into the scaling behavior of LLMs, highlight their limitations, and outline potential directions for advancing their reasoning capabilities.

The promise of autonomous scientific discovery (ASD) hinges not only on answering questions, but also on knowing which questions to ask. Most recent works in ASD explore the use of large language models (LLMs) in goal-driven settings, relying on human-specified research questions to guide hypothesis generation. However, scientific discovery may be accelerated further by allowing the AI system to drive exploration by its own criteria. The few existing approaches in open-ended ASD select hypotheses based on diversity heuristics or subjective proxies for human interestingness, but the former struggles to meaningfully navigate the typically vast hypothesis space, and the latter suffers from imprecise definitions. This paper presents AutoDiscovery—a method for open-ended ASD that instead drives scientific exploration using Bayesian surprise. Here, we quantify the epistemic shift from the LLM’s prior beliefs about a hypothesis to its posterior beliefs after gathering experimental results. To efficiently explore the space of nested hypotheses, our method employs a Monte Carlo tree search (MCTS) strategy with progressive widening using surprisal as the reward function. We evaluate AutoDiscovery in the setting of data-driven discovery across 21 real-world datasets spanning domains such as biology, economics, finance, and behavioral science. Our results demonstrate that under a fixed budget, AutoDiscovery substantially outperforms competitors by producing 5-29% more discoveries deemed surprising by the LLM. Our human evaluation further reveals that two-thirds of discoveries made by our system are surprising to domain experts as well, suggesting this is an important step towards building open-ended ASD systems.

Recent theoretical results show transformers cannot express sequential reasoning problems over long inputs, intuitively because their computational *depth* is bounded. However, prior work treats the depth as a constant, leaving it unclear to what degree bounded depth may suffice for solving problems over short inputs, or how increasing the transformer's depth affects its expressive power. We address these questions by analyzing transformers whose depth can grow minimally with context length $n$. We show even highly uniform transformers with depth $\Theta(\log n)$ can express two important problems: *recognizing regular languages*, which captures state tracking abilities and was known to be expressible only by an unconventional, non-uniform model of transformers, and *graph connectivity*, which underlies multi-step reasoning. Notably, both of these problems cannot be expressed by fixed-depth transformers under standard complexity conjectures, demonstrating the expressivity benefit of growing depth. Moreover, our theory quantitatively predicts how depth must grow with input length to express these problems, showing that depth scaling is more efficient than scaling width or chain-of-thought steps. Empirically, our detailed experiments designed to bridge the expressivity vs. learnability gap reveal that our theoretical depth requirements for regular language recognition closely match the practical depth requirements for successfully training transformers. Thus, our results clarify how depth affects a transformer's reasoning capabilities, and provide practical guidance for effective depth selection for sequential reasoning.

Chain of thought is a natural inference-time method for increasing the computational power of transformer-based large language models (LLMs), but comes at the cost of sequential decoding. Are there more efficient alternatives to expand a transformer's expressive power without adding parameters? We consider transformers with *padding* tokens as a form of parallelizable test-time compute. We show that averaging-hard-attention, masked-pre-norm transformers with polynomial padding recognize precisely the class $\mathsf{FO}$-uniform $\mathsf{TC}^0$ of extremely parallelizable problems. While the $\mathsf{TC}^0$ upper bound was known, proving a matching lower bound had been elusive. Further, our novel analysis reveals the precise expanded power of padded transformers when coupled with another form of inference-time compute, namely dynamically increasing depth via *looping*. Our core technical contribution is to show how padding helps bring the notions of *complete problems* and *reductions*, which have been a cornerstone of classical complexity theory, to the formal study of transformers. Armed with this new tool, we prove that padded transformers with $\mathrm{O}(\log^d n)$ looping on inputs of length $n$ recognize exactly the class $\mathsf{FO}$-uniform $\mathsf{TC}^d$ of moderately parallelizable problems. Thus, padding and looping together systematically expand transformers' expressive power: with polylogarithmic looping, polynomially padded transformers recognize precisely the class $\mathsf{FO}$-uniform $\mathsf{NC}$, the best that could be expected without losing parallelism (unless $\mathsf{NC} = \mathsf{P}$). Our results thus motivate further exploration of padding and looping as parallelizable alternatives to chain of thought for test-time compute.

Abstract We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of (total functional) transductions. We do so using variants of RASP, a programming language designed to help people “think like transformers,” as an intermediate representation. We extend the existing Boolean variant B-RASP to sequence-to-sequence transductions and show that it computes exactly the first-order rational transductions (such as string rotation). Then, we introduce two new extensions. B-RASP[pos] enables calculations on positions (such as copying the first half of a string) and contains all first-order regular transductions. S-RASP adds prefix sum, which enables additional arithmetic operations (such as squaring a string) and contains all first-order polyregular transductions. Finally, we show that masked average-hard attention transformers can simulate S-RASP.

Harsh Trivedi, Tushar Khot, Mareike Hartmann, Ruskin Manku, Vinty Dong, Edward Li, Shashank Gupta, Ashish Sabharwal, Niranjan Balasubramanian. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2024.

Ben Bogin, Kejuan Yang, Shashank Gupta, Kyle Richardson, Erin Bransom, Peter Clark, Ashish Sabharwal, Tushar Khot. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. 2024.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

Recent works have showcased the ability of large-scale language models (LLMs) to embody diverse personas in their responses, exemplified by prompts like ‘_You are Yoda. Explain the Theory of Relativity._’ While this ability allows personalization of LLMs and enables human behavior simulation, its effect on LLMs’ capabilities remains unclear. To fill this gap, we present the first extensive study of the unintended side-effects of persona assignment on the ability of LLMs to perform _basic reasoning tasks_. Our study covers 24 reasoning datasets (spanning mathematics, law, medicine, morals, and more), 4 LLMs (2 versions of ChatGPT-3.5, GPT-4-Turbo, and Llama-2-70b-chat), and 19 diverse personas (e.g., ‘an Asian person’) spanning 5 socio-demographic groups: race, gender, religion, disability, and political affiliation. Our experiments unveil that LLMs harbor deep rooted bias against various socio-demographics underneath a veneer of fairness. While they overtly reject stereotypes when explicitly asked (‘_Are Black people less skilled at mathematics?_’), they manifest stereotypical and often erroneous presumptions when prompted to answer questions while adopting a persona. These can be observed as abstentions in the model’s response, e.g., ‘_As a Black person, I am unable to answer this question as it requires math knowledge_’, and generally result in a substantial drop in performance on reasoning tasks. Our experiments with ChatGPT-3.5 show that this bias is _ubiquitous_—80% of our personas demonstrate bias; it is _significant_—some datasets show performance drops of 70%+; and can be especially _harmful for certain groups_—some personas suffer statistically significant drops on 80%+ of the datasets. Overall, all four LLMs exhibit persona-induced bias to varying extents, with GPT-4-Turbo showing the least but still a problematic amount of bias (evident in 42% of the personas). Further analysis shows that these persona-induced errors can be hard-to-discern as they do not always manifest as explicit abstentions, and can also be hard-to-avoid—we find de-biasing prompts to have minimal to no effect. Our findings serve as a cautionary tale that the practice of assigning personas to LLMs—a trend on the rise—can surface their deep-rooted biases and have unforeseeable and detrimental side-effects.

