Puzzle

Despite recent advances in large language models (LLMs), performing logically consistent deductive reasoning over extended interactions remains challenging. Tasks that require integrating evidence across multiple reasoning steps, maintaining consistency with prior inferences, and updating beliefs under new constraints can surface limitations in current models while providing a useful testbed for evaluating reasoning enhancements. In this paper, we implement a text-based, multi-agent version of the classic board game Clue as an environment to evaluate multi-step, agentic deductive reasoning. In this setting, agents must infer hidden information from a sequence of observations, maintain consistency across turns, and reason over an evolving set of logical constraints. We instantiate six LLM-based agents (GPT-4o-mini and Gemini-2.5-Flash) as players that engage in turn-based gameplay; using three agents per model family, we establish baseline performance across repeated games. We then introduce a tool-augmented approach in which a structured possibility matrix converts implicit game state from generated reasoning logs into an explicit representation of remaining possibilities. The possibility matrix encodes extended-turn memory and deductive constraints, offloading these tasks from the agent. We compare this approach against the baseline to evaluate how tool augmentation supports reasoning quality and task success for autonomous agents in a strategic reasoning environment.

Structured visual reasoning, such as image puzzles, demands fine-grained visual perception, an ability current Vision Language Models (VLMs) lack. VLMs built on CLIP-based ViT backbones trade fine-grained detail for high-level semantics, and we show this loss propagates downstream. To recover it, we fuse DINOv3 and CleanDIFT representations into a perception encoder (DiffusedDINO) and align it with RoBERTa-L, yielding a text-aligned model TDDN that preserves this perceptual advantage: with frozen backbones and only $\sim$590K alignment pairs, TDDN matches CLIP on image-text retrieval, surpassing it on three of four settings. It does so while more than tripling CLIP's dense-prediction accuracy (ADE20K 5.20 $\to$ 18.11 mIoU, COCO-Stuff 7.35 $\to$ 24.44), despite CLIP's massive training corpus. TDDN leads on segmentation benchmarks among general-purpose contrastive encoders, including SigLIP$\,$2. We further introduce Puzzle Perception, a segmentation and visual question answering dataset that probes fine-grained spatial understanding, on which TDDN doubles CLIP's segmentation accuracy (11.04 $\to$ 22.51 mIoU).

The Tower of Hanoi is a simple planning puzzle that in prior work has proven challenging for large reasoning models (LRMs). Current models solve the standard formulation of the puzzle, but still struggle with the flat-to-flat variant (where initial and goal states are not restricted to have all rings on a single peg). This paper presents an in-depth study of how both small, in-house Transformers and large, third-party LRMs solve this task. To understand the failures mechanistically, we first train small Transformers from scratch on precomputed solution traces. Using a variety of interpretability techniques, we show that these Transformers develop an emergent world model: a linearly decodable, geometrically faithful representation of the puzzle's state space (the Sierpinski triangle), that is causally involved in solving the puzzles. Second, we return to the large LLMs and apply our techniques to two frontier reasoning models, Qwen3.6-27B and DeepSeek-R1-Distill-Qwen-32B, that attempt to solve the task through extended chain-of-thought. Surprisingly, we find that both models encode the Sierpinski world model near-perfectly at the end of the prompt, and yet fail at the majority of tasks when there are more than 3 rings. We locate the source of this failure in the decaying representation of the world model. We probe for the representation at different stages during planning, and establish causality by showing that performance can be improved by injecting the prompt-time representation at inference. The failure of the models is thus one of maintenance of the required representations, not their absence, and performance is at least partially recoverable. These results thus reframe the reported collapse in performance from prior work: current Large Reasoning Models build a world model, and then lose it.

Jigsaw puzzle solving requires jointly reasoning about visual content and geometric constraints, yet existing benchmarks use rectangular cuts that create ambiguous ground truth in texture-repeated regions. We introduce \textit{\ours{}}, a benchmark with tab-and-blank interlocking pieces where geometric constraints provide strong local compatibility requirements that, combined with visual content, yield unambiguous ground truth. Across 95K instances at four grid densities (4$\times$4 to 16$\times$16), we find that \textbf{zero-shot VLMs largely lack geometric reasoning}: only one of five frontier models (GPT-5.5) exceeds random baseline on 4$\times$4 puzzles, while all others perform at chance level. While supervised fine-tuning achieves $>$97% on 4$\times$4, \textbf{all models collapse on larger grids}: GPT-5.5 drops from 70% to near-random on 8$\times$8, and even fine-tuned models fall below 5% on 12$\times$12. This ``scaling cliff'' suggests current architectures cannot maintain consistent constraint satisfaction as the number of pieces increases. \ours{} establishes scalable geometric reasoning as an open challenge for vision-language models.

