arXiv subjects

Xiaowei Shao

Publications and source records attributed to Xiaowei Shao.

5 recordsLinked to original sources

arXiv2026

Learning Multiband Signals and Fourier-sparse Signals

We consider efficient algorithms to learn multiband signals and Fourier-sparse signals. A mutliband signal has a Fourier transform supported by a bounded number of intervals, say $I_1 \cup I_2 \cdots \cup I_n$. There is a long line of research on multiband signals. In particular, Avron et al. showed an efficient reconstructing algorithm whose sample complexity is almost optimal. However, all previous algorithms for multiband signals consider the reconstructing problem in which the locations of $I_1,\ldots,I_n$ are given as a priori knowledge. On the other hand, although the problem of learning Fourier-sparse signals with $k$ arbitrary frequencies dates at least to Prony in 1795, designing efficient and robust learning algorithms is still an open problem. The state-of-the-art is an efficient algorithm of $\tilde{O}(k^3)$ samples and $\tilde{O}(k^{3 \omega})$ time from the very recent work by Cai et al., while the statistical upper bound is $\tilde{O}(k^2)$ samples. Let $[-1,1]$ be the time window in which the noise is $\ell_2$ bounded. 1. We show an efficient algorithm to recover the locations of the bands $I_1,\ldots,I_n$ in $\hat{x}$ within $\tilde{O}(n+\sum_i |I_i|)$ samples and $\tilde{O}(n+\sum_i |I_i|)$ time. Furthermore, combining this with the reconstructing algorithm by Avron et al. provides an efficient interpolation algorithm within $\tilde{O}(n+\sum_i |I_i|)$ samples. 2. We show that every $k$-Fourier-sparse signal $x$ admits a multiband approximation $z$ whose Fourier transform is of support size $|\mathrm{supp}(\hat{z})|=\tilde{O}(k^2)$. Furthermore, we show an interpolation algorithm for $k$-Fourier-sparse signals with $\tilde{O}(k^2)$ samples and $\tilde{O}(k^5)$ time.

cs.DS↗

arXiv2026

The Illusion of Control: Why Bare Classifier Inversion Silently Fails in Concept-Bottleneck Text Generation

Concept-bottleneck controllable generation routes multi-attribute control through a low-dimensional concept code that, at deployment, must be synthesised from a target attribute configuration. We study this problem in concept-bottleneck text generation under multi-axis compositional generalisation, comparing three ways to obtain the inference-time code: classifier inversion against the encoder heads, reference-text encoding, and a post-hoc label-conditioned prior. Since a concept code admits no direct LM-fluency term, regularising inversion must instead constrain the code toward the encoder's training distribution. We therefore test bare inversion and three regularised variants: label-agnostic and label-conditioned Mahalanobis penalties, and a conditional normalising-flow density baseline. Every inversion variant we test underperforms a simple post-hoc prior fitted to per-combination encoder means on the same checkpoints, across three backbone families spanning $124$M to $8$B parameters. The bare form of classifier inversion also silently collapses to chance, traceable to a directly measured off-manifold code. We validate this diagnosis on real-world benchmarks and under external evaluators, enabling fair comparison with published baselines.

