Large Reasoning Models (LRMs) achieve state-of-the-art performance in mathematics, code generation, and task planning. Inspired by the Language of Thought Hypothesis --which posits that human reasoning operates over a symbolic, compositional mental language called Mentalese--we introduce a cognitively motivated framework that trains models to reason in a similar compact style. Mentalese encodes abstract reasoning as ultra-compressed, structured tokens, enabling models to solve complex problems with far fewer steps. When applied to Mentalese-aligned models, SLPO achieves much larger compression rates by enabling compressed reasoning that preserves the benefits of detailed thinking without the computational overhead, allowing us to present the best-performing models at each compression level along the performance-efficiency Pareto frontier. Across mathematical benchmarks -- including AIME 2024 & 2025, Minerva-Math, OlympiadBench, Math500, and AMC -- our ORION models generate reasoning traces with 4-16 fewer tokens, achieve up to 5 lower inference latency, and reduce training costs by 7-9 relative to the base DeepSeek R1 Distilled model, while maintaining 90-98% of the baseline accuracy. ORION models also surpass Claude and ChatGPT -4o by up to 5% in accuracy while maintaining 2 compression. Our findings demonstrate Mentalese-style compressed reasoning offers a breakthrough toward human-like cognitive efficiency, opening new possibilities for real-time, cost-effective reasoning without sacrificing accuracy. The dotted curve indicates the Pareto frontier, which illustrates the trade-off between higher compression rates and loss in accuracy. Our proposed method, combining Mentalese alignment with SLPO, consistently lies on this frontier, identifying an optimal operating point that achieves a balance between accuracy and efficiency. Work done during internship at Hippocratic AI. Recent advances such as OpenAI o1 (OpenAI et al., 2024b) and DeepSeek R1 (DeepSeek-AI et al., 2025) have reshaped how we think about language model reasoning. By letting models "think before they answer," these systems dramatically improved credibility and performance--achievements that were once thought impossible for LLMs (Wu et al., 2024). Explicit reasoning has thus emerged as a central focus of LLM research (Xu et al., 2025).

Large Language Models (LLMs) have transformed artificial intelligence, offering profound opportunities for educational applications. However, their ability to provide fine-grained educational feedback for K-12 English writing remains underexplored. In this paper, we challenge the error analysis and pedagogical skills of LLMs by introducing the problem of Fine-grained Error Analysis for English Learners and present the Fine-grained Error ANalysis for English Learners (FEANEL) Benchmark. The benchmark comprises 1,000 essays written by elementary and secondary school students, and a well-developed English writing error taxonomy. Each error is annotated by language education experts and categorized by type, severity, and explanatory feedback, using a part-of-speech-based taxonomy they co-developed. We evaluate state-of-the-art LLMs on the FEANEL Benchmark to explore their error analysis and pedagogical abilities. Experimental results reveal significant gaps in current LLMs' ability to perform fine-grained error analysis, highlighting the need for advancements in particular methods for educational applications.

Many machine learning models perform well when making predictions within the training data range, but often struggle when required to extrapolate beyond it. Symbolic regression (SR) using genetic programming (GP) can generate flexible models but is prone to unreliable behaviour in extrapolation. This paper investigates whether adding synthetic data can help improve performance in such cases. We apply Kernel Density Estimation (KDE) to identify regions in the input space where the training data is sparse. Synthetic data is then generated in those regions using a knowledge distillation approach: a teacher model generates predictions on new input points, which are then used to train a student model. We evaluate this method across six benchmark datasets, using neural networks (NN), random forests (RF), and GP both as teacher models (to generate synthetic data) and as student models (trained on the augmented data). Results show that GP models can often improve when trained on synthetic data, especially in extrapolation areas. However, the improvement depends on the dataset and teacher model used. The most important improvements are observed when synthetic data from GPe is used to train GPp in extrapolation regions. Changes in interpolation areas show only slight changes. We also observe heterogeneous errors, where model performance varies across different regions of the input space. Overall, this approach offers a practical solution for better extrapolation. Note: An earlier version of this work appeared in the GECCO 2025 Workshop on Symbolic Regression. This arXiv version corrects several parts of the original submission.

