Smita Krishnaswamy

Understanding cellular trajectories via time-resolved single-cell transcriptomics is vital for studying development, regeneration, and disea… (voir plus)se. A key challenge is inferring continuous trajectories from discrete snapshots. Biological complexity stems from stochastic cell fate decisions, temporal proliferation changes, and spatial environmental influences. Current methods often use deterministic interpolations treating cells in isolation, failing to capture the probabilistic branching, population shifts, and niche-dependent signaling driving real biological processes. We introduce Manifold Interpolating Optimal-Transport Flow (MIOFlow) 2.0. This framework learns biologically informed cellular trajectories by integrating manifold learning, optimal transport, and neural differential equations. It models three core processes: (1) stochasticity and branching via Neural Stochastic Differential Equations; (2) non-conservative population changes using a learned growth-rate model initialized with unbalanced optimal transport; and (3) environmental influence through a joint latent space unifying gene expression with spatial features like local cell type composition and signaling. By operating in a PHATE-distance matching autoencoder latent space, MIOFlow 2.0 ensures trajectories respect the data's intrinsic geometry. Empirical comparisons show expressive trajectory learning via neural differential equations outperforms existing generative models, including simulation-free flow matching. Validated on synthetic datasets, embryoid body differentiation, and spatially resolved axolotl brain regeneration, MIOFlow 2.0 improves trajectory accuracy and reveals hidden drivers of cellular transitions, like specific signaling niches. MIOFlow 2.0 thus bridges single-cell and spatial transcriptomics to uncover tissue-scale trajectories.

2026-03-22

arXiv (prépublication)

HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation

Hiren Madhu

Ngoc Bui

Ali Maatouk

Leandros Tassiulas

Menglin Yang 0001

Sukanta Ganguly

Kiran Srinivasan

Rex Ying

Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain large… (voir plus)ly confined to Euclidean space. However, natural language exhibits hierarchical structure from broad topics to specific entities that Euclidean embeddings fail to preserve, causing semantically distant documents to appear spuriously similar and increasing hallucination risk. To address these limitations, we introduce hyperbolic dense retrieval, developing two model variants in the Lorentz model of hyperbolic space: HyTE-FH, a fully hyperbolic transformer, and HyTE-H, a hybrid architecture projecting pre-trained Euclidean embeddings into hyperbolic space. To prevent representational collapse during sequence aggregation, we introduce the Outward Einstein Midpoint, a geometry-aware pooling operator that provably preserves hierarchical structure. On MTEB, HyTE-FH outperforms equivalent Euclidean baselines, while on RAGBench, HyTE-H achieves up to 29% gains over Euclidean baselines in context relevance and answer relevance using substantially smaller models than current state-of-the-art retrievers. Our analysis also reveals that hyperbolic representations encode document specificity through norm-based separation, with over 20% radial increase from general to specific concepts, a property absent in Euclidean embeddings, underscoring the critical role of geometric inductive bias in faithful RAG systems.

2026-02-07

ArXiv (prépublication)

Dispersion Loss Counteracts Embedding Condensation and Improves Generalization in Small Language Models

Chen Liu

Xingzhi Sun

Xi Xiao

Alexandre Van Tassel

Ke Xu

Kristof Reimann

Danqi Liao

Mark B. Gerstein

Tianyang Wang

Xiao Wang

Large language models (LLMs) achieve remarkable performance through ever-increasing parameter counts, but scaling incurs steep computational… (voir plus) costs. To better understand LLM scaling, we study representational differences between LLMs and their smaller counterparts, with the goal of replicating the representational qualities of larger models in the smaller models. We observe a geometric phenomenon which we term

2026-01-29

ArXiv (prépublication)