Chain-of-thought (CoT) prompting can fail severely on constraint-dense logical reasoning tasks, where unverified errors accumulate silently across steps. We introduce SymStep: an LLM makes one atomic claim at a time (DEDUCE: Alice, pet, Cat), then a lightweight constraint propagator checks the claim for consistency with prior accepted deductions, rejects contradictions, and cascades implied facts automatically. SymStep+G additionally provides MRV guidance after each accepted step, directing the LLM toward the most constrained unresolved variable. On a 35-puzzle retained subset of ZebraLogicBench, a benchmark of 1,000 Einstein-style logic puzzles, Direct and CoT both achieve 0%, while SymStep+G reaches 97%. On AR-LSAT analytical reasoning problems, SymStep achieves 100% vs. CoT's 87%. On LGP-14, SymStep+G achieves 100% vs. 0% for CoT and Logic-LM, the strongest prior symbolic+LLM baseline we compare against. Ablation studies reveal that MRV guidance is a key mechanism for reducing directionless cycling, while consistency checking provides a safety net against explicit contradictions. Across six benchmarks spanning five task domains, SymStep variants match or exceed every baseline on constraint-dense and arithmetic tasks. Experiments on AQUA-RAT algebra confirm the advantage is constraint-density-specific.

Chess is a two player strategic game that is embedded in classical AI culture as it was once the frontier for intelligent behaviour. There was the silent assumption that the advent of computer engines that play better than the best humans will extinguish interest in the game. However, the opposite has come to pass, with a growing following for the game. A lot of the computational resources are now centered around training of players, where the engine output is just one aspect. Access to past games is also an essential part, both in knowing what games a specific player has played previously, and also which continuations at a certain position have led to victory more often for each of the two colour players. We present Chess_db a suite of logic programming tools that can effectively manipulate games both in memory and via creating back end databases. In particular, we provide versatile code that creates databases from PGN (portable game notation) game files and explore the suitability of open source key-value databases for storing position tables that provide near-instant access to information pertaining to substantially large number of games.

Neural solvers are built to deduce, branch, and revise intermediate states. The Lattice Deduction Transformer (LDT) appears to do exactly that. In clue-rich Sudoku, it does not: one forward pass commits essentially the entire grid (every blank cell on standard 6x6, 94-96% on augmented 9x9), turning the iterative solver into a one-shot predictor wrapped in an exact verifier. All hard-slice failures are decided before search begins, when the first pass confidently deletes a value required by the true solution. We call this first-pass poisoning. Adding learned branching, MRV, backtracking, value exclusion, and shared nogoods (CoLT) does not change which Sudoku instances are solved; it cuts repeated invalid derivations 1,497-fold. At the frozen training budget, constraint-graph attention alone matches full-CoLT accuracy, while positional tables recover only under substantially longer training, indicating an optimization and sample-efficiency advantage rather than an absolute capacity difference. The diagnosis predicts two effective interventions. Digit-permutation augmentation raises 9x9 accuracy from below 1% to 96.5 +/- 0.3 across three training seeds on a symmetry-disjoint split. Test-time union over symmetry-transformed passes raises all three hard-slice checkpoints from 72.8-78.9% to 100% without retraining. On from-scratch graph coloring, one-shot behavior disappears and search changes accuracy. In clue-rich completion, LDT-like systems are one-shot amortized predictors rather than learned search procedures: accuracy is determined by calibration and symmetry, while search primarily removes computational waste.