We explore the possibility of exact algorithmic learning with gradient-based methods and introduce a differentiable framework capable of strong length generalization on arithmetic tasks. Our approach centers on Differentiable Finite-State Transducers (DFSTs), a Turing-complete model family that avoids the pitfalls of prior architectures by enabling constant-precision, constant-time generation, and end-to-end log-parallel differentiable training. Leveraging policy-trajectory observations from expert agents, we train DFSTs to perform binary and decimal addition and multiplication. Remarkably, models trained on tiny datasets generalize without error to inputs thousands of times longer than the training examples. These results show that training differentiable agents on structured intermediate supervision could pave the way towards exact gradient-based learning of algorithmic skills. Code available at \href{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}.

Recent progress in legged locomotion has allowed highly dynamic and parkour-like behaviors for robots, similar to their biological counterparts. Yet, these methods mostly rely on egocentric (first-person) perception, limiting their performance, especially when the viewpoint of the robot is occluded. A promising solution would be to enhance the robot's environmental awareness by using complementary viewpoints, such as multiple actors exchanging perceptual information. Inspired by this idea, this work proposes a multi-view depth-based locomotion framework that combines egocentric and exocentric observations to provide richer environmental context during agile locomotion. Using a teacher-student distillation approach, the student policy learns to fuse proprioception with dual depth streams while remaining robust to real-world sensing imperfections. To further improve robustness, we introduce extensive domain randomization, including stochastic remote-camera dropouts and 3D positional perturbations that emulate aerial-ground cooperative sensing. Simulation results show that multi-viewpoints policies outperform single-viewpoint baseline in gap crossing, step descent, and other dynamic maneuvers, while maintaining stability when the exocentric camera is partially or completely unavailable. Additional experiments show that moderate viewpoint misalignment is well tolerated when incorporated during training. This study demonstrates that heterogeneous visual feedback improves robustness and agility in quadrupedal locomotion. Furthermore, to support reproducibility, the implementation accompanying this work is publicly available at https://anonymous.4open.science/r/multiview-parkour-6FB8

Document visual question answering (DocVQA) requires models to jointly reason over textual content and spatial layout, yet current systems exhibit a sharp accuracy--efficiency trade-off: large teacher models achieve strong grounding but are too expensive for deployment, while compact students suffer substantial drops in localization performance. We propose DocVAL, a validated chain-of-thought distillation framework that transfers the spatial reasoning ability of a large teacher into a deployable student VLM through three key components: (1) teacher supervision with validation-time text detection to filter and denoise training signals, (2) a multi-module validator (VAL) that enforces answer correctness and geometric consistency while producing fine-grained, pixel-level error feedback, and (3) a two-stage student training scheme that first learns from validated CoT traces and then undergoes iterative refinement driven by VAL feedback. Our student (Gemma-3 12B) achieves 91.4\% ANLS and 82.4\% mAP on DocVQA as a pure VLM requiring no text detection or OCR at inference. Extensive ablations demonstrate that validated feedback contributes 6.3 mAP gain and iterative refinement accounts for 9.7 mAP improvement. We release 95k high-quality, validator-verified CoT traces to advance spatial reasoning research in document understanding.

Visual-Geometry Diffusion Policy (VGDP) is an imitation learning method that fuses 3D observations with 2D images through a Complementarity-Aware Fusion Module, which uses modality-wise dropout to enforce balanced use of RGB and geometry. This design yields substantial improvements in average performance, generalization, and robustness. VGDP is extensively evaluated in both simulation and the real world, covering a wide range of tasks and both visual and spatial randomizations. Abstract-- Imitation learning has emerged as a crucial approach for acquiring visuomotor skills from demonstrations, where designing effective observation encoders is essential for policy generalization. However, existing methods often struggle to generalize under spatial and visual randomizations, instead tending to overfit. T o address this challenge, we propose Visual-Geometry Diffusion Policy (VGDP), a multimodal imitation learning framework built around a Complementarity-Aware Fusion Module where modality-wise dropout enforces balanced use of RGB and point-cloud cues, with cross-attention serving as a lightweight interaction layer . Our experiments show that the expressiveness of the fused latent space is largely induced by the enforced complementarity from modality-wise dropout, with cross-attention serving primarily as a lightweight interaction mechanism rather than the main source of robustness. Across a benchmark of 18 simulated tasks and 4 real-world tasks, VGDP outperforms seven baseline policies with an average performance improvement of 39.1%.

