Daily Papers

Recent mechanistic work has uncovered learned algorithms within neural networks, from modular arithmetic to search and planning in game-playing agents. But does algorithmic structure guarantee algorithmic behavior? We investigate this in Leela Chess Zero, the strongest neural chess engine, where prior work identified learned look-ahead. By extending the logit lens to its move-selecting policy network, we discover that correct puzzle solutions--including immediate checkmates--often appear in intermediate layers but are systematically overridden in the final output, a phenomenon we term "forgotten puzzles". Replicating prior analyses on these positions, we find that look-ahead operates normally--future moves of the correct continuation are represented, causally important, and linearly decodable--ruling out a failure of the algorithm. Instead, late layers increasingly shift toward safe play over aggression. To test whether this shift drives the override, we steer the model against these preferences and recover 71.7% of forgotten puzzles, providing causal evidence that safety priors override algorithmically computed solutions. These findings show that algorithmic structure does not guarantee algorithmic behavior: a model can internally solve a problem and still output the wrong answer.

As language models master existing reasoning benchmarks, we need new challenges to evaluate their cognitive frontiers. Puzzle-solving events are rich repositories of challenging multimodal problems that test a wide range of advanced reasoning and knowledge capabilities, making them a unique testbed for evaluating frontier language models. We introduce EnigmaEval, a dataset of problems and solutions derived from puzzle competitions and events that probes models' ability to perform implicit knowledge synthesis and multi-step deductive reasoning. Unlike existing reasoning and knowledge benchmarks, puzzle solving challenges models to discover hidden connections between seemingly unrelated pieces of information to uncover solution paths. The benchmark comprises 1184 puzzles of varying complexity -- each typically requiring teams of skilled solvers hours to days to complete -- with unambiguous, verifiable solutions that enable efficient evaluation. State-of-the-art language models achieve extremely low accuracy on these puzzles, even lower than other difficult benchmarks such as Humanity's Last Exam, unveiling models' shortcomings when challenged with problems requiring unstructured and lateral reasoning.

Large language models (LLMs) have demonstrated solid zero-shot reasoning capabilities, which is reflected in their performance on the current test tasks. This calls for a more challenging benchmark requiring highly advanced reasoning ability to be solved. In this paper, we introduce such a benchmark, consisting of 191 long-form (1200 words on average) mystery narratives constructed as detective puzzles. Puzzles are sourced from the "5 Minute Mystery" platform and include a multiple-choice question for evaluation. Only 47% of humans solve a puzzle successfully on average, while the best human solvers achieve over 80% success rate. We show that GPT-3 models barely outperform random on this benchmark (with 28% accuracy) while state-of-the-art GPT-4 solves only 38% of puzzles. This indicates that there is still a significant gap in the deep reasoning abilities of LLMs and humans and highlights the need for further research in this area. Our work introduces a challenging benchmark for future studies on reasoning in language models and contributes to a better understanding of the limits of LLMs' abilities.

Recent unlearning methods (e.g. NPO, DPO, LUNAR) make use of refusal alignment to suppress forgotten data. However, it has been shown that refusal responses might leave traces of unlearning, and recent attacks have been able to successfully recover some of the unlearned knowledge. In this paper, we uncover a new vulnerability. Existing attacks typically assume that the forgotten prompts are already known to the adversary and focus on recovering their answers. However, we show that the forgotten prompts themselves can be extracted by using the retained data and black-box access to the model. Our attack, Targeted Active Search (TAS), first identifies the forgotten entities by constructing canonical templates and entity pool, and selectively querying the model using the most informative template-entity pair under a limited query budget. Once the entities are identified, TAS instantiates prompt templates with those entities to probe the unlearned model and reconstruct the forgotten prompts. Experiments across three unlearning methods with three datasets and three LLMs shows that TAS recovers the forgotten entity with 100% accuracy and reconstructs up to 95% of forgotten prompts, all while using up to 99.7% fewer queries than naive probing.