Oscillatory Neural Networks (ONNs) present an attractive physics-based computing paradigm rooted in the dynamics of a network of typically fully coupled oscillators aiming to minimize an underlying energy function. In this paper, we propose an ONN-based solver for one well-known constrained combinatorial optimization problem, namely a Sudoku, by formulating the problem as a Graph Coloring problem. By modifying the already existing Graph Coloring solver to a computationally cheaper version and introducing an additional term ensuring the fulfillment of the Sudoku constraints, our solver is shown to significantly outperform the existing HNN- and ONN solvers in terms of accuracy. In particular, we are able to achieve nearly flawless accuracies on $4 \times 4$ as well as rather high accuracies on $9 \times 9$ Sudoku puzzles for different numbers of unknown digits.

We present cayleyR, an R package for solving permutation puzzles by detecting cycle intersections in Cayley graphs. The core algorithm performs an iterative bidirectional search: from both the initial and target permutation states, random operation sequences generate cycles in the Cayley graph of the symmetric group Sn; their intersection yields a connecting path. When no direct intersection is found, a distance-guided bridge selection narrows the gap, and the process repeats. The package targets the TopSpin(n,k) puzzle, whose state space is a Cayley graph of Sn generated by a cyclic shift and a prefix reversal. We describe the mathematical framework, the algorithm, and its implementation, which combines a C++ hash-indexed state store with optional Vulkan GPU acceleration. The software is publicly available on CRAN.

Vision--Language Models (VLMs) have recently demonstrated promising performance on structured visual reasoning tasks, including grid-based puzzles. However, despite strong perceptual capabilities, these models lack explicit mechanisms for enforcing logical consistency and frequently generate assignments that violate underlying constraints. In this paper, we propose a neuro-symbolic approach that integrates formal constraint reasoning into the VLM solving process via a Maximum Satisfiability (MaxSAT) oracle. Rather than computing solutions directly, the symbolic component acts as a consistency validator and refinement engine. Candidate placements generated by the VLM are encoded as soft clauses in a partial MaxSAT formulation, while Sudoku constraints remain hard clauses. When inconsistencies arise, the MaxSAT solver identifies a largest mutually consistent subset of assignments, which is then translated into structured textual and visual feedback to guide subsequent refinements. We evaluate our approach on a Sudoku dataset across multiple open-source and closed-access VLMs. Results show that MaxSAT-based feedback improves logical consistency and increases the number of solved instances, particularly in full-board refinement mode. These findings demonstrate that symbolic optimisation can enhance the reliability of vision-language reasoning.

Accurately modeling and understanding player experience is crucial for designing engaging puzzle games. To achieve this, a common approach involves collecting diverse user data to train predictive playtesting models that mimic player behavior. However, existing data-driven methods often lack the ability to capture the full range of player strategies and require extensive feature engineering and network architecture modeling. This limitation becomes particularly evident when new game mechanics or features are introduced, which necessitate continual adjustments to the models. To addrss these challenges, we propose a more generalized representation that reduces - or even eliminates - the need for ongoing feature-engineering maintenance. Specifically, we investigate two general-purpose network architectures: (a) a transformer-based model (BERT) and (b) a graph attention model (GAT), both of which are designed to effectively capture the relational structure of Candy Crush Saga (CCS) game boards. Our experiments compare these approaches to Convolutional Neural Networks (CNN) baselines, revealing better performance on challenging board configurations and underscoring the benefits of our generalizable representation.

Compositional generalization, the ability to understand and produce novel combinations of known components, remains a fundamental challenge for modern artificial intelligence. While few benchmarks exist, many focus on linguistic tasks and lack complex, explicit compositional structures. We introduce ClassicLogic, a new benchmark suite designed to evaluate an agent's ability to learn and compose problem-solving strategies. The benchmark consists of four classic logic puzzles: Sudoku, KenKen, Kakuro, and Futoshiki. Its core innovation is a hierarchical, explicit knowledge base for each game, where complex solving strategies are formally defined as compositions of simpler, foundational strategies. This structure allows for fine-grained evaluation of an agent's reasoning capabilities, from learning basic rules to applying multi-step compositional strategies to solve puzzles of increasing, mathematically validated difficulty. The open-source benchmark provides a challenging new testbed for advancing neuro-symbolic and other advanced AI reasoning systems.

