Zhijun Chen

Qianren Mao, Jiaxun Lyu, Junnan Liu et al.

Document hashing provides compact representations for efficient similarity search and document deduplication, but existing studies rarely compare hashing pipelines under a unified protocol for fine-grained scientific documents. H3D is an unsupervised text hashing benchmark for fine-grained document deduplication. It evaluates representative unsupervised non-learning hashing approaches (MinHash, SimHash, Winnowing, FuzzyHash, FlyHash) together with semantic-sensitive methods built from frozen BGE embeddings and two quantization strategies (BGE-BIHash and BGE-LSHash). The non-learning methods generate hash fingerprints through manually designed mathematical rules without training or labeled similarity pairs, which distinguishes them from neural semantic hashing models. We benchmark all methods on CSFCube and RELISH, two datasets that provide complementary evaluation settings: facet-level analysis for scientific-document similarity and larger-scale split-level evaluation for biomedical similarity search. H3D jointly reports ranking quality (MAP, NDCG@20), efficiency, and robustness under controlled text compression. The results show a consistent trade-off: lexical and structural fingerprints are competitive for near-duplicate matching, while semantic-sensitive representations better preserve similarity under content rewriting, at higher computational cost. We further analyze when different similarity measures become rank-equivalent for specific hash representations, improving the interpretability and reproducibility of method comparisons.

Zhijun Chen, Hayden Schaeffer, Rachel Ward

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models. Random feature matrices are asymmetric rectangular nonlinear matrices depending on two input variables, the data and the weights, which can make their characterization challenging. We consider two settings for the two input variables, either both are random variables or one is a random variable and the other is well-separated, i.e. there is a minimum distance between points. With conditions on the dimension, the complexity ratio, and the sampling variance, we show that the singular values of these matrices concentrate near their full expectation and near one with high-probability. In particular, since the dimension depends only on the logarithm of the number of random weights or the number of data points, our complexity bounds can be achieved even in moderate dimensions for many practical setting. The theoretical results are verified with numerical experiments.

Zhijun Chen, Hayden Schaeffer

We provide (high probability) bounds on the condition number of random feature matrices. In particular, we show that if the complexity ratio $\frac{N}{m}$ where $N$ is the number of neurons and $m$ is the number of data samples scales like $\log^{-1}(N)$ or $\log(m)$, then the random feature matrix is well-conditioned. This result holds without the need of regularization and relies on establishing various concentration bounds between dependent components of the random feature matrix. Additionally, we derive bounds on the restricted isometry constant of the random feature matrix. We prove that the risk associated with regression problems using a random feature matrix exhibits the double descent phenomenon and that this is an effect of the double descent behavior of the condition number. The risk bounds include the underparameterized setting using the least squares problem and the overparameterized setting where using either the minimum norm interpolation problem or a sparse regression problem. For the least squares or sparse regression cases, we show that the risk decreases as $m$ and $N$ increase, even in the presence of bounded or random noise. The risk bound matches the optimal scaling in the literature and the constants in our results are explicit and independent of the dimension of the data.