Large Reasoning Models (LRMs) have demonstrated impressive performance on complex tasks, including logical puzzle games that require deriving solutions satisfying all constraints. However, whether they can flexibly apply appropriate rules to varying conditions, particularly when faced with non-canonical game variants, remains an open question. Existing corpora focus on popular puzzles like 9x9 Sudoku, risking overfitting to canonical formats and memorization of solution patterns, which can mask deficiencies in understanding novel rules or adapting strategies to new variants. To address this, we introduce HardcoreLogic, a challenging benchmark of over 5,000 puzzles across 10 games, designed to test the robustness of LRMs on the "long-tail" of logical games. HardcoreLogic systematically transforms canonical puzzles through three dimensions: Increased Complexity (IC), Uncommon Elements (UE), and Unsolvable Puzzles (UP), reducing reliance on shortcut memorization. Evaluations on a diverse set of LRMs reveal significant performance drops, even for models achieving top scores on existing benchmarks, indicating heavy reliance on memorized stereotypes. While increased complexity is the dominant source of difficulty, models also struggle with subtle rule variations that do not necessarily increase puzzle difficulty. Our systematic error analysis on solvable and unsolvable puzzles further highlights gaps in genuine reasoning. Overall, HardcoreLogic exposes the limitations of current LRMs and establishes a benchmark for advancing high-level logical reasoning.

Jigsaw puzzle solving is an intriguing problem which has been explored in computer vision for decades. This paper focuses on a specific variant of the problem - solving puzzles with eroded boundaries. Such erosion makes the problem extremely difficult, since most existing solvers utilize solely the information at the boundaries. Nevertheless, this variant is important since erosion and missing data often occur at the boundaries. The key idea of our proposed approach is to inpaint the eroded boundaries between puzzle pieces and later leverage the quality of the inpainted area to classify a pair of pieces as 'neighbors or not'. An interesting feature of our architecture is that the same GAN discriminator is used for both inpainting and classification; Training of the second task is simply a continuation of the training of the first, beginning from the point it left off. We show that our approach outperforms other SOTA methods

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

We discover that DALLE-2 seems to have a hidden vocabulary that can be used to generate images with absurd prompts. For example, it seems that Apoploe vesrreaitais means birds and Contarra ccetnxniams luryca tanniounons (sometimes) means bugs or pests. We find that these prompts are often consistent in isolation but also sometimes in combinations. We present our black-box method to discover words that seem random but have some correspondence to visual concepts. This creates important security and interpretability challenges.

GUI agents need long-horizon visual reasoning: they must interpret a changing interface while keeping a multi-step plan viable as earlier actions constrain later ones. Existing benchmarks evaluate grounding, computer use, and game play, but rarely test whether agents stay coherent across long chains of coupled decisions. Long-horizon visual puzzles expose this capability directly: a legal move that looks like progress can make the puzzle unsolvable, and the loss shows only several moves later. We introduce LongPuzzleBench, 114 levels in six puzzle games played through native GUI actions, where one objective can take a human over a thousand actions on persistent boards and dead ends go unannounced. With Native GUI Actions alone, the strongest agents solve most objectives, but success falls sharply on harder, longer boards: seven of ten general-purpose agents solve nothing harder than Medium, and none completes Bolt Unscrew Hard, which a human solves along with every other objective. Code Execution CUA does not close this gap, and its scores mix visual solving with algorithmic search. Controlled diagnostics trace these failures to one limitation that neither rules, state hints, nor failure memory removes: agents judge each move by the visible progress it makes, not by the future options it leaves.

In this paper, we examine linguistic puzzles used in high school linguistics competitions, focusing on two common formats: Rosetta Stone and Match-Up. We propose a systematic procedure for converting existing Rosetta Stone puzzles into corresponding Match-Up counterparts. Because linguistic puzzle creation is complex and time-consuming, our method provides an efficient way to accelerate the generation of new puzzles. We evaluate the resulting Rosetta Stone-Match-Up pairs with both human participants and large language models (LLMs). Our results show that both expert human solvers and LLMs display an all-or-nothing pattern on Match-Up puzzles, either solving them completely or failing entirely. This work contributes a new dataset of paired puzzles and provides a detailed evaluation of puzzle difficulty across formats, offering insights into both human and machine linguistic reasoning.

We explore the ability of large language models to solve and generate puzzles from the NPR Sunday Puzzle game show using PUZZLEQA, a dataset comprising 15 years of on-air puzzles. We evaluate four large language models using PUZZLEQA, in both multiple choice and free response formats, and explore two prompt engineering techniques to improve free response performance: chain-of-thought reasoning and prompt summarization. We find that state-of-the-art large language models can solve many PUZZLEQA puzzles: the best model, GPT-3.5, achieves 50.2% loose accuracy. However, in our few-shot puzzle generation experiment, we find no evidence that models can generate puzzles: GPT-3.5 generates puzzles with answers that do not conform to the generated rules. Puzzle generation remains a challenging task for future work.

