When you purchase through links in our articles, we may earn a small commission. The price, starting at around $3,199, seems high at first but is justified by the unusually robust technology, the long-lasting LiFePO4 battery, the high coverage rate, and the extreme off-road capability. Robotic mowers without boundary wires have long been standard, but the Lymow One Plus takes a radically different approach. Instead of wheels and a compact design, the manufacturer has opted for caterpillar tracks, a front-mounted dual cutting deck, and high engine power. We tested the system on hilly, uneven terrain and checked whether the tank-like appearance is more than just marketing hype.

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Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed constants for specific scenarios. However, they rely on domain expertise and fail to consider the instance-wise features for individual problems, limiting their performance. In contrast, machine learning (ML) approaches, though promising, are hindered by high inference costs and limited interpretability. To combine the strengths of both approaches, we propose a symbolic discovery framework-namely, Symbolic Matrix Preconditioning (SymMaP)-to learn efficient symbolic expressions for preconditioning parameters. Specifically, we employ a neural network to search the high-dimensional discrete space for expressions that can accurately predict the optimal parameters. The learned expression allows for high inference efficiency and excellent interpretability (expressed in concise symbolic formulas), making it simple and reliable for deployment. Experimental results show that SymMaP consistently outperforms traditional strategies across various benchmarks 1.

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The Johnson-Lindenstrauss (JL) lemma is a cornerstone of dimensionality reduction in Euclidean space, but its applicability to non-Euclidean data has remained limited. This paper extends the JL lemma beyond Euclidean geometry to handle general dissimilarity matrices that are prevalent in real-world applications. We present two complementary approaches: First, we show the JL transform can be applied to vectors in pseudo-Euclidean space with signature (p,q), providing theoretical guarantees that depend on the ratio of the (p,q)norm and Euclidean norm of two vectors, measuring the deviation from Euclidean geometry. Second, we prove that any symmetric hollow dissimilarity matrix can be represented as a matrix of generalized power distances, with an additional parameter representing the uncertainty level within the data. In this representation, applying the JL transform yields multiplicative approximation with a controlled additive error term proportional to the deviation from Euclidean geometry. Our theoretical results provide fine-grained performance analysis based on the degree to which the input data deviates from Euclidean geometry, making practical and meaningful reduction in dimensionality accessible to a wider class of data.

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SOLIDGEO, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry.

Web navigation is a unique domain that can automate many repetitive real-life tasks beyond and typical is challenging multimodal as lar it ge requires language long-horizon model (MLLM) sequential tasks.

We propose KNOTGYM, an interactive environment for complex, spatial reasoning and manipulation.

Large language models (LLMs) are increasingly fine-tuned on domain-specific datasets to support applications in fields such as healthcare, finance, and law. These fine-tuning datasets often have sensitive and confidential dataset-level properties -- such as patient demographics or disease prevalence--that are not intended to be revealed. While prior work has studied property inference attacks on discriminative models (e.g., image classification models) and generative models (e.g., GANs for image data), it remains unclear if such attacks transfer to LLMs. In this work, we introduce PropInfer, a benchmark task for evaluating property inference in LLMs under two fine-tuning paradigms: question-answering and chat-completion. Built on the ChatDoctor dataset, our benchmark includes a range of property types and task configurations. We further propose two tailored attacks: a prompt-based generation attack and a shadow-model attack leveraging word frequency signals.

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