Recent theoretical work has identified surprisingly simple reasoning problems, such as checking if two nodes in a graph are connected or simulating finite-state machines, that are provably unsolvable by standard transformers that answer immediately after reading their input. However, in practice, transformers' reasoning can be improved by allowing them to use a "chain of thought" or "scratchpad", i.e., generate and condition on a sequence of intermediate tokens before answering. Motivated by this, we ask: *Does such intermediate generation fundamentally extend the computational power of a decoder-only transformer?* We show that the answer is *yes*, but the amount of increase depends crucially on the amount of intermediate generation. For instance, we find that transformer decoders with a logarithmic number of decoding steps (w.r.t. the input length) push the limits of standard transformers only slightly, while a linear number of decoding steps, assuming projected pre-norm (a slight generalization of standard pre-norm), adds a clear new ability (under standard complexity conjectures): recognizing all regular languages. Our results also imply that linear steps keep transformer decoders within context-sensitive languages, and polynomial steps with generalized pre-norm make them recognize exactly the class of polynomial-time solvable problems—the first exact characterization of a type of transformers in terms of standard complexity classes. Together, this provides a nuanced framework for understanding how the length of a transformer’s chain of thought or scratchpad impacts its reasoning power.

With the accumulation of data at an unprecedented rate, its potential to fuel scientific discovery is growing exponentially. This position paper urges the Machine Learning (ML) community to exploit the capabilities of large generative models (LGMs) to develop automated systems for end-to-end data-driven discovery—a paradigm encompassing the search and verification of hypotheses purely from a set of provided datasets, without the need for additional data collection or physical experiments. We first outline several desiderata for an ideal data-driven discovery system. Then, through DataVoyager, a proof-of-concept utilizing GPT-4, we demonstrate how LGMs fulfill several of these desiderata—a feat previously unattainable—while also highlighting important limitations in the current system that open up opportunities for novel ML research. We contend that achieving accurate, reliable, and robust end-to-end discovery systems solely through the current capabilities of LGMs is challenging. We instead advocate for fail-proof tool integration, along with active user moderation through feedback mechanisms, to foster data-driven scientific discoveries with efficiency and reproducibility.

State-space models (SSMs) have emerged as a potential alternative architecture for building large language models (LLMs) compared to the previously ubiquitous transformer architecture. One theoretical weakness of transformers is that they cannot express certain kinds of sequential computation and state tracking (Merrill & Sabharwal, 2023), which SSMs are explicitly designed to address via their close architectural similarity to recurrent neural networks (RNNs). *But do SSMs truly have an advantage (over transformers) in expressive power for state tracking?* Surprisingly, the answer is no. Our analysis reveals that the expressive power of SSMs is limited very similarly to transformers: SSMs cannot express computation outside the complexity class $\mathsf{TC}^0$. In particular, this means they cannot solve simple state-tracking problems like permutation composition. It follows that SSMs are provably unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. To supplement our formal analysis, we report experiments showing that Mamba-style SSMs indeed struggle with state tracking. Thus, despite its recurrent formulation, the "state'' in an SSM is an illusion: SSMs have similar expressiveness limitations to non-recurrent models like transformers, which may fundamentally limit their ability to solve real-world state-tracking problems.

Ben Bogin, Shivanshu Gupta, Peter Clark, Ashish Sabharwal. Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2024.

Vishvak Murahari, Ameet Deshpande, Peter Clark, Tanmay Rajpurohit, Ashish Sabharwal, Karthik Narasimhan, Ashwin Kalyan. Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2024.

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 highquality 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 DISCOgenerated counterfactuals are more robust (6% absolute) and generalize better across distributions (2%) compared to models trained without data augmentation.Furthermore, DISCOaugmented 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

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, what to retrieve depends on what has already been derived, which in turn may depend on 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-ofdistribution (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.1 .erdotii Nostri Primordia died?

Although counterfactual reasoning is a fundamental aspect of intelligence, the lack of largescale counterfactual open-domain questionanswering (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.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 3,800 questions that were 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 (F1 score 44.5), as well as recent few-shot approaches such as chain-of-thought prompting with ChatGPT (F1 score 57.2).We hope the unique challenges posed by IfQA will push open-domain QA research on both retrieval and reasoning fronts, while also helping endow counterfactual reasoning abilities to today's language understanding models.The IfQA dataset can be found and downloaded at https://allenai.org/data/ifqa.

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs".This lack of interpretability is a growing impediment to widespread use of LLMs.To address this, our goals are to make model beliefs and their inferential relationships explicit, and to resolve inconsistencies that may exist, so that answers are supported by interpretable 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 their inferential relationships.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 can provide an interpretable window into system beliefs, add a systematic reasoning capability, and repair latent inconsistencies present in the LLM.

When pretrained language models (LMs) are applied to discriminative tasks such as multiplechoice questions, they place probability mass on vocabulary tokens that aren't among the given answer choices.Spreading probability mass across multiple surface forms with identical meaning (such as "bath" and "bathtub") 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? Are there direct ways of reducing it, and does doing so improve task performance?We propose a mathematical formalism for SFC which allows us to quantify and bound its impact for the first time.We identify a simple method for reducing it-namely, increasing probability mass on the given answer choices by a) including them in the prompt and b) using in-context learning with even just one example.We show this method eliminates the impact of SFC in the majority of instances.Our experiments on three diverse datasets and six LMs reveal several additional surprising findings.For example, both normalization and prompting methods for reducing SFC can be ineffective or even detrimental to task performance for some LMs.We conclude with practical insights for effectively prompting LMs for multiple-choice tasks. 1 * Work done at AI2. 1 Code available at https://github.com/allenai/ revisiting_surface_form_competition.