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.

In this paper, we introduce a combination of novel and exciting tasks: the solution and generation of linguistic puzzles. We focus on puzzles used in Linguistic Olympiads for high school students. We first extend the existing benchmark for the task of solving linguistic puzzles. We explore the use of Large Language Models (LLMs), including recent state-of-the-art models such as OpenAI's o1, for solving linguistic puzzles, analyzing their performance across various linguistic topics. We demonstrate that LLMs outperform humans on most puzzles types, except for those centered on writing systems, and for the understudied languages. We use the insights from puzzle-solving experiments to direct the novel task of puzzle generation. We believe that automating puzzle generation, even for relatively simple puzzles, holds promise for expanding interest in linguistics and introducing the field to a broader audience. This finding highlights the importance of linguistic puzzle generation as a research task: such puzzles can not only promote linguistics but also support the dissemination of knowledge about rare and understudied languages.

Existing reasoning benchmarks for large language models (LLMs) frequently fail to capture authentic creativity, often rewarding memorization of previously observed patterns. We address this shortcoming with Sudoku-Bench, a curated benchmark of challenging and unconventional Sudoku variants specifically selected to evaluate creative, multi-step logical reasoning. Sudoku variants form an unusually effective domain for reasoning research: each puzzle introduces unique or subtly interacting constraints, making memorization infeasible and requiring solvers to identify novel logical breakthroughs (``break-ins''). Despite their diversity, Sudoku variants maintain a common and compact structure, enabling clear and consistent evaluation. Sudoku-Bench includes a carefully chosen puzzle set, a standardized text-based puzzle representation, and flexible tools compatible with thousands of publicly available puzzles -- making it easy to extend into a general research environment. Baseline experiments show that state-of-the-art LLMs solve fewer than 15\% of puzzles unaided, highlighting significant opportunities to advance long-horizon, strategic reasoning capabilities.

Crossword puzzles are popular linguistic games often used as tools to engage students in learning. Educational crosswords are characterized by less cryptic and more factual clues that distinguish them from traditional crossword puzzles. Despite there exist several publicly available clue-answer pair databases for traditional crosswords, educational clue-answer pairs datasets are missing. In this article, we propose a methodology to build educational clue generation datasets that can be used to instruct Large Language Models (LLMs). By gathering from Wikipedia pages informative content associated with relevant keywords, we use Large Language Models to automatically generate pedagogical clues related to the given input keyword and its context. With such an approach, we created clue-instruct, a dataset containing 44,075 unique examples with text-keyword pairs associated with three distinct crossword clues. We used clue-instruct to instruct different LLMs to generate educational clues from a given input content and keyword. Both human and automatic evaluations confirmed the quality of the generated clues, thus validating the effectiveness of our approach.

Most LLM unlearning methods aim to approximate retrain-from-scratch behaviors with minimal distribution shift, often via alignment-style objectives defined in the prediction space. While effective at reducing forgotten content generation, such approaches may act as suppression: forgotten concepts can persist in representations and remain entangled with retained knowledge. We introduce CLReg, a contrastive representation regularizer that identifies forget features while pushing them away from retain features, explicitly reducing forget-retain interference with minimal shifts on retain features. We provide first theoretical insights that relate representation shaping to entanglement reduction. Across unlearning benchmarks and LLMs of different sizes, CLReg decreases forget-retain representation entanglement that facilitates mainstream unlearning methods without positing extra privacy risks, inspiring future work that reshapes the representation space to remove forget concepts.

The LLM unlearning aims to eliminate the influence of undesirable data without affecting causally unrelated information. This process typically involves using a forget set to remove target information, alongside a retain set to maintain non-target capabilities. While recent localization-based methods demonstrate promise in identifying important neurons to be unlearned, they fail to disentangle neurons responsible for forgetting undesirable knowledge or retaining essential skills, often treating them as a single entangled group. As a result, these methods apply uniform interventions, risking catastrophic over-forgetting or incomplete erasure of the target knowledge. To address this, we turn to circuit discovery, a mechanistic interpretability technique, and propose the Conflict-guided Localization for LLM Unlearning framEwork (CLUE). This framework identifies the forget and retain circuit composed of important neurons, and then the circuits are transformed into conjunctive normal forms (CNF). The assignment of each neuron in the CNF satisfiability solution reveals whether it should be forgotten or retained. We then provide targeted fine-tuning strategies for different categories of neurons. Extensive experiments demonstrate that, compared to existing localization methods, CLUE achieves superior forget efficacy and retain utility through precise neural localization.