The Muddy Children Puzzle is a puzzle about knowledge and ignorance that has been inspiring for the development of epistemic logic. Who came up with it first? This is unclear. We trace the origin of the Muddy Children Puzzle through logical and literary publications over the past two centuries. The puzzle inspired a numerous variations such as involving numbers or coloured hats. We also present a novel hats puzzle involving self-reference.

Robot manipulation of physical puzzles is important for automatic assembly and disassembly tasks. However, to enable robots to solve physical puzzles, manipulation skills need to be learned, which requires large training datasets, the generation of which is often time consuming and tedious. To overcome this problem, we propose the Physical Robot Manipulation Puzzle Generation framework (PhyRoGen), which leverages procedural content generation (PCG) for automated generation of synthetic datasets of manipulation puzzles. PhyRoGen is a general-purpose puzzle generator, which can generate physical puzzles with interlocking object dependencies, where one articulated object must be manipulated before another can be moved. Based upon PhyRoGen, we define six concrete generators which we use to generate 24 physical puzzles. By using a benchmarking framework, we are able to solve all puzzles in 1 to 300 seconds using sampling-based planning algorithms. Finally, we demonstrate that every generated puzzle is manipulatable by using a KUKA LBR iiwa robot in a physical simulation. This shows that our framework is able to procedurally generate unique, solvable robot manipulation puzzles, which is a crucial ingredient to benchmark manipulation algorithms and to develop robust foundation models.

Multi-turn LLM serving accumulates dialogue history whose Key-Value (KV) cache grows with every turn and every user, quickly exceeding the model weights themselves and making memory -- not compute -- the binding constraint on throughput. Non-uniform KV compression, which allocates heterogeneous budgets across attention heads, preserves accuracy far better than uniform schemes, yet remains impractical: modern serving stacks assume identical KV lengths across heads, so heterogeneity traps freed memory as page fragmentation, spends up to 25% of prefill time reclaiming scattered pages, and skews GPU workloads that inflate decode latency by up to $1.7\times$ or burn 15--20% of each decode step on re-planning. We observe that this heterogeneity need not be discovered at runtime: head-wise retention follows a two-level structural regularity -- an input-invariant head ranking with narrowly bounded per-head ratios -- that can be calibrated offline from as few as 50 samples. Building on this insight, we present Tangram, a serving framework that statically resolves what prior systems handle dynamically: Budget Reservation fixes each head's post-compression footprint at scheduling time, eliminating page reclamation; Ragged Paging clusters similar-budget heads into independent page tables, turning fragmentation into reclaimable memory; and Ahead-of-Time Load Balancing precomputes balanced GPU partitions with zero runtime planning. Implemented on vLLM, Tangram serves as a drop-in substrate for existing non-uniform compression methods, matching their accuracy while improving end-to-end throughput by up to $2.6\times$ over the full-KV baseline. Our implementation is publicly available at https://github.com/aiha-lab/TANGRAM.

Multi-party dialogue is a critical setting for studying collaborative reasoning and decision-making, yet existing datasets rarely focus on structured, in-depth complex reasoning tasks. We introduce DeliChess, a novel dataset of group deliberation dialogues in which participants collaboratively solve multiple-choice chess puzzles. Each group first completes the puzzle individually, then engages in a multi-party discussion before submitting a revised collective answer. The dataset includes 107 dialogues with full transcripts, pre- and post-discussion choices, and metadata on puzzle difficulty and move quality. We evaluate performance using three metrics based on chess engine evaluations, and find that deliberation significantly improves group accuracy. We further analyse the role of probing utterances (i.e., messages that elicit proposals, justifications, or strategic reflection) using a classifier trained on prior deliberation data. While probing makes group performance more variable after discussion, it does not consistently lead to better performance. Our dataset offers a rich testbed for modelling group reasoning, dialogue dynamics, and the resolution of differing perspectives and opinions in a well-defined strategic domain.

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.

