Grand Theft Auto VI, left, and Lenny Kravitz as the villain in 007 First Light. Grand Theft Auto VI, left, and Lenny Kravitz as the villain in 007 First Light. Live your mountaineering fantasies and brave the elements in a wonderfully illustrated climbing game. You must carefully place climber Aava's hands and feet to make your way up a forbidding mountain, camping on ledges and bandaging her fingers as you go. Like real climbing, it is challenging and somewhat brutal.

We present a theoretical framework for an Exam Readiness Index (ERI): a composite, blueprint-aware score R in [0,100] that summarizes a learner's readiness for a high-stakes exam while remaining interpretable and actionable. The ERI aggregates six signals -- Mastery (M), Coverage (C), Retention (R), Pace (P), Volatility (V), and Endurance (E) -- each derived from a stream of practice and mock-test interactions. We formalize axioms for component maps and the composite, prove monotonicity, Lipschitz stability, and bounded drift under blueprint re-weighting, and show existence and uniqueness of the optimal linear composite under convex design constraints. We further characterize confidence bands via blueprint-weighted concentration and prove compatibility with prerequisite-admissible curricula (knowledge spaces / learning spaces). The paper focuses on theory; empirical study is left to future work.

We propose a neural network-based computational framework for the simultaneous optimization of structural topology, curved layers, and path orientations to achieve strong anisotropic strength in fiber-reinforced thermoplastic composites while ensuring manufacturability. Our framework employs three implicit neural fields to represent geometric shape, layer sequence, and fiber orientation. This enables the direct formulation of both design and manufacturability objectives - such as anisotropic strength, structural volume, machine motion control, layer curvature, and layer thickness - into an integrated and differentiable optimization process. By incorporating these objectives as loss functions, the framework ensures that the resultant composites exhibit optimized mechanical strength while remaining its manufacturability for filament-based multi-axis 3D printing across diverse hardware platforms. Physical experiments demonstrate that the composites generated by our co-optimization method can achieve an improvement of up to 33.1% in failure loads compared to composites with sequentially optimized structures and manufacturing sequences.

Difficult problems, which often result in long reasoning traces, are widely recognized as key factors for enhancing the performance of reasoning models. However, such high-challenge problems are scarce, limiting the size of available datasets. In this paper, we propose a simple method to decouple the reliance on problem difficulty. First, we empirically demonstrate that reasoning length, rather than problem difficulty, primarily influences the performance of trained models. Second, we identify a scaling law on reasoning length, showing that model performance increases in a log-linear fashion as the reasoning data length grows. Finally, we introduce a straightforward technique to generate reasoning data of arbitrary length, and show that synthesized data is effective for training reasoning models. After fine-tuning the Qwen2.5-32B-Instruct language model on our Long1K dataset, we present our model, Long1K-32B, which achieves remarkable performance with only 1,000 training samples, achieving 95.6\% accuracy on MATH, and 71.1\% on GPQA outperforming DeepSeek-R1-Distill-Qwen-32B. The model, code, and dataset are all open-sourced, available at https://huggingface.co/ZTss/LONG1.

Low-Rank Adaptation (LoRA) has emerged as a widely adopted technique in text-to-image models, enabling precise rendering of multiple distinct elements, such as characters and styles, in multi-concept image generation. However, current approaches face significant challenges when composing these LoRAs for multi-concept image generation, resulting in diminished generated image quality. In this paper, we initially investigate the role of LoRAs in the denoising process through the lens of the Fourier frequency domain. Based on the hypothesis that applying multiple LoRAs could lead to "semantic conflicts", we find that certain LoRAs amplify high-frequency features such as edges and textures, whereas others mainly focus on low-frequency elements, including the overall structure and smooth color gradients. Building on these insights, we devise a frequency domain based sequencing strategy to determine the optimal order in which LoRAs should be integrated during inference. This strategy offers a methodical and generalizable solution compared to the naive integration commonly found in existing LoRA fusion techniques. To fully leverage our proposed LoRA order sequence determination method in multi-LoRA composition tasks, we introduce a novel, training-free framework, Cached Multi-LoRA (CMLoRA), designed to efficiently integrate multiple LoRAs while maintaining cohesive image generation. With its flexible backbone for multi-LoRA fusion and a non-uniform caching strategy tailored to individual LoRAs, CMLoRA has the potential to reduce semantic conflicts in LoRA composition and improve computational efficiency. Our experimental evaluations demonstrate that CMLoRA outperforms state-of-the-art training-free LoRA fusion methods by a significant margin -- it achieves an average improvement of $2.19\%$ in CLIPScore, and $11.25\%$ in MLLM win rate compared to LoraHub, LoRA Composite, and LoRA Switch.