Puzzlehunts are a genre of complex, multi-step puzzles lacking well-defined problem definitions. In contrast to conventional reasoning benchmarks consisting of tasks with clear instructions, puzzlehunts require models to discover the underlying problem structure from multimodal evidence and iterative reasoning, mirroring real-world domains such as scientific discovery, exploratory data analysis, or investigative problem-solving. Despite recent progress in foundation models, their performance on such open-ended settings remains largely untested. In this paper, we introduce PuzzleWorld, a large-scale benchmark of 667 puzzlehunt-style problems designed to assess step-by-step, open-ended, and creative multimodal reasoning. Each puzzle is annotated with the final solution, detailed reasoning traces, and cognitive skill labels, enabling holistic benchmarking and fine-grained diagnostic analysis. Most state-of-the-art models achieve only 1-2% final answer accuracy, with the best model solving only 14% of puzzles and reaching 40% stepwise accuracy. To demonstrate the value of our reasoning annotations, we show that fine-tuning a small model on reasoning traces improves stepwise reasoning from 4% to 11%, while training on final answers alone degrades performance to near zero. Our error analysis reveals that current models exhibit myopic reasoning, are bottlenecked by the limitations of language-based inference, and lack sketching capabilities crucial for visual and spatial reasoning. We release PuzzleWorld at https://github.com/MIT-MI/PuzzleWorld to support future work on building more general, open-ended, and creative reasoning systems.

Solving grid puzzles involves a significant amount of logical reasoning. Hence, it is a good domain to evaluate the reasoning capability of a model which can then guide us to improve the reasoning ability of models. However, most existing works evaluate only the final predicted answer of a puzzle, without delving into an in-depth analysis of the LLMs' reasoning chains (such as where they falter) or providing any finer metrics to evaluate them. Since LLMs may rely on simple heuristics or artifacts to predict the final answer, it is crucial to evaluate the generated reasoning chain beyond overall correctness measures, for accurately evaluating the reasoning abilities of LLMs. To this end, we first develop GridPuzzle, an evaluation dataset comprising 274 grid-based puzzles with different complexities. Second, we propose a new error taxonomy derived from manual analysis of reasoning chains from LLMs including GPT-4, Claude-3, Gemini, Mistral, and Llama-2. Then, we develop an LLM-based framework for large-scale subjective evaluation (i.e., identifying errors) and an objective metric, PuzzleEval, to evaluate the correctness of reasoning chains. Evaluating reasoning chains from LLMs leads to several interesting findings. We further show that existing prompting methods used for enhancing models' reasoning abilities do not improve performance on GridPuzzle. This highlights the importance of understanding fine-grained errors and presents a challenge for future research to enhance LLMs' puzzle-solving abilities by developing methods that address these errors. Data and source code are available at https://github.com/Mihir3009/GridPuzzle.

The task of predicting time and location from images is challenging and requires complex human-like puzzle-solving ability over different clues. In this work, we formalize this ability into core skills and implement them using different modules in an expert pipeline called PuzzleGPT. PuzzleGPT consists of a perceiver to identify visual clues, a reasoner to deduce prediction candidates, a combiner to combinatorially combine information from different clues, a web retriever to get external knowledge if the task can't be solved locally, and a noise filter for robustness. This results in a zero-shot, interpretable, and robust approach that records state-of-the-art performance on two datasets -- TARA and WikiTilo. PuzzleGPT outperforms large VLMs such as BLIP-2, InstructBLIP, LLaVA, and even GPT-4V, as well as automatically generated reasoning pipelines like VisProg, by at least 32% and 38%, respectively. It even rivals or surpasses finetuned models.