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. We show that such abilities can, in fact, be distilled down from GPT-3.5 (≥ 175B) to T5 variants (≤ 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 such that they can perform a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we specialize their capacity towards a target task, the model can achieve decent performance improvements. 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) balancing language model’s performance on multiple tasks is a delicate matter, as improvements on one task may compromise other tasks; (2) yet by intentionally paying the price of decreased generic ability, we can clearly improve across different model scales 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 data format mixture and the start model checkpoint. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs.

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 transformer classifiers 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 any log-precision transformer classifier 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.

Abstract 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 L≠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.

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: 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.

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

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 endtasks.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). 1

The instruction learning paradigm-where a model learns to perform new tasks from task descriptions alone-has become popular in research on general-purpose models.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.Instruction executions that require tracking longer contexts of prior steps are also 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 (with at least 90% accuracy) only 65.6% of test instructions, and 11%-24% of the instructions in out-of-distribution generalization settings.We thus propose Hard RegSet as a challenging instruction learning dataset, and a controlled environment for studying instruction learning.1

Swaroop Mishra, Matthew Finlayson, Pan Lu, Leonard Tang, Sean Welleck, Chitta Baral, Tanmay Rajpurohit, Oyvind Tafjord, Ashish Sabharwal, Peter Clark, Ashwin Kalyan. Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing. 2022.

Question-answering datasets require a broad set of reasoning skills.We show how to use question decompositions to teach language models these broad reasoning skills in a robust fashion.Specifically, we use widely available QDMR representations to programmatically create hard-to-cheat synthetic contexts for real questions in six multi-step reasoning datasets.These contexts are carefully designed to avoid common reasoning shortcuts prevalent in real contexts that prevent models from learning the right skills.This results in a pretraining dataset, named TeaBReaC, containing 525K multi-step questions (with associated formal programs) covering about 900 reasoning patterns.We show that pretraining standard language models (LMs) on TeaBReaC before fine-tuning them on target datasets improves their performance by up to 13 F1 points across 4 multi-step QA datasets, with up to 21 point gain on more complex questions.The resulting models also demonstrate higher robustness, with a 5-8 F1 point improvement on two contrast sets.Furthermore, TeaBReaC pretraining substantially improves model performance and robustness even when starting with numerate LMs pretrained using recent methods (e.g., PReasM, POET).Our work thus shows how to effectively use decomposition-guided contexts to robustly teach multi-step reasoning.1

Daniel Khashabi, Xinxi Lyu, Sewon Min, Lianhui Qin, Kyle Richardson, Sean Welleck, Hannaneh Hajishirzi, Tushar Khot, Ashish Sabharwal, Sameer Singh, Yejin Choi. Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2022.

Abstract 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., 2022). 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 TC0 as an upper bound on the formal languages they recognize.

Abstract Multihop reasoning remains an elusive goal as existing multihop benchmarks are known to be largely solvable via shortcuts. Can we create a question answering (QA) dataset that, by construction, requires proper multihop reasoning? To this end, we introduce a bottom–up approach that systematically selects composable pairs of single-hop questions that are connected, that is, where one reasoning step critically relies on information from another. This bottom–up methodology lets us explore a vast space of questions and add stringent filters as well as other mechanisms targeting connected reasoning. It provides fine-grained control over the construction process and the properties of the resulting k-hop questions. We use this methodology to create MuSiQue-Ans, a new multihop QA dataset with 25K 2–4 hop questions. Relative to existing datasets, MuSiQue-Ans is more difficult overall (3× increase in human–machine gap), and harder to cheat via disconnected reasoning (e.g., a single-hop model has a 30-point drop in F1). We further add unanswerable contrast questions to produce a more stringent dataset, MuSiQue-Full. We hope our datasets will help the NLP community develop models that perform genuine multihop reasoning.1

Shih-Ting Lin, Ashish Sabharwal, Tushar Khot. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

Many real-world problems require the combined application of multiple reasoning abilities-employing suitable abstractions, commonsense knowledge, and creative synthesis of problem-solving strategies.To help advance AI systems towards such capabilities, we propose a new reasoning challenge, namely Fermi Problems (FPs), which are questions whose answers can only be approximately estimated because their precise computation is either impractical or impossible.For example, "How much would the sea level rise if all ice in the world melted?"FPs are commonly used in quizzes and interviews to bring out and evaluate the creative reasoning abilities of humans.To do the same for AI systems, we present two datasets: 1) A collection of 1k real-world FPs sourced from quizzes and olympiads; and 2) a bank of 10k synthetic FPs of intermediate complexity to serve as a sandbox for the harder real-world challenge.In addition to question-answer pairs, the datasets contain detailed solutions in the form of an executable program and supporting facts, helping in supervision and evaluation of intermediate steps.We demonstrate that even extensively fine-tuned large-scale language models perform poorly on these datasets, on average making estimates that are off by two orders of magnitude.Our contribution is thus the crystallization of several unsolved AI problems into a single, new challenge that we hope will spur further advances in building systems that can reason. Solving a Fermi Problem How much would the sea level rise if all the ice melted?Ice on land causes rise in sea levels. Div(a, b)Vol. of ice in the world? million mi²Area of ice?Area of ocean?Thickness of ice? 3 mi Area of Antarctica?Vol. of ice on land?How many Antarcticas fit in the world map?Vol. of ice in Antarctica?Mul(a, b) Ice on land Ice in Antarctica ≈ Area of Antarctica Area of ice in Antarctica

Tushar Khot, Daniel Khashabi, Kyle Richardson, Peter Clark, Ashish Sabharwal. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

Ben Zhou, Kyle Richardson, Qiang Ning, Tushar Khot, Ashish Sabharwal, Dan Roth. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

Composing knowledge from multiple pieces of texts is a key challenge in multi-hop question answering. We present a multi-hop reasoning dataset, Question Answering via Sentence Composition (QASC), that requires retrieving facts from a large corpus and composing them to answer a multiple-choice question. QASC is the first dataset to offer two desirable properties: (a) the facts to be composed are annotated in a large corpus, and (b) the decomposition into these facts is not evident from the question itself. The latter makes retrieval challenging as the system must introduce new concepts or relations in order to discover potential decompositions. Further, the reasoning model must then learn to identify valid compositions of these retrieved facts using common-sense reasoning. To help address these challenges, we provide annotation for supporting facts as well as their composition. Guided by these annotations, we present a two-step approach to mitigate the retrieval challenges. We use other multiple-choice datasets as additional training data to strengthen the reasoning model. Our proposed approach improves over current state-of-the-art language models by 11% (absolute). The reasoning and retrieval problems, however, remain unsolved as this model still lags by 20% behind human performance.