Continual learning, one's ability to adapt to a sequence of tasks without forgetting previously acquired knowledge, remains a major challenge in machine learning and a key gap between artificial and human intelligence. While regularisation and replay perform well in vision, they lag behind multi-task learning for large language models (LLMs), especially at scale with many tasks. We revisit replay and argue that two failure modes drive this gap: selection (what to rehearse) and integration (how to consolidate new knowledge). To address selection, we propose Surprise-prioritised Replay (SuRe), a simple, architecture-agnostic rule that ranks and stores the most surprising (high Negative Log-Likelihood) sequences. SuRe achieves state-of-the-art performance in the Large Number of Tasks (LNT) setting and delivers the best overall average across both Standard CL and LNT benchmarks. To address integration, we add a dual-learner design with fast and slow LoRA adapters merged via an exponential moving average (EMA), enabling rapid adaptation while stabilising long-term knowledge. Combining SuRe with the dual learner yields further gains, including improvements of up to +5 accuracy points on LNT over prior SOTA. Ablation studies confirm that our proposed method remains robust under reduced replay frequency and small buffer size, demonstrating both effectiveness and sample efficiency. Taken together, our results establish replay as a strong baseline for continual LLM fine-tuning and demonstrate that surprise-based selection and slow-weight consolidation are complementary components for mitigating catastrophic forgetting.

Traditional pricing paradigms, once dominated by static models and rule-based heuristics, are increasingly being replaced by dynamic, data-driven approaches powered by machine learning algorithms. Despite their growing sophistication, most dynamic pricing algorithms focus on optimizing the price of each product independently, disregarding potential interactions among items. By neglecting these interdependencies in consumer demand across related goods, sellers may fail to capture the full potential of coordinated pricing strategies. In this paper, we address this problem by exploring dynamic pricing mechanisms designed explicitly for complementary products, aiming to exploit their joint demand structure to maximize overall revenue. We present an online learning algorithm considering both positive and negative interactions between products' demands. The algorithm utilizes transaction data to identify advantageous complementary relationships through an integer programming problem between different items, and then optimizes pricing strategies using data-driven and computationally efficient multi-armed bandit solutions based on heteroscedastic Gaussian processes. We validate our solution in a simulated environment, and we demonstrate that our solution improves the revenue w.r.t. a comparable learning algorithm ignoring such interactions.

Can language models (LMs) self-refine their own responses? This question is increasingly relevant as a wide range of real-world user interactions involve refinement requests. However, prior studies have largely tested LMs' refinement abilities on verifiable tasks such as competition math or symbolic reasoning with simplified scaffolds, whereas users often pose open-ended queries and provide varying degrees of feedback on what they desire. The recent advent of reasoning models that exhibit self-reflection patterns in their chains-of-thought further motivates this question. To analyze this, we introduce RefineBench, a benchmark of 1,000 challenging problems across 11 domains paired with a checklist-based evaluation framework. We evaluate two refinement modes: (1) guided refinement, where an LM is provided natural language feedback, and (2) self-refinement, where LMs attempt to improve without guidance. In the self-refinement setting, even frontier LMs such as Gemini 2.5 Pro and GPT-5 achieve modest baseline scores of 31.3% and 29.1%, respectively, and most models fail to consistently improve across iterations (e.g., Gemini-2.5-Pro gains only +1.8%, while DeepSeek-R1 declines by -0.1%). By contrast, in guided refinement, both proprietary LMs and large open-weight LMs (>70B) can leverage targeted feedback to refine responses to near-perfect levels within five turns. These findings suggest that frontier LMs require breakthroughs to self-refine their incorrect responses, and that RefineBench provides a valuable testbed for tracking progress.