Sudoku is a representative constraint satisfaction problem that requires global structural reasoning under strict discrete constraints. The existing works of solving Sudoku mainly focus on two dominant approaches, i.e., traditional heuristic and deep learning solver. However, they suffer from two complementary limitations: learning-based solvers lack hard correctness guarantees, while complete symbolic solvers are still prone to long-tail search. To address these shortcomings, we propose a novel diffusion model-guided approach, termed as DiBS, for the branch selection search process. Specifically, DiBS keeps the symbolic solver complete and uses the diffusion model as a branch-ordering guide. The core method is ranking candidate values under the current partial assignment and lightweight consistency signal. Furthermore, we provide an in-depth theoretical proof to reveal how it works and why it works. Experiments on the challenging Royle 17-clue Sudoku benchmark show that our DiBS substantially reduces search cost relative to strong heuristic baselines, especially in nodes, backtracks, and long-tail percentiles. Besides, these results confirm that learned global guidance is effective on hard instances where branch-order mistakes are most expensive. All codes are available at https://github.com/shanxierdan/DiBS.

Many learning problems require uncovering a hidden ordering that reveals structure in unordered data, such as monotonicity in sorting or spatial continuity in jigsaw reconstruction. In these settings, permutations can be learned as latent operators by optimizing objectives defined directly on the reordered output, often without access to ground-truth orderings. Differentiable relaxations such as Gumbel-Sinkhorn make this approach practical by approximating permutation matrices with doubly stochastic matrices. However, learning from structure without supervision induces a non-uniform uncertainty: some assignments become confident early, while others remain ambiguous. Existing methods control this process using a single global temperature, forcing all assignments to sharpen or diffuse simultaneously and leading to instability at scale. We introduce an entropy-adaptive formulation of Gumbel-Sinkhorn that locally modulates temperature based on assignment uncertainty. This allows confident assignments to discretize early while preserving exploration where uncertainty remains. Across sorting and jigsaw reconstruction tasks and in routing-style settings, adaptive entropy control improves training stability and final permutation quality relative to fixed-temperature baselines, particularly as problem size and assignment ambiguity increase.

The rapid adoption of Generative AI, including LLM-based chatbots like ChatGPT, has highlighted the need for accessible ways to support public understanding and AI literacy. To address this need, we introduce a game-based, interactive approach in the form of a jigsaw puzzle whose completed image is a comic-based infographic illustrating the workings, capabilities, limitations, and societal implications of these technologies. Each comic sketch also functions as a standalone informational card, providing focused explanations of specific facets of AI use, design, and impact. The visual content was created in a live collaborative session with a professional illustrator and a multidisciplinary group of experts and non experts, combining structured knowledge with informal, exploratory reflections shared during the discussion. By integrating hands-on assembly, visual storytelling, and collaborative interaction, the puzzle provides an engaging and playful tool for exploring the mechanisms, perks, and perils of AI systems in informal learning contexts.

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.

Vision-Language(-Action) Models (VLMs) are increasingly applied to interactive environments, yet existing benchmarks often overlook the complex physical reasoning required for point-and-click puzzle games. This paper introduces Vision-Language Against The Incredible Machine (VLATIM), a benchmark designed to evaluate human-like logical problem-solving capabilities within the classic physics puzzle game The Incredible Machine 2 (TIM). Unlike existing benchmarks, VLATIM specifically targets the critical gap between high-level logical reasoning and continuous action spaces requiring precise mouse interactions. This benchmark is structured into five progressive parts, assessing capabilities that range from basic visual grounding and domain understanding to multi-step manipulation and full puzzle solving. Our results reveal a significant disparity between reasoning and execution. While large proprietary models demonstrate superior planning abilities, they struggle with precise visual grounding. Consequently, they do not yet show human-like problem-solving capabilities.

Yes. We find that large multimodal models develop mental imagery when solving spatial puzzles, and they do imagine sheep when solving sheep puzzles. We fine-tune a Qwen3.5 VLM to solve twelve diverse visual reasoning tasks -- including tangram, jigsaw, sokoban, 3D mental rotation, and rush hour -- that require understanding geometry, spatial relationships, and the consequences of actions. By supervising the model to predict the open-loop sequence of actions to solve a puzzle from an initial state, we show that the model's activations after each action encode meaningful visual information about the intermediate state. This finding suggests that an imperfect visual world model begins to form as a byproduct of learning to select correct actions, in the absence of any explicit visual supervision. Building on this observation, we propose two ways to sharpen and use the mental images formed by the model. We find that integrating as few as sixteen visual tokens per step into the chain of thought improves the average solve rate from 83% to 89%, with particularly strong gains on reasoning-heavy tasks such as jigsaw and 3D mental rotation.