Self-Supervised Visual Prompting for Cross-Domain Road Damage Detection

Xi Xiao

Zhuxuanzi Wang

Mingqiao Mo

Chen Liu

Chenrui Ma

Yanshu Li

Xiao Wang

Tianyang Wang

The deployment of automated pavement defect detection is often hindered by poor cross-domain generalization. Supervised detectors achieve st… (voir plus)rong in-domain accuracy but require costly re-annotation for new environments, while standard self-supervised methods capture generic features and remain vulnerable to domain shift. We propose \ours, a self-supervised framework that \emph{visually probes} target domains without labels. \ours introduces a Self-supervised Prompt Enhancement Module (SPEM), which derives defect-aware prompts from unlabeled target data to guide a frozen ViT backbone, and a Domain-Aware Prompt Alignment (DAPA) objective, which aligns prompt-conditioned source and target representations. Experiments on four challenging benchmarks show that \ours consistently outperforms strong supervised, self-supervised, and adaptation baselines, achieving robust zero-shot transfer, improved resilience to domain variations, and high data efficiency in few-shot adaptation. These results highlight self-supervised prompting as a practical direction for building scalable and adaptive visual inspection systems. Source code is publicly available: https://github.com/xixiaouab/PROBE/tree/main

2025-11-15

ArXiv (prépublication)

Graph topological property recovery with heat and wave dynamics-based features on graphs

Dhananjay Bhaskar

Yanlei Zhang

Charles Xu

Xingzhi Sun

Oluwadamilola Fasina

Arman Afrasiyabi

Siddharth Viswanath

Guy Wolf

Maximilian Nickel

Michael Perlmutter

2025-11-12

TAG-DS/2025/Conference (spotlight)

openreview.net

Neural FIM: Bridging Statistical Manifolds and Generative Modeling through Fisher Geometry

Yanlei Zhang

Guillaume Huguet

Edward De Brouwer

Danqi Liao

Oluwadamilola Fasina

Alexander Tong

Ricky T. Q. Chen

Guy Wolf

Maximilian Nickel

Ian Adelstein

While data diffusion-based embeddings are widely used in unsupervised learning to reveal the intrinsic geometry of data, they are fundamenta… (voir plus)lly constrained by their discrete nature and inability to generalize beyond training points. This limitation ob

2025-10-20

TechRxiv (accepté)

RNAGenScape: Property-guided Optimization and Interpolation of mRNA Sequences with Manifold Langevin Dynamics

Danqi Liao

Chen Liu

Xingzhi Sun

Di'e Tang

Haochen Wang

Scott E. Youlten

Srikar Krishna Gopinath

Haejeong Lee

Ethan C. Strayer

Antonio J. Giraldez

2025-10-13

ArXiv (prépublication)

CTR-LoRA: Curvature-Aware and Trust-Region Guided Low-Rank Adaptation for Large Language Models

Zhuxuanzi Wang

Mingqiao Mo

Xi Xiao

Chen Liu

Chenrui Ma

Yunbei Zhang

Xiao Wang

Tianyang Wang

Parameter-efficient fine-tuning (PEFT) has become the standard approach for adapting large language models under limited compute and memory … (voir plus)budgets. Although previous methods improve efficiency through low-rank updates, quantization, or heuristic budget reallocation, they often decouple the allocation of capacity from the way updates evolve during training. In this work, we introduce CTR-LoRA, a framework guided by curvature trust region that integrates rank scheduling with stability-aware optimization. CTR-LoRA allocates parameters based on marginal utility derived from lightweight second-order proxies and constrains updates using a Fisher/Hessian-metric trust region. Experiments on multiple open-source backbones (7B-13B), evaluated on both in-distribution and out-of-distribution benchmarks, show consistent improvements over strong PEFT baselines. In addition to increased accuracy, CTR-LoRA enhances training stability, reduces memory requirements, and achieves higher throughput, positioning it on the Pareto frontier of performance and efficiency. These results highlight a principled path toward more robust and deployable PEFT.

2025-10-10

ArXiv (prépublication)

Equivariant Geometric Scattering Networks via Vector Diffusion Wavelets

David R. Johnson

Rishabh Anand

Michael Perlmutter

2025-09-30

ArXiv (prépublication)

VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks

David R. Johnson

Alexander Sietsema

Rishabh Anand

Deanna Needell

Michael Perlmutter

We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduce… (voir plus)d to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets may be effectively incorporated into a family of geometric graph neural networks, which we refer to as VDW-GNNs. We demonstrate that such networks are effective on synthetic point cloud data, as well as on real-world data derived from wind-field measurements and neural activity data. Theoretically, we prove that these new wavelets have desirable frame theoretic properties, similar to traditional diffusion wavelets. Additionally, we prove that these wavelets have desirable symmetries with respect to rotations and translations.

2025-09-30

ArXiv (prépublication)