Large Language Models (LLMs) have surprised the scientific community and even their creators by exhibiting emergent abilities once thought to be uniquely human, such as advanced cognition and reasoning (1-6), although the full extent of these accomplishments is debated (3, 7-10). These capabilities align with the rational and deliberative aspects of human nature, but humans are not purely rational creatures, and it is unclear whether LLMs will mimic a broader spectrum of human psychological tendencies. Here we test whether OpenAI's GPT-4o replicates behaviors associated with the human tendency toward cognitive consistency as well as human sensitivity to choice, characterized by greater attitude shifts when the behaviors inducing these changes are freely chosen. Decades of research demonstrate that humans will irrationally twist their attitudes to align with behaviors they were induced to perform. For example, consider an individual who opposes single-payer healthcare, but volunteers, in response to a request for help, to craft an argument in favor of the policy. Rationally, this individual's attitude toward single-payer healthcare should not move in a more supportive direction; they should be able to discriminate between their genuine attitude and the opposing one that they have articulated only to be helpful.

This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the experiments, two beam-like specimens, one aluminum and one IDOX/Estane composite, are subjected to shear wave excitation in the low frequency regime and the response is measured in the form of particle velocity on the specimen surface. The WSINDy for PDEs algorithm is applied to the resulting spatio-temporal data to discover the effective dynamics of the specimens from a family of potential PDEs. The discovered PDE is of the recognizable Euler-Bernoulli beam model form, from which the Young's modulus for the two materials are estimated. An ensemble version of the WSINDy algorithm is also used which results in information about the uncertainty in the PDE coefficients and Young's moduli. The discovered PDEs are also simulated with a finite element code to compare against the experimental data with reasonable accuracy. Using full-field experimental data and WSINDy together is a powerful non-destructive approach for learning unknown governing equations and gaining insights about mechanical systems in the dynamic regime.

This paper investigates the optimization of 2D and 3D composite structures using machine learning (ML) techniques, focusing on fracture toughness and crack propagation in the Double Cantilever Beam (DCB) test. By exploring the intricate relationship between microstructural arrangements and macroscopic properties of composites, the study demonstrates the potential of ML as a powerful tool to expedite the design optimization process, offering notable advantages over traditional finite element analysis. The research encompasses four distinct cases, examining crack propagation and fracture toughness in both 2D and 3D composite models. Through the application of ML algorithms, the study showcases the capability for rapid and accurate exploration of vast design spaces in composite materials. The findings highlight the efficiency of ML in predicting mechanical behaviors with limited training data, paving the way for broader applications in composite design and optimization. This work contributes to advancing the understanding of ML's role in enhancing the efficiency of composite material design processes.

The Tsetlin Machine (TM) has achieved competitive results on several image classification benchmarks, including MNIST, K-MNIST, F-MNIST, and CIFAR-2. However, color image classification is arguably still in its infancy for TMs, with CIFAR-10 being a focal point for tracking progress. Over the past few years, TM's CIFAR-10 accuracy has increased from around 61% in 2020 to 75.1% in 2023 with the introduction of Drop Clause. In this paper, we leverage the recently proposed TM Composites architecture and introduce a range of TM Specialists that use various image processing techniques. These include Canny edge detection, Histogram of Oriented Gradients, adaptive mean thresholding, adaptive Gaussian thresholding, Otsu's thresholding, color thermometers, and adaptive color thermometers. In addition, we conduct a rigorous hyperparameter search, where we uncover optimal hyperparameters for several of the TM Specialists. The result is a toolbox that provides new state-of-the-art results on CIFAR-10 for TMs with an accuracy of 82.8%. In conclusion, our toolbox of TM Specialists forms a foundation for new TM applications and a landmark for further research on TM Composites in image analysis.

This paper addresses the problem of composite synchronization and learning control in a network of multi-agent robotic manipulator systems with heterogeneous nonlinear uncertainties under a leader-follower framework. A novel two-layer distributed adaptive learning control strategy is introduced, comprising a first-layer distributed cooperative estimator and a second-layer decentralized deterministic learning controller. The first layer is to facilitate each robotic agent's estimation of the leader's information. The second layer is responsible for both controlling individual robot agents to track desired reference trajectories and accurately identifying/learning their nonlinear uncertain dynamics. The proposed distributed learning control scheme represents an advancement in the existing literature due to its ability to manage robotic agents with completely uncertain dynamics including uncertain mass matrices. This allows the robotic control to be environment-independent which can be used in various settings, from underwater to space where identifying system dynamics parameters is challenging. The stability and parameter convergence of the closed-loop system are rigorously analyzed using the Lyapunov method. Numerical simulations validate the effectiveness of the proposed scheme.