Translation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain no distance information, making the estimation problem highly ill-conditioned and highly sensitive to corrupted observations. In this paper, we propose TriP, a triangle-based framework for robust translation averaging. TriP first infers local relative edge scales from triangle geometry, and then synchronizes the scales of overlapping triangles in the logarithmic domain to recover globally consistent edge lengths and camera locations. By leveraging higher-order consistency across triangles, the proposed method is robust to adversarial, cycle-consistent, and other structured corruptions. In addition, TriP avoids the collapse issue without requiring any extra anti-collapse constraints, since log-scale synchronization excludes the degenerate zero-scale solution by construction. These structural advantages enable a particularly strong theory for exact location recovery. On the practical side, TriP is fully parallelizable, computationally efficient, and naturally scalable to graphs with millions of cameras. Moreover, it outperforms all previous translation averaging methods by a large margin on both synthetic and real datasets.

The popular 2009 voxel based videogame, Minecraft, contains several distinct disciplines. One of which is "parkour," gameplay that focuses on traversing a world's environment with maximum efficiency. The Minecraft online community has turned the game's physics engine into dynamic puzzles, requiring players to masterfully manipulate motion mechanics through frame precise timing of keystrokes. Actions such as sprinting, sneaking, and mouse direction are all combined to clear specific difficult jumps. Through this project, we design a genetic algorithm to generate weights for a neural network to autonomously evaluate inputs for block distances, terrain, and obstacles to determine the most optimal pathing.

ARC-AGI-2 is a benchmark of human-intuitive visual puzzles that measures a machine's ability to generalize from limited examples, interpret symbolic meaning, and flexibly apply rules in varying contexts. In this paper, we discuss our approach to solving the ARC-AGI-2 puzzles with TinyLM, with additional fine-tuning at test time, including Test-Time-Training (TTT) and Products of Experts (POE). Our model achieves 96.1% accuracy on the training set and 21.7% accuracy on the evaluation set.

Conversational agents, such as ChatGPT and Doubao, have become essential daily assistants for billions of users. To further enhance engagement, these systems are evolving from passive responders to proactive companions. However, existing efforts focus on activation within ongoing dialogues, while overlooking a key real-world bottleneck. In the conversation initiation stage, users may have a vague need but no explicit query intent, creating a first-message barrier where the conversation holds before it begins. To overcome this, we introduce Conversation Starter Generation: generating personalized starters to guide users into conversation. However, unlike in-conversation stages where immediate context guides the response, initiation must operate in a cold-start moment without explicit user intent. To pioneer in this direction, we present IceBreaker that frames human ice-breaking as a two-step handshake: (i) evoke resonance via Resonance-Aware Interest Distillation from session summaries to capture trigger interests, and (ii) stimulate interaction via Interaction-Oriented Starter Generation, optimized with personalized preference alignment and a self-reinforced loop to maximize engagement. Online A/B tests on one of the world's largest conversational agent products show that IceBreaker improves user active days by +0.184% and click-through rate by +9.425%, and has been deployed in production.

Large language models often appear strong on symbolic and algorithmic tasks, yet this apparent strength can hide brittle behaviour when problems become longer, harder, or slightly out of distribution. A major limitation of current reasoning benchmarks is that many primarily test whether a model can produce a valid answer, while paying less attention to whether the solution is minimal, robust, and stable under controlled difficulty scaling. We introduce RecurrReason, a difficulty-controlled benchmark of four recurrent logic puzzles (Tower of Hanoi, River Crossing, Block World, and Checkers Jumping) with BFS-optimal trajectories and a single interpretable difficulty parameter $N \in \{1,\dots,10\}$, totalling 10{,}817 unique puzzles and 285{,}933 moves. We benchmark two Transformer families, an encoder-decoder model (T5-style) and a decoder-only model (GPT-2-style), under consistent data splits and evaluation criteria, training on $N{=}1$ to $7$ and evaluating on both held-out in-distribution instances and harder out-of-distribution instances at $N{=}8$ to $10$. Fine-tuned pre-trained T5 achieves 97.27% validation and 81.00% OOD accuracy on Block World; all models score 0.00% on River Crossing under all conditions. Failure mode analysis reveals that architecture is a stronger determinant of success than scale. Pre-training transfers only to puzzles with locally structured transition functions. Our code and dataset will be open-sourced upon acceptance.