Do state-of-the-art models for language understanding already have, or can they easily learn, abilities such as boolean coordination, quantification, conditionals, comparatives, and monotonicity reasoning (i.e., reasoning about word substitutions in sentential contexts)? While such phenomena are involved in natural language inference (NLI) and go beyond basic linguistic understanding, it is unclear the extent to which they are captured in existing NLI benchmarks and effectively learned by models. To investigate this, we propose the use of semantic fragments—systematically generated datasets that each target a different semantic phenomenon—for probing, and efficiently improving, such capabilities of linguistic models. This approach to creating challenge datasets allows direct control over the semantic diversity and complexity of the targeted linguistic phenomena, and results in a more precise characterization of a model's linguistic behavior. Our experiments, using a library of 8 such semantic fragments, reveal two remarkable findings: (a) State-of-the-art models, including BERT, that are pre-trained on existing NLI benchmark datasets perform poorly on these new fragments, even though the phenomena probed here are central to the NLI task; (b) On the other hand, with only a few minutes of additional fine-tuning—with a carefully selected learning rate and a novel variation of “inoculation”—a BERT-based model can master all of these logic and monotonicity fragments while retaining its performance on established NLI benchmarks.

Empirical research in Natural Language Processing (NLP) has adopted a narrow set of principles for assessing hypotheses, relying mainly on p-value computation, which suffers from several known issues.While alternative proposals have been well-debated and adopted in other fields, they remain rarely discussed or used within the NLP community.We address this gap by contrasting various hypothesis assessment techniques, especially those not commonly used in the field (such as evaluations based on Bayesian inference).Since these statistical techniques differ in the hypotheses they can support, we argue that practitioners should first decide their target hypothesis before choosing an assessment method.This is crucial because common fallacies, misconceptions, and misinterpretation surrounding hypothesis assessment methods often stem from a discrepancy between what one would like to claim versus what the method used actually assesses.Our survey reveals that these issues are omnipresent in the NLP research community.As a step forward, we provide best practices and guidelines tailored towards NLP research, as well as an easy-to-use package called HyBayes for Bayesian assessment of hypotheses, 1 complementing existing tools.

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.

State-of-the-art models for multi-hop question answering typically augment large-scale language models like BERT with additional, intuitively useful capabilities such as named entity recognition, graph-based reasoning, and question decomposition.However, does their strong performance on popular multihop datasets really justify this added design complexity?Our results suggest that the answer may be no, because even our simple pipeline based on BERT, named QUARK, performs surprisingly well.Specifically, on Hot-potQA, QUARK outperforms these models on both question answering and support identification (and achieves performance very close to a RoBERTa model).Our pipeline has three steps: 1) use BERT to identify potentially relevant sentences independently of each other; 2) feed the set of selected sentences as context into a standard BERT span prediction model to choose an answer; and 3) use the sentence selection model, now with the chosen answer, to produce supporting sentences.The strong performance of QUARK resurfaces the importance of carefully exploring simple model designs before using popular benchmarks to justify the value of complex techniques.

Deep learning models for linguistic tasks require large training datasets, which are expensive to create.As an alternative to the traditional approach of creating new instances by repeating the process of creating one instance, we propose doing so by first collecting a set of seed examples and then applying humandriven natural perturbations (as opposed to rule-based machine perturbations), which often change the gold label as well.Such perturbations have the advantage of being relatively easier (and hence cheaper) to create than writing out completely new examples.Further, they help address the issue that even models achieving human-level scores on NLP datasets are known to be considerably sensitive to small changes in input.To evaluate the idea, we consider a recent question-answering dataset (BOOLQ) and study our approach as a function of the perturbation cost ratio, the relative cost of perturbing an existing question vs. creating a new one from scratch.We find that when natural perturbations are moderately cheaper to create (cost ratio under 60%), it is more effective to use them for training BOOLQ models: such models exhibit 9% higher robustness and 4.5% stronger generalization, while retaining performance on the original BOOLQ dataset.

Has there been real progress in multi-hop question-answering?Models often exploit dataset artifacts to produce correct answers, without connecting information across multiple supporting facts.This limits our ability to measure true progress and defeats the purpose of building multi-hop QA datasets.We make three contributions towards addressing this.First, we formalize such undesirable behavior as disconnected reasoning across subsets of supporting facts.This allows developing a model-agnostic probe for measuring how much any model can cheat via disconnected reasoning.Second, using a notion of contrastive support sufficiency, we introduce an automatic transformation of existing datasets that reduces the amount of disconnected reasoning.Third, our experiments 1 suggest that there hasn't been much progress in multifact QA in the reading comprehension setting.For a recent large-scale model (XLNet), we show that only 18 points out of its answer F1 score of 72 on HotpotQA are obtained through multifact reasoning, roughly the same as that of a simpler RNN baseline.Our transformation substantially reduces disconnected reasoning (19 points in answer F1).It is complementary to adversarial approaches, yielding further reductions in conjunction.Original Dataset D ⇒ Question q = (Q, C; A) in D is assumed to be annotated with supporting facts {f 1 , f 2 }.Probing Dataset P ans+supp (D) for Answer Prediction and Support Identification tests: ⇒ Probing question collection P ans+supp (q) has only one group, corresponding to the unique bi-partition {{f 1 }, {f 2 }}, containing:Transformed Dataset T(D) for evaluating Constrastive Support Sufficiency: ⇒ Transformed question group T(q) in T(D) is defined using a single replacement fact f r ∈ C \ {f 1 , f 2 }:Probing Dataset P ans+supp+suff (T(D)) for all three tests: ⇒ Probing question collection P ans+supp+suff (T(q)) for the transformed question T(q) has only one group, corresponding to the unique bi-partition {{f 1 }, {f 2 }}, and is defined as:

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.

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.

Open-domain question answering (QA) involves many knowledge and reasoning challenges, but are successful QA models actually learning such knowledge when trained on benchmark QA tasks? We investigate this via several new diagnostic tasks probing whether multiple-choice QA models know definitions and taxonomic reasoning—two skills widespread in existing benchmarks and fundamental to more complex reasoning. We introduce a methodology for automatically building probe datasets from expert knowledge sources, allowing for systematic control and a comprehensive evaluation. We include ways to carefully control for artifacts that may arise during this process. Our evaluation confirms that transformer-based multiple-choice QA models are already predisposed to recognize certain types of structural linguistic knowledge. However, it also reveals a more nuanced picture: their performance notably degrades even with a slight increase in the number of “hops” in the underlying taxonomic hierarchy, and with more challenging distractor candidates. Further, existing models are far from perfect when assessed at the level of clusters of semantically connected probes, such as all hypernym questions about a single concept.

