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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We present a general framework for determining the number of solutions of constraint satisfaction problems (CSPs) with a high precision. Our first strategy uses additional binary variables for the CSP, and applies an XOR or parity constraint based method introduced previously for Boolean satisfiability (SAT) problems. In the CSP framework, in addition to the naive individual filtering of XOR constraints used in SAT, we are able to apply a global domain filtering algorithm by viewing these constraints as a collection of linear equalities over the field of two elements. Our most promising strategy extends this approach further to larger domains, and applies the so-called generalized XOR constraints directly to CSP variables. This allows us to reap the benefits of the compact and structured representation that CSPs offer. We demonstrate the effectiveness of our counting framework through experimental comparisons with the solution enumeration approach (which, we believe, is the current best generic solution counting method for CSPs), and with solution counting in the context of SAT and integer programming.

Set variables provide convenient modeling shorthands for many combinatorial problems. However, it is often challenging to efficiently handle set constraints when solving the problem. We present efficient filtering algorithms, establishing bounds consistency, for two such constraints: the sum-free constraint, and the atmost1 constraint on pairs of set variables with known cardinality. The filtering algorithm for the sum-free constraint achieves the same pruning as the corresponding collection of constraints on the binary representation, but it does so more efficiently and without running into memory bottlenecks. For the atmost1 constraint on pairs of set variables, the additional time spent on pruning more values pays off well in terms of overall efficiency. Our results show that set constraints can not only ease modeling the problem, they can also decrease the solution time and memory requirements.

In an attempt to address the negative ecological impacts of habitat fragmentation, wildlife corridors have been proposed as a way to connect areas of biological significance. In this paper, a model to maximize the amount of suitable wildlife habitat in a fully connected parcel network linking core habitat areas subject to a budget constraint is introduced. The standard economic framework of maximizing habitat benefits subject to a budget constraint that we employ in this paper is a divergence from other recently proposed models that focus only on minimizing the cost of a single parcel-wide corridor. While the budget constrained optimization model that we introduce is intuitively appealing, it presents substantial computational challenges above determining the cost-minimizing corridor. The optimization model is applied to the design of a wildlife corridor for grizzly bears in the U.S. Northern Rockies and is shown to drastically increase the aggregate habitat suitability of the corridor over parcel selection based on cost minimization alone. The relative tradeoffs between corridor cost and habitat suitability are illustrated through the construction of an efficiency frontier and, for cases where optimization is computationally impractical, a heuristic is suggested that closely approximates the optimally selected corridor.