Reinforcement learning has become a powerful approach for enhancing large language model reasoning, but faces a fundamental dilemma: training on easy problems can cause overfitting and pass@k degradation, while training on hard problems often results in sparse rewards. Recent question augmentation methods address this by prepending partial solutions as hints. However, uniform hint provision may introduce redundant information while missing critical reasoning bottlenecks, and excessive hints can reduce reasoning diversity, causing pass@k degradation. We propose \textbf{PieceHint}, a hint injection framework that strategically identifies and provides critical reasoning steps during training. By scoring the importance of different reasoning steps, selectively allocating hints based on problem difficulty, and progressively withdrawing scaffolding, PieceHint enables models to transition from guided learning to independent reasoning. Experiments on six mathematical reasoning benchmarks show that our 1.5B model achieves comparable average performance to 32B baselines while preserving pass@k diversity across all $k$ values.

Mixture-of-Experts (MoE) models have shown strong potential in scaling language models efficiently by activating only a small subset of experts per input. However, their widespread deployment remains limited due to the high memory overhead associated with storing all expert parameters, particularly as the number of experts increases. To address this challenge, prior works have explored expert dropping and merging strategies, yet they often suffer from performance drop at high compression ratios. In this paper, we introduce PuzzleMoE, a training-free MoE compression method that achieves both high accuracy and efficient inference through two key innovations: First, PuzzleMoE performs sparse expert merging by identifying element-wise weight redundancy and specialization. It uses a dual-mask to capture both shared and expert-specific parameters. Second, to avoid the overhead of storing binary masks and signs, PuzzleMoE introduces a bit-packed encoding scheme that reuses underutilized exponent bits, enabling efficient MoE inference on GPUs. Extensive experiments demonstrate that PuzzleMoE can compress MoE models by up to 50% while maintaining accuracy across various tasks. Specifically, it outperforms prior MoE compression methods by up to 16.7% on MMLU at 50% compression ratio, and achieves up to 1.28\times inference speedup.

We create high-quality datasets for LLM evaluation of logical reasoning skills across nine different languages, which have been manually checked by fluent speakers. The datasets consist of so-called zebra puzzles, and we analyse different ways of tuning the difficulty of the puzzles to fit modern LLMs. This includes the size of the puzzle (number of objects and number of clues), as well as a novel addition of red herring clues containing only irrelevant information. We show that presence of red herrings indeed makes the puzzles significantly harder for the models, and 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. We analyse whether LLM performance of these are sensitive to the language, the cultural sensitivity of the puzzle theme, and the choice of clue types. These analyses are conducted with English and Danish, where we show that there is no significant difference for either of these three aspects, at least for the OpenAI models GPT-4o mini and o3-mini, chosen as representative non-reasoning and reasoning models, respectively. We publish the datasets for each of the nine languages for the identified sizes 2x3 and 4x5. We also publish the code used to generate the puzzles, which can be used to extend the benchmark into more languages.

While Large Language Model (LLM) agents are often approached from the angle of action planning/generation to accomplish a goal (e.g., given by language descriptions), their abilities to collaborate with each other to achieve a joint goal are not well explored. To address this limitation, this paper studies LLM agents in task collaboration, particularly under the condition of information asymmetry, where agents have disparities in their knowledge and skills and need to work together to complete a shared task. We extend Einstein Puzzles, a classical symbolic puzzle, to a table-top game. In this game, two LLM agents must reason, communicate, and act to satisfy spatial and relational constraints required to solve the puzzle. We apply a fine-tuning-plus-verifier framework in which LLM agents are equipped with various communication strategies and verification signals from the environment. Empirical results highlight the critical importance of aligned communication, especially when agents possess both information-seeking and -providing capabilities. Interestingly, agents without communication can still achieve high task performance; however, further analysis reveals a lack of true rule understanding and lower trust from human evaluators. Instead, by integrating an environment-based verifier, we enhance agents' ability to comprehend task rules and complete tasks, promoting both safer and more interpretable collaboration in AI systems. https://github.com/Roihn/EinsteinPuzzles