This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language models in solving algorithmic puzzles that necessitate both visual understanding, language understanding, and complex algorithmic reasoning. We create the puzzles to encompass a diverse array of mathematical and algorithmic topics such as boolean logic, combinatorics, graph theory, optimization, search, etc., aiming to evaluate the gap between visual data interpretation and algorithmic problem-solving skills. The dataset is generated automatically from code authored by humans. All our puzzles have exact solutions that can be found from the algorithm without tedious human calculations. It ensures that our dataset can be scaled up arbitrarily in terms of reasoning complexity and dataset size. Our investigation reveals that large language models (LLMs) such as GPT4V and Gemini exhibit limited performance in puzzle-solving tasks. We find that their performance is near random in a multi-choice question-answering setup for a significant number of puzzles. The findings emphasize the challenges of integrating visual, language, and algorithmic knowledge for solving complex reasoning problems.

Understanding Rebus Puzzles (Rebus Puzzles use pictures, symbols, and letters to represent words or phrases creatively) requires a variety of skills such as image recognition, cognitive skills, commonsense reasoning, multi-step reasoning, image-based wordplay, etc., making this a challenging task for even current Vision-Language Models. In this paper, we present left|,circlearrowright,text{BUS},right|, a large and diverse benchmark of 1,333 English Rebus Puzzles containing different artistic styles and levels of difficulty, spread across 18 categories such as food, idioms, sports, finance, entertainment, etc. We also propose RebusDescProgICE, a model-agnostic framework which uses a combination of an unstructured description and code-based, structured reasoning, along with better, reasoning-based in-context example selection, improving the performance of Vision-Language Models on left|,circlearrowright,text{BUS},right| by 2.1-4.1% and 20-30% using closed-source and open-source models respectively compared to Chain-of-Thought Reasoning.

We study the Levine hat problem, a classic combinatorial puzzle introduced by Lionel Levine in 2010. This problem involves a game in which n geq 2 players, each seeing an infinite stack of hats on each of their teammates' heads but not on their own, must simultaneously guess the index of a black hat on their own stack. If one of the players fails to do so, the team loses collectively. The players must therefore come up with a good strategy before the game starts. While the optimal winning probability V_{n} remains unknown even for n=2, we make three key advances. First, we develop a novel geometric framework for representing strategies through measurable functions, providing a new expression of V_{n} and a unified treatment of the game for finite and for infinite stacks via integral formulations. Secondly, we construct a new strategy K_{5} that reaches the conjectured optimal probability of victory : 0.35. We also show that K_{5} is part of a larger class of strategies that allow us to improve current bounds and resolve conjectured inequalities. Finally, we introduce and entirely solve a continuous generalization of the problem, demonstrating that extending to uncountable hat stacks increases the optimal winning probability to exactly 1/2. This generalization naturally leads to a broader and smoother strategic framework, within which we also describe how to compute optimal responses to a range of strategies.

Most benchmarks hand the model a question. EnigmaForge hands it a stack of old documents and no question at all. Buried in the letters, receipts, and logbook margins is a small logic puzzle whose solution is unique - proved by a SAT solver at generation time, with an ablation certificate showing every clue is load-bearing. Because instances are generated rather than collected, the corpus renews forever. The headline measure is intuition: task success when handed only the story, with world reconstruction as the secondary axis. Twenty-five frontier models ran over 600 instances (17,400 scored records) under three matched conditions. Intuition reshuffles the leaderboard: a 22x spread where fact recovery spans 1.6x, the second-best fact-recoverer ranks fourteenth, one model is indifferent to being told the question, and another is significantly better without it. Several models were blocked by their own content filters before reaching the puzzle - any benchmark scoring refusals as failure is quietly measuring filter behavior.

Jigsaw puzzle solving has been an increasingly popular task in the computer vision research community. Recent works have utilized cutting-edge architectures and computational approaches to reassemble groups of pieces into a coherent image, while achieving increasingly good results on well established datasets. However, most of these approaches share a common, restricting setting: operating solely on strictly square puzzle pieces. In this work, we introduce GAP, a set of novel jigsaw puzzles datasets containing synthetic, heavily eroded pieces of unrestricted shapes, generated by a learned distribution of real-world archaeological fragments. We also introduce PuzzleFlow, a novel ViT and Flow-Matching based framework for jigsaw puzzle solving, capable of handling complex puzzle pieces and demonstrating superior performance on GAP when compared to both classic and recent prominent works in this domain.