Many natural la guage questions require recognizing and reasoning with qualitative relationships (e.g., in science, economics, and medicine), but are challenging to answer with corpus-based methods. Qualitative modeling provides tools that support such reasoning, but the semantic parsing task of mapping questions into those models has formidable challenges. We present QUAREL, a dataset of diverse story questions involving qualitative relationships that characterize these challenges, and techniques that begin to address them. The dataset has 2771 questions relating 19 different types of quantities. For example, “Jenny observes that the robot vacuum cleaner moves slower on the living room carpet than on the bedroom carpet. Which carpet has more friction?” We contribute (1) a simple and flexible conceptual framework for representing these kinds of questions; (2) the QUAREL dataset, including logical forms, exemplifying the parsing challenges; and (3) two novel models for this task, built as extensions of type-constrained semantic parsing. The first of these models (called QUASP+) significantly outperforms off-the-shelf tools on QUAREL. The second (QUASP+ZERO) demonstrates zero-shot capability, i.e., the ability to handle new qualitative relationships without requiring additional training data, something not possible with previous models. This work thus makes inroads into answering complex, qualitative questions that require reasoning, and scaling to new relationships at low cost. The dataset and models are available at http://data.allenai.org/quarel.

We propose a novel, path-based reasoning approach for the multi-hop reading comprehension task where a system needs to combine facts from multiple passages to answer a question.Although inspired by multi-hop reasoning over knowledge graphs, our proposed approach operates directly over unstructured text.It generates potential paths through passages and scores them without any direct path supervision.The proposed model, named PathNet, attempts to extract implicit relations from text through entity pair representations, and compose them to encode each path.To capture additional context, Path-Net also composes the passage representations along each path to compute a passage-based representation.Unlike previous approaches, our model is then able to explain its reasoning via these explicit paths through the passages.We show that our approach outperforms prior models on the multi-hop Wikihop dataset, and also can be generalized to apply to the OpenBookQA dataset, matching stateof-the-art performance.

Tushar Khot, Ashish Sabharwal, Peter Clark. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.

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 exact sampling of permutations, each associated with a weight as determined by a matrix. ADAPART uses an adaptive, iterative partitioning strategy over permutations to convert any upper bounding method for the permanent into one that satisfies a desirable `nesting' property over the partition used. These samples are then used to construct tight bounds on the permanent which hold with a high probability. Empirically, ADAPART provides significant speedups (sometimes exceeding 50x) over prior work. We also empirically observe polynomial scaling in some cases. In the context of multi-target tracking, ADAPART allows us to use the optimal proposal distribution during particle filtering, leading to orders of magnitude fewer samples and improved tracking performance.

We propose a novel method for exploiting the semantic structure of text to answer multiple-choice questions. The approach is especially suitable for domains that require reasoning over a diverse set of linguistic constructs but have limited training data. To address these challenges, we present the first system, to the best of our knowledge, that reasons over a wide range of semantic abstractions of the text, which are derived using off-the-shelf, general-purpose, pre-trained natural language modules such as semantic role labelers, coreference resolvers, and dependency parsers. Representing multiple abstractions as a family of graphs, we translate question answering (QA) into a search for an optimal subgraph that satisfies certain global and local properties. This formulation generalizes several prior structured QA systems. Our system, SEMANTICILP, demonstrates strong performance on two domains simultaneously. In particular, on a collection of challenging science QA datasets, it outperforms various state-of-the-art approaches, including neural models, broad coverage information retrieval, and specialized techniques using structured knowledge bases, by 2%-6%.

We present a new dataset and model for textual entailment, derived from treating multiple-choice question-answering as an entailment problem. SciTail is the first entailment set that is created solely from natural sentences that already exist independently ``in the wild'' rather than sentences authored specifically for the entailment task. Different from existing entailment datasets, we create hypotheses from science questions and the corresponding answer candidates, and premises from relevant web sentences retrieved from a large corpus. These sentences are often linguistically challenging. This, combined with the high lexical similarity of premise and hypothesis for both entailed and non-entailed pairs, makes this new entailment task particularly difficult. The resulting challenge is evidenced by state-of-the-art textual entailment systems achieving mediocre performance on SciTail, especially in comparison to a simple majority class baseline. As a step forward, we demonstrate that one can improve accuracy on SciTail by 5% using a new neural model that exploits linguistic structure.

Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary weighted set, defined as the sum of weights of all elements in the set. Our technique provides upper and lower bounds on a novel generalization of Rademacher complexity to the weighted setting in terms of the weighted set size. This generalizes Massart’s Lemma, a known upper bound on the Rademacher complexity in terms of the unweighted set size. We show that the weighted Rademacher complexity can be estimated by solving a randomly perturbed optimization problem, allowing us to derive high probability bounds on the size of any weighted set. We apply our method to the problems of calculating the partition function of an Ising model and computing propositional model counts (#SAT). Our experiments demonstrate that we can produce tighter bounds than competing methods in both the weighted and unweighted settings.

We consider the problem of learning textual entailment models with limited supervision (5K-10K training examples), and present two complementary approaches for it.First, we propose knowledge-guided adversarial example generators for incorporating large lexical resources in entailment models via only a handful of rule templates.Second, to make the entailment model-a discriminator-more robust, we propose the first GAN-style approach for training it using a natural language example generator that iteratively adjusts based on the discriminator's performance.We demonstrate effectiveness using two entailment datasets, where the proposed methods increase accuracy by 4.7% on SciTail and by 2.8% on a 1% training sub-sample of SNLI.Notably, even a single hand-written rule, negate, improves the accuracy on the negation examples in SNLI by 6.1%.P: The dog did not eat all of the chickens.H: The dog ate all of the chickens.S: entails (score 56:5%) P: The red box is in the blue box.H: The blue box is in the red box.

Most textual entailment models focus on lexical gaps between the premise text and the hypothesis, but rarely on knowledge gaps.We focus on filling these knowledge gaps in the Science Entailment task, by leveraging an external structured knowledge base (KB) of science facts.Our new architecture combines standard neural entailment models with a knowledge lookup module.To facilitate this lookup, we propose a fact-level decomposition of the hypothesis, and verifying the resulting sub-facts against both the textual premise and the structured KB.Our model, NSnet, learns to aggregate predictions from these heterogeneous data formats.On the SciTail dataset, NSnet outperforms a simpler combination of the two predictions by 3% and the base entailment model by 5%.

