Recent advancements in language models have led to significant improvements in mathematical reasoning across various benchmarks.However, most of these benchmarks rely on automatic evaluation methods that only compare final answers using heuristics, without verifying the underlying reasoning steps.This limitation results in false positive solutions, where models may produce correct final answers but with flawed deduction paths.In this paper, we systematically examine the prevalence of false positive solutions in mathematical problem solving for language models.We analyze the characteristics and extent of this issue across different open-source models, datasets of varying difficulty levels, and decoding strategies.Specifically, we explore how "false positives" influence the inference time scaling behavior of language models.Our experimental results reveal that: (1) false positive solutions persist across different models, datasets, and decoding methods, (2) sampling-based inference time scaling methods do not alleviate the problem, and (3) the pass@N evaluation metric is more susceptible to "false positives", suggesting a significantly lower scaling ceiling than what automatic evaluations indicate.Additionally, we analyze specific instances of "false positives" and discuss potential limitations in self-improvement techniques and synthetic data generation under such conditions.Our data and code are publicly available at https://github.com/Wloner0809/False- Positives-in-Math.

Learning from implicit feedback is one of the most common cases in the application of recommender systems. Generally speaking, interacted examples are considered as positive while negative examples are sampled from uninteracted ones. However, noisy examples are prevalent in real-world implicit feedback. A noisy positive example could be interacted but it actually leads to negative user preference. A noisy negative example which is uninteracted because of user unawareness could also denote potential positive user preference. Conventional training methods overlook these noisy examples, leading to sub-optimal recommendations.

This paper targets to bring together the research efforts on two fields that are growing actively in the past few years: multicamera person Re-Identification (ReID) and large-scale image retrieval. We demonstrate that the essentials of image retrieval and person ReID are the same, i.e., measuring the similarity between images. However, person ReID requires more discriminative and robust features to identify the subtle differences of different persons and overcome the large variance among images of the same person. Specifically, we propose a coarse-to-fine (C2F) framework and a Convolutional Neural Network structure named as Conv-Net to tackle the large-scale person ReID as an image retrieval task. Given a query person image, the C2F firstly employ Conv-Net to extract a compact descriptor and perform the coarse-level search. A robust descriptor conveying more spatial cues is hence extracted to perform the fine-level search. Extensive experimental results show that the proposed method outperforms existing methods on two public datasets. Further, the evaluation on a large-scale Person-520K dataset demonstrates that our work is significantly more efficient than existing works, e.g., only needs 180ms to identify a query person from 520K images.

Spectral hashing (SpH) is an efficient and simple binary hashing method, which assumes that data are sampled from a multidimensional uniform distribution. However, this assumption is too restrictive in practice. In this paper we propose an improved method, Fitted Spectral Hashing, to relax this distribution assumption. Our work is based on the fact that one-dimensional data of any distribution could be mapped to a uniform distribution without changing the local neighbor relations among data items. We have found that this mapping on each PCA direction has certain regular pattern, and could fit data well by S-Curve function, Sigmoid function. With more parameters Fourier function also fit data well. Thus with Sigmoid function and Fourier function, we propose two binary hashing methods. Experiments show that our methods are efficient and outperform state-of-the-art methods.

This work presents a novel sparse ensemble learning scheme for concept detection in videos. The proposed ensemble first exploits a sparse non-negative matrix factorization (NMF) process to represent data instances in parts and partition the data space into localities, and then coordinates the individual classifiers in each locality for final classification. In the sparse NMF, data exemplars are projected to a set of locality bases, in which the non-negative superposition of basis images reconstructs the original exemplars. This additive combination ensures that each locality captures the characteristics of data exemplars in part, thus enabling the local classifiers to hold reasonable diversity in their own regions of expertise. More importantly, the sparse NMF ensures that an exemplar is projected to only a few bases (localities) with non-zero coefficients. The resultant ensemble model is, therefore, sparse, in the way that only a small number of efficient classifiers in the ensemble will fire on a testing sample. Extensive tests on the TRECVid 08 and 09 datasets show that the proposed ensemble learning achieves promising results and outperforms existing approaches. The proposed scheme is feature-independent, and can be applied in many other large scale pattern recognition problems besides visual concept detection.

This paper provides a simple but effective approach, named ECON, to fully-automatically extract content from Web news page. ECON uses a DOM tree to represent the Web news page and leverages the substantial features of the DOM tree. ECON finds a snippet-node by which a part of the content of news is wrapped firstly, then backtracks from the snippet-node until a summary-node is found, and the entire content of news is wrapped by the summary-node. During the process of backtracking, ECON removes noise. Experimental results showed that ECON can achieve high accuracy and fully satisfy the requirements for scalable extraction. Moreover, ECON can be applied to Web news page written in many popular languages such as Chinese, English, French, German, Italian, Japanese, Portuguese, Russian, Spanish, Arabic. ECON can be implemented much easily.