We propose a new benchmark evaluating the performance of multimodal large language models on rebus puzzles. The dataset covers 333 original examples of image-based wordplay, cluing 13 categories such as movies, composers, major cities, and food. To achieve good performance on the benchmark of identifying the clued word or phrase, models must combine image recognition and string manipulation with hypothesis testing, multi-step reasoning, and an understanding of human cognition, making for a complex, multimodal evaluation of capabilities. We find that proprietary models such as GPT-4V and Gemini Pro significantly outperform all other tested models. However, even the best model has a final accuracy of just 24%, highlighting the need for substantial improvements in reasoning. Further, models rarely understand all parts of a puzzle, and are almost always incapable of retroactively explaining the correct answer. Our benchmark can therefore be used to identify major shortcomings in the knowledge and reasoning of multimodal large language models.

Finding optimal solution paths for combinatorial puzzles like the Rubik's Cube, sliding tile puzzles, and Lights Out remains a classical challenge in artificial intelligence. Heuristic search algorithms, such as A* , guarantee path optimality only when using an admissible heuristic-one that never overestimates the true remaining cost-to-go. Deep reinforcement learning (RL) methods like DeepCubeA train deep neural networks to approximate cost-to-go heuristics. However, standard mean-squared error (MSE) training regularly yields overestimations, violating admissibility and compromising solution optimality. In this paper, we introduce a generalizable framework for learning validation-calibrated admissible neural heuristics. We train a value network using an underestimating Admissible Bellman Operator combined with an Asymmetric Loss function to penalize overestimation. To account for residual neural function approximation errors, we propose a post-hoc calibration safety offset computed over validation scrambles. We demonstrate that our calibrated neural heuristics achieve no observed admissibility violations under the evaluation protocol and preserve path optimality in practice while reducing search node expansions by up to 83.0% on a 2 by 2 Rubik's Cube, 19.9% on a 3 by 3 Lights Out grid, and 1.9% on an 8-Puzzle compared to standard analytical baselines.

Measuring the full abilities of large language models (LLMs) requires benchmarks representing multiple tasks. We aim to create large, high-quality datasets for comparison of logical reasoning skills across several languages and of suitable difficulty for LLMs of various reasoning ability. We explore multiple ways of increasing difficulty. We generate zebra puzzles in multiple languages, themes, sizes and including 14 different clue types and 8 red herring types (uninformative clues). We find puzzle sizes 2x3 and 4x5 are sufficiently challenging for GPT-4o mini (a non-reasoning model) and o3-mini (a reasoning model), respectively. Including 5 red herrings decreases o3-mini puzzle-level accuracy on 4x5 puzzles by 15pm7 %. Scores of o3-mini on 4x5 puzzles are not significantly affected by use of English vs. Danish or the common houses theme vs. the country-specific smoerrebroed theme. We find no correlation between difficulty and the selected clue types. Datasets of 128+1024 puzzles are published as MultiZebraLogic in each of nine Germanic languages for sizes 2x3 and 4x5. We publish code for puzzle generation, designed for adaptablity into more languages and themes.

Imagine observing someone scratching their arm; to understand why, additional context would be necessary. However, spotting a mosquito nearby would immediately offer a likely explanation for the person's discomfort, thereby alleviating the need for further information. This example illustrates how subtle visual cues can challenge our cognitive skills and demonstrates the complexity of interpreting visual scenarios. To study these skills, we present Visual Riddles, a benchmark aimed to test vision and language models on visual riddles requiring commonsense and world knowledge. The benchmark comprises 400 visual riddles, each featuring a unique image created by a variety of text-to-image models, question, ground-truth answer, textual hint, and attribution. Human evaluation reveals that existing models lag significantly behind human performance, which is at 82\% accuracy, with Gemini-Pro-1.5 leading with 40\% accuracy. Our benchmark comes with automatic evaluation tasks to make assessment scalable. These findings underscore the potential of Visual Riddles as a valuable resource for enhancing vision and language models' capabilities in interpreting complex visual scenarios.

