Controllable Generation via Locally Constrained Resampling

Autoregressive models have demonstrated an unprecedented ability at modeling the intricacies of natural language. However, they continue to struggle with generating complex outputs that adhere to logical constraints. Sampling from a fully-independent distribution subject to a constraint is hard. Sampling from an autoregressive distribution subject to a constraint is doubly hard: We have to contend not only with the hardness of the constraint but also the distribution's lack of structure. We propose a tractable probabilistic approach that performs Bayesian conditioning to draw samples subject to a constraint. Our approach considers the entire sequence, leading to a more globally optimal constrained generation than current greedy methods. Starting from a model sample, we induce a local, factorized distribution which we can tractably condition on the constraint. To generate samples that satisfy the constraint, we sample from the conditional distribution, correct for biases in the samples and resample. The resulting samples closely approximate the target distribution and are guaranteed to satisfy the constraints. We evaluate our approach on several tasks, including LLM detoxification and solving Sudoku puzzles. We show that by disallowing a list of toxic expressions our approach is able to steer the model's outputs away from toxic generations, outperforming similar approaches to detoxification. We conclude by showing that our approach achieves a perfect accuracy on Sudoku compared to <50% for GPT4-o and Gemini 1.5.

Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles

Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves $94.21\%$ of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves $92.04 \%$ of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

Neural Concept Binder

The challenge in object-based visual reasoning lies in generating descriptive yet distinct concept representations. Moreover, doing this in an unsupervised fashion requires human users to understand a model's learned concepts and potentially revise false concepts. In addressing this challenge, we introduce the Neural Concept Binder, a new framework for deriving discrete concept representations resulting in what we term "concept-slot encodings". These encodings leverage both "soft binding" via object-centric block-slot encodings and "hard binding" via retrieval-based inference. The Neural Concept Binder facilitates straightforward concept inspection and direct integration of external knowledge, such as human input or insights from other AI models like GPT-4. Additionally, we demonstrate that incorporating the hard binding mechanism does not compromise performance; instead, it enables seamless integration into both neural and symbolic modules for intricate reasoning tasks, as evidenced by evaluations on our newly introduced CLEVR-Sudoku dataset.

MARVEL: Multidimensional Abstraction and Reasoning through Visual Evaluation and Learning

While multi-modal large language models (MLLMs) have shown significant progress on many popular visual reasoning benchmarks, whether they possess abstract visual reasoning abilities remains an open question. Similar to the Sudoku puzzles, abstract visual reasoning (AVR) problems require finding high-level patterns (e.g., repetition constraints) that control the input shapes (e.g., digits) in a specific task configuration (e.g., matrix). However, existing AVR benchmarks only considered a limited set of patterns (addition, conjunction), input shapes (rectangle, square), and task configurations (3 by 3 matrices). To evaluate MLLMs' reasoning abilities comprehensively, we introduce MARVEL, a multidimensional AVR benchmark with 770 puzzles composed of six core knowledge patterns, geometric and abstract shapes, and five different task configurations. To inspect whether the model accuracy is grounded in perception and reasoning, MARVEL complements the general AVR question with perception questions in a hierarchical evaluation framework. We conduct comprehensive experiments on MARVEL with nine representative MLLMs in zero-shot and few-shot settings. Our experiments reveal that all models show near-random performance on the AVR question, with significant performance gaps (40%) compared to humans across all patterns and task configurations. Further analysis of perception questions reveals that MLLMs struggle to comprehend the visual features (near-random performance) and even count the panels in the puzzle ( <45%), hindering their ability for abstract reasoning. We release our entire code and dataset.

PuzzleBench: Can LLMs Solve Challenging First-Order Combinatorial Reasoning Problems?

Recent works have explored the use of LLMs for reasoning tasks focussing on relatively simple problems, such as logical question answering. In our work, we wish to tackle more complicated problems, significantly expanding the capabilities of these models. Particularly, we explore whether LLMs can solve challenging first-order combinatorial reasoning problems, an example being the popular puzzle Sudoku. These problems have an underlying first-order structure described by a general description in natural language and can be instantiated to instances of varying sizes. Moreover these problems are computationally intensive requiring several reasoning steps to reach the solution. We present PuzzleBench a dataset of 31 such challenging puzzles. We observe that LLMs even when aided by symbolic solvers perform rather poorly on our benchmark. In response we propose a new approach, Puzzle-LM which combines LLMs with both symbolic solvers and program interpreters enabling them to reason about such challenging problems. We also show how feedback from smaller solved instances can help improve this reasoning ability.

Bridging Logic and Learning: A Neural-Symbolic Approach for Enhanced Reasoning in Neural Models

Neural-symbolic learning, an intersection of neural networks and symbolic reasoning, aims to blend neural networks' learning capabilities with symbolic AI's interpretability and reasoning. This paper introduces an approach designed to improve the performance of neural models in learning reasoning tasks. It achieves this by integrating Answer Set Programming (ASP) solvers and domain-specific expertise, which is an approach that diverges from traditional complex neural-symbolic models. In this paper, a shallow artificial neural network (ANN) is specifically trained to solve Sudoku puzzles with minimal training data. The model has a unique loss function that integrates losses calculated using the ASP solver outputs, effectively enhancing its training efficiency. Most notably, the model shows a significant improvement in solving Sudoku puzzles using only 12 puzzles for training and testing without hyperparameter tuning. This advancement indicates that the model's enhanced reasoning capabilities have practical applications, extending well beyond Sudoku puzzles to potentially include a variety of other domains. The code can be found on GitHub: https://github.com/Fadi2200/ASPEN.

