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Weiyan Chen

Weiyan Chen appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.AT math.GT math.AG Computer Vision Machine Learning math.CO math.OC math.RT Robotics

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preprint2026arXiv

Robust Conditional Conformal Prediction via Branched Normalizing Flow

Conformal prediction (CP) constructs prediction sets with marginal coverage guarantees under the assumption that the calibration and test distributions are identical. However, under distribution shift, existing approaches primarily align marginal conformal score distributions, which is sufficient to preserve marginal coverage but does not control the conditional coverage error at individual test inputs. As a consequence, CP can remain unreliable in regions where the conditional score distributions are mismatched. In this work, we bound the conditional invalidity of CP under distribution shift in terms of the Wasserstein distance between the calibration and test distributions. This result highlights the role of invertible transport in mitigating conditional coverage degradation. Motivated by this insight, we introduce Branched Normalizing Flow (BNF), a two-branch architecture that normalizes a test input to the calibration distribution and transforms the prediction set of the normalized input back to the test distribution while preserving conditional guarantees. Empirically, BNF consistently improves conditional coverage robustness on nine datasets across a wide range of confidence levels.

preprint2026arXiv

When Preference Labels Fall Short: Aligning Diffusion Models from Real Data

Preference alignment aims to guide generative models by learning from comparisons between preferred and non-preferred samples. In practice, most existing approaches rely on preference pairs constructed from model-generated images. Such supervision is inherently relative and can be ambiguous when both samples exhibit artifacts or limited visual quality, making it difficult to infer what constitutes a truly desirable output. In this work, we investigate whether real data can serve as an alternative source of supervision for preference alignment. We adopt a data-centric perspective and study a curation strategy that treats real images as reference points and constructs preference signals by contrasting them with generated or perturbed samples, without requiring manually annotated preference pairs. Through empirical analysis, we show that real-data-based supervision provides effective guidance for aligning diffusion models and achieves performance comparable to existing preference-based methods. Our results suggest that real data offers a practical and complementary source of supervision for preference alignment and highlight directions of label-efficient alignment strategies. Code and models are available at https://cwyxx.github.io/RealAlign.

preprint2019arXiv

Stability in the cohomology of the space of complex irreducible polynomials in several variables

We prove that the space of complex irreducible polynomials of degree $d$ in $n$ variables satisfies two forms of homological stability: first, its cohomology stabilizes as $d$ increases, and second, its compactly supported cohomology stabilizes as $n$ increases. Our topological results are inspired by counting results over finite fields due to Carlitz and Hyde.

preprint2016arXiv

Twisted cohomology of configuration spaces and spaces of maximal tori via point-counting

We consider two families of algebraic varieties $Y_n$ indexed by natural numbers $n$: the configuration space of unordered $n$-tuples of distinct points on $\mathbb{C}$, and the space of unordered $n$-tuples of linearly independent lines in $\mathbb{C}^n$. Let $W_n$ be any sequence of virtual $S_n$-representations given by a character polynomial, we compute $H^i(Y_n; W_n)$ for all $i$ and all $n$ in terms of double generating functions. One consequence of the computation is a new recurrence phenomenon: the stable twisted Betti numbers $\lim_{n\to\infty}\dim H^i(Y_n; W_n)$ are linearly recurrent in $i$. Our method is to compute twisted point-counts on the $F_q$-points of certain algebraic varieties, and then pass through the Grothendieck-Lefschetz fixed point formula to prove results in topology. We also generalize a result of Church-Ellenberg-Farb about the configuration spaces of the affine line to those of a general smooth variety.

preprint2015arXiv

Homology of the braid group with coefficients in the reduced Burau representation

The reduced Burau representation $V_n$ of the braid group $B_n$ is obtained from the action of $B_n$ on the homology of an infinite cyclic cover of the $n$-punctured disc. In this note, we calculate $H_*(B_n;V_n)$ as a module over the Laurent polynomial ring $\mathbb{Q}[t,t^{-1}]$.

preprint2014arXiv

Optimal control with reset-renewable resources

We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider both deterministic and stochastic shortest path problems with full budget resets in all preferred nodes. In the continuous case, we derive augmented PDEs of optimal control, which are then solved numerically on the extended state space with a full/instantaneous budget reset on the preferred subset. We introduce an iterative algorithm for solving these problems efficiently. The method's performance is demonstrated on a range of computational examples, including the optimal path planning with constraints on prolonged visibility by a static enemy observer. In addition, we also develop an algorithm that works on the original state space to solve a related but simpler problem: finding the subsets of the domain "reachable-within-the-budget". This manuscript is an extended version of the paper accepted for publication by SIAM J. on Control and Optimization. In the journal version, Section 3 and the Appendix were omitted due to space limitations.

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