Solving topological grid puzzles requires reasoning over global spatial invariants such as connectivity, loop closure, and region symmetry and remains challenging for even the most powerful large language models (LLMs). To study these abilities under controlled settings, we introduce TopoBench, a benchmark of six puzzle families across three difficulty levels. We evaluate strong reasoning LLMs on TopoBench and find that even frontier models solve fewer than one quarter of hard instances, with two families nearly unsolved. To investigate whether these failures stem from reasoning limitations or from difficulty extracting and maintaining spatial constraints, we annotate 750 chain of thought traces with an error taxonomy that surfaces four candidate causal failure modes, then test them with targeted interventions simulating each error type. These interventions show that certain error patterns like premature commitment and constraint forgetting have a direct impact on the ability to solve the puzzle, while repeated reasoning is a benign effect of search. Finally we study mitigation strategies including prompt guidance, cell-aligned grid representations and tool-based constraint checking, finding that the bottleneck lies in extracting constraints from spatial representations and not in reasoning over them. Code and data are available at github.com/mayug/topobench-benchmark.

While Large Language Models (LLMs) have demonstrated proficiency in handling complex queries, much of the past work has depended on extensively annotated datasets by human experts. However, this reliance on fully-supervised annotations poses scalability challenges, particularly as models and data requirements grow. To mitigate this, we explore the potential of enhancing LLMs' reasoning abilities with minimal human supervision. In this work, we introduce self-reinforcement, which begins with Supervised Fine-Tuning (SFT) of the model using a small collection of annotated questions. Then it iteratively improves LLMs by learning from the differences in responses from the SFT and unfinetuned models on unlabeled questions. Our approach provides an efficient approach without relying heavily on extensive human-annotated explanations. However, current reasoning benchmarks typically only include golden-reference answers or rationales. Therefore, we present PuzzleBen, a weakly supervised benchmark that comprises 25,147 complex questions, answers, and human-generated rationales across various domains, such as brainteasers, puzzles, riddles, parajumbles, and critical reasoning tasks. A unique aspect of our dataset is the inclusion of 10,000 unannotated questions, enabling us to explore utilizing fewer supersized data to boost LLMs' inference capabilities. Our experiments underscore the significance of PuzzleBen, as well as the effectiveness of our methodology as a promising direction in future endeavors. Our dataset and code will be published soon on Anonymity Link.

We analyze the general version of the classic guessing game Mastermind with n positions and k colors. Since the case k le n^{1-varepsilon}, varepsilon>0 a constant, is well understood, we concentrate on larger numbers of colors. For the most prominent case k = n, our results imply that Codebreaker can find the secret code with O(n log log n) guesses. This bound is valid also when only black answer-pegs are used. It improves the O(n log n) bound first proven by Chvátal (Combinatorica 3 (1983), 325--329). We also show that if both black and white answer-pegs are used, then the O(n loglog n) bound holds for up to n^2 loglog n colors. These bounds are almost tight as the known lower bound of Ω(n) shows. Unlike for k le n^{1-varepsilon}, simply guessing at random until the secret code is determined is not sufficient. In fact, we show that an optimal non-adaptive strategy (deterministic or randomized) needs Θ(n log n) guesses.

A riddle is a question or statement with double or veiled meanings, followed by an unexpected answer. Solving riddle is a challenging task for both machine and human, testing the capability of understanding figurative, creative natural language and reasoning with commonsense knowledge. We introduce BiRdQA, a bilingual multiple-choice question answering dataset with 6614 English riddles and 8751 Chinese riddles. For each riddle-answer pair, we provide four distractors with additional information from Wikipedia. The distractors are automatically generated at scale with minimal bias. Existing monolingual and multilingual QA models fail to perform well on our dataset, indicating that there is a long way to go before machine can beat human on solving tricky riddles. The dataset has been released to the community.

This paper investigates the capabilities of Large Language Models (LLMs) in the context of understanding their own knowledge and measuring their uncertainty. We argue this is an important feature for mitigating hallucinations. Specifically, we focus on addressing known-unknown questions, characterized by high uncertainty due to the absence of definitive answers. To facilitate our study, we collect a dataset with new Known-Unknown Questions (KUQ) and propose a novel categorization scheme to elucidate the sources of uncertainty. Subsequently, we assess the LLMs' ability to differentiate between known and unknown questions and classify them accordingly. Moreover, we evaluate the quality of their answers in an Open-Ended QA setting. To quantify the uncertainty expressed in the answers, we create a semantic evaluation method that measures the model's accuracy in expressing uncertainty between known vs unknown questions.