Assessing SATNet's Ability to Solve the Symbol Grounding Problem

SATNet is an award-winning MAXSAT solver that can be used to infer logical rules and integrated as a differentiable layer in a deep neural network. It had been shown to solve Sudoku puzzles visually from examples of puzzle digit images, and was heralded as an impressive achievement towards the longstanding AI goal of combining pattern recognition with logical reasoning. In this paper, we clarify SATNet's capabilities by showing that in the absence of intermediate labels that identify individual Sudoku digit images with their logical representations, SATNet completely fails at visual Sudoku (0% test accuracy). More generally, the failure can be pinpointed to its inability to learn to assign symbols to perceptual phenomena, also known as the symbol grounding problem, which has long been thought to be a prerequisite for intelligent agents to perform real-world logical reasoning. We propose an MNIST based test as an easy instance of the symbol grounding problem that can serve as a sanity check for differentiable symbolic solvers in general. Naive applications of SATNet on this test lead to performance worse than that of models without logical reasoning capabilities. We report on the causes of SATNet's failure and how to prevent them.

A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraints

Neuro-symbolic AI bridges the gap between purely symbolic and neural approaches to learning. This often requires maximizing the likelihood of a symbolic constraint w.r.t the neural network's output distribution. Such output distributions are typically assumed to be fully-factorized. This limits the applicability of neuro-symbolic learning to the more expressive autoregressive distributions, e.g., transformers. Under such distributions, computing the likelihood of even simple constraints is #P-hard. Instead of attempting to enforce the constraint on the entire output distribution, we propose to do so on a random, local approximation thereof. More precisely, we optimize the likelihood of the constraint under a pseudolikelihood-based approximation centered around a model sample. Our approximation is factorized, allowing the reuse of solutions to sub-problems, a main tenet for efficiently computing neuro-symbolic losses. Moreover, it is a local, high-fidelity approximation of the likelihood, exhibiting low entropy and KL-divergence around the model sample. We evaluate our approach on Sudoku and shortest-path prediction cast as autoregressive generation, and observe that we greatly improve upon the base model's ability to predict logically-consistent outputs. We also evaluate on the task of detoxifying large language models. Using a simple constraint disallowing a list of toxic words, we are able to steer the model's outputs away from toxic generations, achieving SoTA detoxification compared to previous approaches.

Measuring reasoning capabilities of ChatGPT

I shall quantify the logical faults generated by ChatGPT when applied to reasoning tasks. For experiments, I use the 144 puzzles from the library \url{https://users.utcluj.ro/~agroza/puzzles/maloga}~\cite{groza:fol}. The library contains puzzles of various types, including arithmetic puzzles, logical equations, Sudoku-like puzzles, zebra-like puzzles, truth-telling puzzles, grid puzzles, strange numbers, or self-reference puzzles. The correct solutions for these puzzles were checked using the theorem prover Prover9~\cite{mccune2005release} and the finite models finder Mace4~\cite{mccune2003mace4} based on human-modelling in Equational First Order Logic. A first output of this study is the benchmark of 100 logical puzzles. For this dataset ChatGPT provided both correct answer and justification for 7\% only. %, while BARD for 5\%. Since the dataset seems challenging, the researchers are invited to test the dataset on more advanced or tuned models than ChatGPT3.5 with more crafted prompts. A second output is the classification of reasoning faults conveyed by ChatGPT. This classification forms a basis for a taxonomy of reasoning faults generated by large language models. I have identified 67 such logical faults, among which: inconsistencies, implication does not hold, unsupported claim, lack of commonsense, wrong justification. The 100 solutions generated by ChatGPT contain 698 logical faults. That is on average, 7 fallacies for each reasoning task. A third ouput is the annotated answers of the ChatGPT with the corresponding logical faults. Each wrong statement within the ChatGPT answer was manually annotated, aiming to quantify the amount of faulty text generated by the language model. On average, 26.03\% from the generated text was a logical fault.

Learning Reliable Logical Rules with SATNet

Bridging logical reasoning and deep learning is crucial for advanced AI systems. In this work, we present a new framework that addresses this goal by generating interpretable and verifiable logical rules through differentiable learning, without relying on pre-specified logical structures. Our approach builds upon SATNet, a differentiable MaxSAT solver that learns the underlying rules from input-output examples. Despite its efficacy, the learned weights in SATNet are not straightforwardly interpretable, failing to produce human-readable rules. To address this, we propose a novel specification method called "maximum equality", which enables the interchangeability between the learned weights of SATNet and a set of propositional logical rules in weighted MaxSAT form. With the decoded weighted MaxSAT formula, we further introduce several effective verification techniques to validate it against the ground truth rules. Experiments on stream transformations and Sudoku problems show that our decoded rules are highly reliable: using exact solvers on them could achieve 100% accuracy, whereas the original SATNet fails to give correct solutions in many cases. Furthermore, we formally verify that our decoded logical rules are functionally equivalent to the ground truth ones.