通过仿真，我们发现并证明了凌乱的谐波多边形的好奇新的欧几里德特性和不变性。
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我们描述了平铺的“侧翼”三角形和常规六边形的好奇特性，包括（i）在固定六边形周围的侧翼的侧翼的普通突出（II）保护中的常见六边形（II）保护，（iii）能够建立无限的能力栅格或平铺，（iv）共聚焦抛物线的家庭编织成平铺，其（v）三个不同的焦点是等边的顶点。
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我们调查Poncelet $ N $ -GON系列的属性，刻在抛物线中，并围绕着焦点中心的圆圈。这些可以被认为是相对于恒定围绕的双重家庭的极性图像，使得双面载体含有圆形。我们派生了几个$ n $的闭合条件，并描述了大核，圆形，圆形和点，基因座等好奇的欧几里德属性，以及（也许是新的）保守量。
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我们提出了一个预测某些Poncelet三角形家族的三角形中心的轨迹是圆锥形的理论。我们认为（i）共聚焦对（I）分叉的家庭和（ii）外椭圆形和内部同心圆形腐蚀性。以前，确定轨迹是否是圆锥的案例依据。在共聚焦案例中，我们还导出了轨迹在遗迹到段或圆圈的条件下。我们展示了基因座的转弯号是+/- 3，同时预测其对三角形家族的顶点的运动的单调性。
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在“椭圆台椭圆板球仍然惊讶我们的椭圆板球仍然会惊讶的时候，椭圆板三级轨道的一维系列的新不变性是在椭圆板的三维轨道上的一维系列轨道中的新不变性。（2020），数学。情报人，42（1）：6--17，其中一些人推广到$ n> 3美元。不变性提到包括RADII和/或区域的比率，角度余弦和一个特殊的固定圈。在这里，我们展示了一些证据，以及一些新的相关事实。
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Reading comprehension of legal text can be a particularly challenging task due to the length and complexity of legal clauses and a shortage of expert-annotated datasets. To address this challenge, we introduce the Merger Agreement Understanding Dataset (MAUD), an expert-annotated reading comprehension dataset based on the American Bar Association's 2021 Public Target Deal Points Study, with over 39,000 examples and over 47,000 total annotations. Our fine-tuned Transformer baselines show promising results, with models performing well above random on most questions. However, on a large subset of questions, there is still room for significant improvement. As the only expert-annotated merger agreement dataset, MAUD is valuable as a benchmark for both the legal profession and the NLP community.
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We show for the first time that large-scale generative pretrained transformer (GPT) family models can be pruned to at least 50% sparsity in one-shot, without any retraining, at minimal loss of accuracy. This is achieved via a new pruning method called SparseGPT, specifically designed to work efficiently and accurately on massive GPT-family models. When executing SparseGPT on the largest available open-source models, OPT-175B and BLOOM-176B, we can reach 60% sparsity with negligible increase in perplexity: remarkably, more than 100 billion weights from these models can be ignored at inference time. SparseGPT generalizes to semi-structured (2:4 and 4:8) patterns, and is compatible with weight quantization approaches.
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Despite the success of large language models (LLMs) in various natural language processing (NLP) tasks, the stored knowledge in these models may inevitably be incomplete, out-of-date, or incorrect. This motivates the need to utilize external knowledge to assist LLMs. Unfortunately, current methods for incorporating external knowledge often require additional training or fine-tuning, which can be costly and may not be feasible for LLMs. To address this issue, we propose a novel post-processing approach, rethinking with retrieval (RR), which retrieves relevant external knowledge based on the decomposed reasoning steps obtained from the chain-of-thought (CoT) prompting. This lightweight approach does not require additional training or fine-tuning and is not limited by the input length of LLMs. We evaluate the effectiveness of RR through extensive experiments with GPT-3 on three complex reasoning tasks: commonsense reasoning, temporal reasoning, and tabular reasoning. Our results show that RR can produce more faithful explanations and improve the performance of LLMs.
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Model quantization enables the deployment of deep neural networks under resource-constrained devices. Vector quantization aims at reducing the model size by indexing model weights with full-precision embeddings, i.e., codewords, while the index needs to be restored to 32-bit during computation. Binary and other low-precision quantization methods can reduce the model size up to 32$\times$, however, at the cost of a considerable accuracy drop. In this paper, we propose an efficient framework for ternary quantization to produce smaller and more accurate compressed models. By integrating hyperspherical learning, pruning and reinitialization, our proposed Hyperspherical Quantization (HQ) method reduces the cosine distance between the full-precision and ternary weights, thus reducing the bias of the straight-through gradient estimator during ternary quantization. Compared with existing work at similar compression levels ($\sim$30$\times$, $\sim$40$\times$), our method significantly improves the test accuracy and reduces the model size.
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Most existing pruning works are resource-intensive, requiring retraining or fine-tuning of the pruned models for accuracy. We propose a retraining-free pruning method based on hyperspherical learning and loss penalty terms. The proposed loss penalty term pushes some of the model weights far from zero, while the rest weight values are pushed near zero and can be safely pruned with no need for retraining and a negligible accuracy drop. In addition, our proposed method can instantly recover the accuracy of a pruned model by replacing the pruned values with their mean value. Our method obtains state-of-the-art results in retraining-free pruning and is evaluated on ResNet-18/50 and MobileNetV2 with ImageNet dataset. One can easily get a 50\% pruned ResNet18 model with a 0.47\% accuracy drop. With fine-tuning, the experiment results show that our method can significantly boost the accuracy of the pruned models compared with existing works. For example, the accuracy of a 70\% pruned (except the first convolutional layer) MobileNetV2 model only drops 3.5\%, much less than the 7\% $\sim$ 10\% accuracy drop with conventional methods.
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