We present a new kind of question answering dataset, OpenBookQA, modeled after open book exams for assessing human understanding of a subject.The open book that comes with our questions is a set of 1326 elementary level science facts.Roughly 6000 questions probe an understanding of these facts and their application to novel situations.This requires combining an open book fact (e.g., metals conduct electricity) with broad common knowledge (e.g., a suit of armor is made of metal) obtained from other sources.While existing QA datasets over documents or knowledge bases, being generally self-contained, focus on linguistic understanding, OpenBookQA probes a deeper understanding of both the topic-in the context of common knowledge-and the language it is expressed in.Human performance on OpenBookQA is close to 92%, but many state-of-the-art pre-trained QA methods perform surprisingly poorly, worse than several simple neural baselines we develop.Our oracle experiments designed to circumvent the knowledge retrieval bottleneck demonstrate the value of both the open book and additional facts.We leave it as a challenge to solve the retrieval problem in this multi-hop setting and to close the large gap to human performance.Question: Which of these would let the most heat travel through?A) a new pair of jeans.B) a steel spoon in a cafeteria.C) a cotton candy at a store.D) a calvin klein cotton hat.

Neural models operating over structured spaces such as knowledge graphs require a continuous embedding of the discrete elements of this space (such as entities) as well as the relationships between them. Relational embeddings with high expressivity, however, have high model complexity, making them computationally difficult to train. We propose a new family of embeddings for knowledge graphs that interpolate between a method with high model complexity and one, namely Holographic embeddings (HolE), with low dimensionality and high training efficiency. This interpolation, termed HolEx, is achieved by concatenating several linearly perturbed copies of original HolE. We formally characterize the number of perturbed copies needed to provably recover the full entity-entity or entity-relation interaction matrix, leveraging ideas from Haar wavelets and compressed sensing. In practice, using just a handful of Haar-based or random perturbation vectors results in a much stronger knowledge completion system. On the Freebase FB15K dataset, HolEx outperforms originally reported HolE by 14.7\% on the HITS@10 metric, and the current path-based state-of-the-art method, PTransE, by 4\% (absolute).

Given a knowledge base or KB containing (noisy) facts about common nouns or generics, such as “all trees produce oxygen” or “some animals live in forests”, we consider the problem of inferring additional such facts at a precision similar to that of the starting KB. Such KBs capture general knowledge about the world, and are crucial for various applications such as question answering. Different from commonly studied named entity KBs such as Freebase, generics KBs involve quantification, have more complex underlying regularities, tend to be more incomplete, and violate the commonly used locally closed world assumption (LCWA). We show that existing KB completion methods struggle with this new task, and present the first approach that is successful. Our results demonstrate that external information, such as relation schemas and entity taxonomies, if used appropriately, can be a surprisingly powerful tool in this setting. First, our simple yet effective knowledge guided tensor factorization approach achieves state-of-the-art results on two generics KBs (80% precise) for science, doubling their size at 74%–86% precision. Second, our novel taxonomy guided, submodular, active learning method for collecting annotations about rare entities (e.g., oriole, a bird) is 6x more effective at inferring further new facts about them than multiple active learning baselines.

Question answering (QA) systems are easily distracted by irrelevant or redundant words in questions, especially when faced with long or multi-sentence questions in difficult domains. This paper introduces and studies the notion of essential question terms with the goal of improving such QA solvers. We illustrate the importance of essential question terms by showing that humans' ability to answer questions drops significantly when essential terms are eliminated from questions.We then develop a classifier that reliably (90% mean average precision) identifies and ranks essential terms in questions. Finally, we use the classifier to demonstrate that the notion of question term essentiality allows state-of-the-art QA solver for elementary-level science questions to make better and more informed decisions,improving performance by up to 5%.We also introduce a new dataset of over 2,200 crowd-sourced essential terms annotated science questions.

What capabilities are required for an AI system to pass standard 4th Grade Science Tests? Previous work has examined the use of Markov Logic Networks (MLNs) to represent the requisite background knowledge and interpret test questions, but did not improve upon an information retrieval (IR) baseline. In this paper, we describe an alternative approach that operates at three levels of representation and reasoning: information retrieval, corpus statistics, and simple inference over a semi-automatically constructed knowledge base, to achieve substantially improved results. We evaluate the methods on six years of unseen, unedited exam questions from the NY Regents Science Exam (using only non-diagram, multiple choice questions), and show that our overall system’s score is 71.3%, an improvement of 23.8% (absolute) over the MLN-based method described in previous work. We conclude with a detailed analysis, illustrating the complementary strengths of each method in the ensemble. Our datasets are being released to enable further research.

We consider the problem of sampling from a discrete probability distribution specified by a graphical model. Exact samples can, in principle, be obtained by computing the mode of the original model perturbed with an exponentially many i.i.d. random variables. We propose a novel algorithm that views this as a combinatorial optimization problem and searches for the extreme state using a standard integer linear programming (ILP) solver, appropriately extended to account for the random perturbation. Our technique, GumbelMIP, leverages linear programming (LP) relaxations to evaluate the qualityof samples and prune large portions of the search space, and can thus scale to large tree-width models beyond the reach of current exact inference methods. Further, when the optimization problem is not solved to optimality, our method yields a novel approximate sampling technique. We empirically demonstrate that our approach parallelizes well, our exact sampler scales better than alternative approaches, and our approximate sampler yields better quality samples than a Gibbs sampler and a low-dimensional perturbation method.

We study a novel machine learning (ML) problem setting of sequentially allocating small subsets of training data amongst a large set of classifiers. The goal is to select a classifier that will give near-optimal accuracy when trained on all data, while also minimizing the cost of misallocated samples. This is motivated by large modern datasets and ML toolkits with many combinations of learning algorithms and hyper-parameters. Inspired by the principle of "optimism under uncertainty," we propose an innovative strategy, Data Allocation using Upper Bounds (DAUB), which robustly achieves these objectives across a variety of real-world datasets. We further develop substantial theoretical support for DAUB in an idealized setting where the expected accuracy of a classifier trained on $n$ samples can be known exactly. Under these conditions we establish a rigorous sub-linear bound on the regret of the approach (in terms of misallocated data), as well as a rigorous bound on suboptimality of the selected classifier. Our accuracy estimates using real-world datasets only entail mild violations of the theoretical scenario, suggesting that the practical behavior of DAUB is likely to approach the idealized behavior.