cs.CL↗

arXiv2026

Improved Algorithms for Learning Fourier-sparse Signals

A classical problem in sparse Fourier transforms, which dates back to the work by Prony in 1795 at least, is to learn a $k$-Fourier-sparse signal $x(t):=\sum_{j=1}^k \alpha_j e^{2 \pi \mathbf{i} f_j t}$ with arbitrary frequencies $f_1,\ldots,f_k$. We study this problem of learning $x(t)$ in a fixed time window $[-T,T]$ under adversarial noise with bounded $\ell_2$ norm, where the frequencies $f_1,\ldots,f_k$ may be "off-grid" -- arbitrarily located in a given bandlimit $[-F,F]$. In particular, our goal is to output a sparse interpolation $\tilde{x}$ such that $\tilde{x}(t) \approx x(t)$ in the time window $[-T,T]$. 1. Our first result shows that the sample complexity of interpolation is $k^2 \cdot O(\log \frac{k FT}{\epsilon})^2$. While its running time is $(\frac{k FT}{\epsilon})^{O(k)}$, this improves the previous upper bound $k^{4} \cdot (\log FT)^{O(1)}$ on the sample complexity substantially and leaves a gap of about $k$ to the lower bound $\Omega(k \log FT)$. 2. Our second result provides efficient algorithms to interpolate $x(t)$. The first algorithm takes $m=k^{3.75} \cdot (\log FT)^{O(1)}$ samples and $m^{\omega+o(1)}$ time ($\omega$ is the matrix multiplication exponent). Assuming that the growth of any $k$-Fourier-sparse signal cannot be significantly larger than the growth of the degree-$(k-1)$ Chebyshev polynomial -- specifically, $x(t) \le e^{k \cdot O\big( \sqrt{\frac{|t|}{T}-1} \big)} \cdot \underset{s \in [-1,1]}{\max} |x(s)|$ for any $t \notin [-T,T]$, the second algorithm further improves the sample complexity to $m'=k^{3} \cdot (\log FT)^{O(1)}$ and the time complexity to $(m')^{\omega+o(1)}$.

cs.DS↗

arXiv2025

Bayes-Entropy Collaborative Driven Agents for Research Hypotheses Generation and Optimization

The exponential growth of scientific knowledge has made the automated generation of scientific hypotheses that combine novelty, feasibility, and research value a core challenge. Existing methods based on large language models fail to systematically model the inherent in hypotheses or incorporate the closed-loop feedback mechanisms crucial for refinement. This paper proposes a multi-agent collaborative framework called HypoAgents, which for the first time integrates Bayesian reasoning with an information entropy-driven search mechanism across three stages-hypotheses generation, evidence validation, and hypotheses Refinement-to construct an iterative closed-loop simulating scientists' cognitive processes. Specifically, the framework first generates an initial set of hypotheses through diversity sampling and establishes prior beliefs based on a composite novelty-relevance-feasibility (N-R-F) score. It then employs etrieval-augmented generation (RAG) to gather external literature evidence, updating the posterior probabilities of hypotheses using Bayes' theorem. Finally, it identifies high-uncertainty hypotheses using information entropy $H = - \sum {{p_i}\log {p_i}}$ and actively refines them, guiding the iterative optimization of the hypothesis set toward higher quality and confidence. Experimental results on the ICLR 2025 conference real-world research question dataset (100 research questions) show that after 12 optimization iterations, the average ELO score of generated hypotheses improves by 116.3, surpassing the benchmark of real paper abstracts by 17.8, while the framework's overall uncertainty, as measured by Shannon entropy, decreases significantly by 0.92. This study presents an interpretable probabilistic reasoning framework for automated scientific discovery, substantially improving the quality and reliability of machine-generated research hypotheses.

cs.AI↗

arXiv2018

Semantic Segmentation for Urban Planning Maps based on U-Net

The automatic digitizing of paper maps is a significant and challenging task for both academia and industry. As an important procedure of map digitizing, the semantic segmentation section mainly relies on manual visual interpretation with low efficiency. In this study, we select urban planning maps as a representative sample and investigate the feasibility of utilizing U-shape fully convolutional based architecture to perform end-to-end map semantic segmentation. The experimental results obtained from the test area in Shibuya district, Tokyo, demonstrate that our proposed method could achieve a very high Jaccard similarity coefficient of 93.63% and an overall accuracy of 99.36%. For implementation on GPGPU and cuDNN, the required processing time for the whole Shibuya district can be less than three minutes. The results indicate the proposed method can serve as a viable tool for urban planning map semantic segmentation task with high accuracy and efficiency.

cs.LG↗