Crosswords are a form of word puzzle that require a solver to demonstrate a high degree of proficiency in natural language understanding, wordplay, reasoning, and world knowledge, along with adherence to character and length constraints. In this paper we tackle the challenge of solving crosswords with large language models (LLMs). We demonstrate that the current generation of language models shows significant competence at deciphering cryptic crossword clues and outperforms previously reported state-of-the-art (SoTA) results by a factor of 2-3 in relevant benchmarks. We also develop a search algorithm that builds off this performance to tackle the problem of solving full crossword grids with out-of-the-box LLMs for the very first time, achieving an accuracy of 93% on New York Times crossword puzzles. Additionally, we demonstrate that LLMs generalize well and are capable of supporting answers with sound rationale.

The evaluation of the problem-solving capability under incomplete information scenarios of Large Language Models (LLMs) is increasingly important, encompassing capabilities such as questioning, knowledge search, error detection, and path planning. Current research mainly focus on LLMs' problem-solving capability such as ``Twenty Questions''. However, these kinds of games do not require recognizing misleading cues which are necessary in the incomplete information scenario. Moreover, the existing game such as ``Who is undercover'' are highly subjective, making it challenging for evaluation. Therefore, in this paper, we introduce a novel game named BrainKing based on the ``Who is undercover'' and ``Twenty Questions'' for evaluating LLM capabilities under incomplete information scenarios. It requires LLMs to identify target entities with limited yes-or-no questions and potential misleading answers. By setting up easy, medium, and hard difficulty modes, we comprehensively assess the performance of LLMs across various aspects. Our results reveal the capabilities and limitations of LLMs in BrainKing, providing significant insights of LLM problem-solving levels.

Existing question answering (QA) datasets are no longer challenging to most powerful Large Language Models (LLMs). Traditional QA benchmarks like TriviaQA, NaturalQuestions, ELI5 and HotpotQA mainly study ``known unknowns'' with clear indications of both what information is missing, and how to find it to answer the question. Hence, good performance on these benchmarks provides a false sense of security. A yet unmet need of the NLP community is a bank of non-factoid, multi-perspective questions involving a great deal of unclear information needs, i.e. ``unknown uknowns''. We claim we can find such questions in search engine logs, which is surprising because most question-intent queries are indeed factoid. We present Researchy Questions, a dataset of search engine queries tediously filtered to be non-factoid, ``decompositional'' and multi-perspective. We show that users spend a lot of ``effort'' on these questions in terms of signals like clicks and session length, and that they are also challenging for GPT-4. We also show that ``slow thinking'' answering techniques, like decomposition into sub-questions shows benefit over answering directly. We release sim 100k Researchy Questions, along with the Clueweb22 URLs that were clicked.

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.

Procedural generation of initial states of state-space search problems have applications in human and machine learning as well as in the evaluation of planning systems. In this paper we deal with the task of generating hard and solvable initial states of Sokoban puzzles. We propose hardness metrics based on pattern database heuristics and the use of novelty to improve the exploration of search methods in the task of generating initial states. We then present a system called Beta that uses our hardness metrics and novelty to generate initial states. Experiments show that Beta is able to generate initial states that are harder to solve by a specialized solver than those designed by human experts.

Rebus puzzles, visual riddles that encode language through imagery, spatial arrangement, and symbolic substitution, pose a unique challenge to current vision-language models (VLMs). Unlike traditional image captioning or question answering tasks, rebus solving requires multi-modal abstraction, symbolic reasoning, and a grasp of cultural, phonetic and linguistic puns. In this paper, we investigate the capacity of contemporary VLMs to interpret and solve rebus puzzles by constructing a hand-generated and annotated benchmark of diverse English-language rebus puzzles, ranging from simple pictographic substitutions to spatially-dependent cues ("head" over "heels"). We analyze how different VLMs perform, and our findings reveal that while VLMs exhibit some surprising capabilities in decoding simple visual clues, they struggle significantly with tasks requiring abstract reasoning, lateral thinking, and understanding visual metaphors.

Rebuses are puzzles requiring constrained multi-step reasoning to identify a hidden phrase from a set of images and letters. In this work, we introduce a large collection of verbalized rebuses for the Italian language and use it to assess the rebus-solving capabilities of state-of-the-art large language models. While general-purpose systems such as LLaMA-3 and GPT-4o perform poorly on this task, ad-hoc fine-tuning seems to improve models' performance. However, we find that performance gains from training are largely motivated by memorization. Our results suggest that rebus solving remains a challenging test bed to evaluate large language models' linguistic proficiency and sequential instruction-following skills.