Many recent algorithms for approximate model counting are based on a reduction to combinatorial searches over random subsets of the space defined by parity or XOR constraints. Long parity constraints (involving many variables) provide strong theoretical guarantees but are computationally difficult. Short parity constraints are easier to solve but have weaker statistical properties. It is currently not known how long these parity constraints need to be. We close the gap by providing matching necessary and sufficient conditions on the required asymptotic length of the parity constraints. Further, we provide a new family of lower bounds and the first non-trivial upper bounds on the model count that are valid for arbitrarily short XORs. We empirically demonstrate the effectiveness of these bounds on model counting benchmarks and in a Satisfiability Modulo Theory (SMT) application motivated by the analysis of contingency tables in statistics.

Random projections have played an important role in scaling up machine learning and data mining algorithms. Recently they have also been applied to probabilistic inference to estimate properties of high-dimensional distributions; however, they all rely on the same class of projections based on universal hashing. We provide a general framework to analyze random projections which relates their statistical properties to their Fourier spectrum, which is a well-studied area of theoretical computer science. Using this framework we introduce two new classes of hash functions for probabilistic inference and model counting that show promising performance on synthetic and real-world benchmarks.

A key challenge in sequential decision problems is to determine how many samples are needed for an agent to make reliable decisions with good probabilistic guarantees. We introduce Hoeffding-like concentration inequalities that hold for a random, adaptively chosen number of samples. Our inequalities are tight under natural assumptions and can greatly simplify the analysis of common sequential decision problems. In particular, we apply them to sequential hypothesis testing, best arm identification, and sorting. The resulting algorithms rival or exceed the state of the art both theoretically and empirically.

Elementary-level science exams pose sig-nificant knowledge acquisition and rea-soning challenges for automatic question answering. We develop a system that rea-sons with knowledge derived from text-books, represented in a subset of first-order logic. Automatic extraction, while scalable, often results in knowledge that is incomplete and noisy, motivating use of reasoning mechanisms that handle uncer-tainty. Markov Logic Networks (MLNs) seem a natural model for expressing such knowl-edge, but the exact way of leveraging MLNs is by no means obvious. We in-vestigate three ways of applying MLNs to our task. First, we simply use the extracted science rules directly as MLN clauses and exploit the structure present in hard con-straints to improve tractability. Second, we interpret science rules as describing prototypical entities, resulting in a drasti-cally simplified but brittle network. Our third approach, called Praline, uses MLNs to align lexical elements as well as define and control how inference should be per-formed in this task. Praline demonstrates a 15 % accuracy boost and a 10x reduction in runtime as compared to other MLN-based methods, and comparable accuracy to word-based baseline approaches.

This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as Alges. We compare Alges with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, Alges overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.

Propositional satisfiability (SAT) solvers based on conflict directed clause learning (CDCL) implicitly produce resolution refutations of unsatisfiable formulas. The precise class of formulas for which they can produce polynomial size refutations has been the subject of several studies, with special focus on the clause learning aspect of these solvers. The results, however, assume the use of non-standard and non-asserting learning schemes, or rely on polynomially many restarts for simulating individual steps of a resolution refutation, or work with a theoretical model that significantly deviates from certain key aspects of all modern CDCL solvers such as learning only one asserting clause from each conflict and other techniques such as conflict guided backjumping and phase saving. We study non-restarting CDCL solvers that learn only one asserting clause per conflict and show that, with simple preprocessing that depends only on the number of variables of the input formula, such solvers can polynomially simulate resolution. We show, moreover, that this preprocessing allows one to convert any CDCL solver to one that is non-restarting.

Markov Chains are a fundamental tool for the analysis of real world phenomena and randomized algorithms. Given a graph with some specified sink nodes and an initial probability distribution,we consider the problem of designing an absorbing Markov Chain that minimizes the time required to reach a sink node, by selecting transition probabilities subject to some natural regularity constraints. By exploiting the Markovian structure, we obtain closed form expressions for the objective function as well as its gradient, which can be thus evaluated efficiently without any simulation of the underlying process and fed to a gradient-based optimization package. For the special case of designing reversible Markov Chains, we show that global optimum can be efficiently computed by exploiting convexity. We demonstrate how our method can be used for the evaluation and design of local search methods tailored for certain domains.

In recent years, a number of probabilistic inference and counting techniques have been proposed that exploit pairwise independent hash functions to infer properties of succinctly defined high-dimensional sets. While providing desirable statistical guarantees, typical constructions of such hash functions are themselves not amenable to efficient inference. Inspired by the success of LDPC codes, we propose the use of low-density parity constraints to make inference more tractable in practice. While not strongly universal, we show that such sparse constraints belong to a new class of hash functions that we call Average Universal. These weaker hash functions retain the desirable statistical guarantees needed by most such probabilistic inference methods. Thus, they continue to provide provable accuracy guarantees while at the same time making a number of algorithms significantly more scalable in practice. Using this technique, we provide new, tighter bounds for challenging discrete integration and model counting problems.

Biodiversity underpins ecosystem goods and services and hence protecting it is key to achieving sustainability. However, the persistence of many species is threatened by habitat loss and fragmentation due to human land use and climate change. Conservation efforts are implemented under very limited economic resources, and therefore designing scalable, cost-efficient and systematic approaches for conservation planning is an important and challenging computational task. In particular, preserving landscape connectivity between good habitat has become a key conservation priority in recent years. We give an overview of landscape connectivity conservation and some of the underlying graph-theoretic optimization problems. We present a synthetic generator capable of creating families of randomized structured problems, capturing the essential features of real-world instances but allowing for a thorough typical-case performance evaluation of different solution methods. We also present two large-scale real-world datasets, including economic data on land cost, and species data for grizzly bears, wolverines and lynx.

Recent attempts to create versions of Satisfiability (SAT) solversthat exploit parallel hardware and information sharing have met withlimited success. In fact,the most successful parallel solvers in recent competitions were basedon portfolio approaches with little to no exchange of informationbetween processors. This experience contradicts the apparentparallelizability of exploring a combinatorial search space. Wepresent evidence that this discrepancy can be explained by studyingSAT solvers through a proof complexity lens, as resolution refutationengines. Starting with theobservation that a recently studied measure of resolution proofs,namely depth, provides a (weak) upper bound to the best possiblespeedup achievable by such solvers, we empirically show the existenceof bottlenecks to parallelizability that resolution proofs typicallygenerated by SAT solvers exhibit. Further, we propose a new measureof parallelizability based on the best-case makespan of an offlineresource constrained scheduling problem. This measureexplicitly accounts for a bounded number of parallel processors andappears to empirically correlate with parallel speedups observed inpractice. Our findings suggest that efficient parallelization of SATsolvers is not simply a matter of designing the right clause sharingheuristics; even in the best case, it can be --- and indeed is ---hindered by the structure of the resolution proofs current SAT solverstypically produce.

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.

We consider the problem of sampling from a probability distribution defined over a high-dimensional discrete set, specified for instance by a graphical model. We propose a sampling algorithm, called PAWS, based on embedding the set into a higher-dimensional space which is then randomly projected using universal hash functions to a lower-dimensional subspace and explored using combinatorial search methods. Our scheme can leverage fast combinatorial optimization tools as a blackbox and, unlike MCMC methods, samples produced are guaranteed to be within an (arbitrarily small) constant factor of the true probability distribution. We demonstrate that by using state-of-the-art combinatorial search tools, PAWS can efficiently sample from Ising grids with strong interactions and from software verification instances, while MCMC and variational methods fail in both cases.

Given a probabilistic graphical model, its density of states is a function that, for any likelihood value, gives the number of configurations with that probability. We introduce a novel message-passing algorithm called Density Propagation (DP) for estimating this function. We show that DP is exact for tree-structured graphical models and is, in general, a strict generalization of both sum-product and max-product algorithms. Further, we use density of states and tree decomposition to introduce a new family of upper and lower bounds on the partition function. For any tree decompostion, the new upper bound based on finer-grained density of state information is provably at least as tight as previously known bounds based on convexity of the log-partition function, and strictly stronger if a general condition holds. We conclude with empirical evidence of improvement over convex relaxations and mean-field based bounds.

We formulate a general framework for pseudo-Boolean multi-valued nogood-learning, generalizing conflict analysis performed by modern SAT solvers and its recent extension for disjunctions of multi-valued variables. This framework can handle more general constraints as well as different domain representations, such as interval domains which are commonly used for bounds consistency in constraint programming (CP), and even set variables. Our empirical evaluation shows that our solver, built upon this framework, works robustly across a number of challenging domains.

We propose a novel Adaptive Markov Chain Monte Carlo algorithm to compute the partition function. In particular, we show how to accelerate a flat histogram sampling technique by significantly reducing the number of ``null moves'' in the chain, while maintaining asymptotic convergence properties. Our experiments show that our method converges quickly to highly accurate solutions on a range of benchmark instances, outperforming other state-of-the-art methods such as IJGP, TRW, and Gibbs sampling both in run-time and accuracy. We also show how obtaining a so-called density of states distribution allows for efficient weight learning in Markov Logic theories.

Planning as satisfiability, as implemented in, for instance, the SATPLAN tool, is a highly competitive method for finding parallel step-optimal plans. A bottleneck in this approach is to *prove the absence* of plans of a certain length. Specifically, if the optimal plan has N steps, then it is typically very costly to prove that there is no plan of length N-1. We pursue the idea of leading this proof within solution length preserving abstractions (over-approximations) of the original planning task. This is promising because the abstraction may have a much smaller state space; related methods are highly successful in model checking. In particular, we design a novel abstraction technique based on which one can, in several widely used planning benchmarks, construct abstractions that have exponentially smaller state spaces while preserving the length of an optimal plan. Surprisingly, the idea turns out to appear quite hopeless in the context of planning as satisfiability. Evaluating our idea empirically, we run experiments on almost all benchmarks of the international planning competitions up to IPC 2004, and find that even hand-made abstractions do not tend to improve the performance of SATPLAN. Exploring these findings from a theoretical point of view, we identify an interesting phenomenon that may cause this behavior. We compare various planning-graph based CNF encodings F of the original planning task with the CNF encodings F_abs of the abstracted planning task. We prove that, in many cases, the shortest resolution refutation for F_abs can never be shorter than that for F. This suggests a fundamental weakness of the approach, and motivates further investigation of the interplay between declarative transition-systems, over-approximating abstractions, and SAT encodings.

We show that an important and computationally challenging solution space feature of the graph coloring problem (COL), namely the number of clusters of solutions, can be accurately estimated by a technique very similar to one for counting the number of solutions. This cluster counting approach can be naturally written in terms of a new factor graph derived from the factor graph representing the COL instance. Using a variant of the Belief Propagation inference framework, we can efficiently approximate cluster counts in random COL problems over a large range of graph densities. We illustrate the algorithm on instances with up to 100, 000 vertices. Moreover, we supply a methodology for computing the number of clus- ters exactly using advanced techniques from the knowledge compilation literature. This methodology scales up to several hundred variables.

We propose a new technique for sampling the solutions of combinatorial problems in a near-uniform manner. We focus on problems specified as a Boolean formula, i.e., on SAT instances. Sampling for SAT problems has been shown to have interesting connections with probabilistic reasoning, making practical sampling algorithms for SAT highly desirable. The best current approaches are based on Markov Chain Monte Carlo methods, which have some practical limitations. Our approach exploits combinatorial properties of random parity (X O R) constraints to prune away solutions near-uniformly. The final sample is identified amongst the remaining ones using a state-of-the-art SAT solver. The resulting sampling distribution is provably arbitrarily close to uniform. Our experiments show that our technique achieves a significantly better sampling quality than the best alternative.

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and Davis-Putnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speed-ups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas.

We prove a quasi-polynomial lower bound on the size of bounded-depth Frege proofs of the pigeonhole principle $PHP^{m}_n$ where $m= (1+1/{ípolylog n})n$. This lower bound qualitatively matches the known quasi-polynomial-size bounded-depth Frege proofs for these principles. Our technique, which uses a switching lemma argument like other lower bounds for bounded-depth Frege proofs, is novel in that the tautology to which this switching lemma is applied remains random throughout the argument.

We prove a quasi-polynomial lower bound on the size of bounded-depth Frege proofs of the pigeonhole principle PHP/sub n//sup m/ where m = (1 + 1/polylog n)n. This lower bound qualitatively matches the known quasipolynomial-size bounded-depth Frege proofs for these principles. Our technique, which uses a switching lemma argument like other lower bounds for bounded-depth Frege proofs, is novel in that the tautology to which this switching lemma is applied remains random throughout the argument.

We consider the problem of providing a resolution proof of the statement that a given graph with n vertices and /spl Delta/n edges does not contain an independent set of size k. For randomly chosen graphs with constant /spl Delta/, we show that such proofs almost surely require size exponential in n. Further, for /spl Delta/=o(n/sup 1/5/) and any k/spl les/n/5, we show that these proofs almost surely require size 2(n/sup /spl delta//) for some global constant /spl delta/>0, even though the largest independent set in graphs with /spl Delta//spl ap/n/sup 1/5/ is much smaller than n/5. Our result shows that almost all instances of the independent set problem are hard for resolution. It also provides a lower bound on the running time of a certain class of search algorithms for finding a largest independent set in a given graph.