Bayesian Multiple Multivariate Density-Density Regression

We propose the first approach for multiple multivariate density-density regression (MDDR), making it possible to consider the regression of a multivariate density-valued response on multiple multivariate density-valued predictors. The core idea is to define a fitted distribution using a sliced Wasserstein barycenter (SWB) of push-forwards of the predictors and to quantify deviations from the observed response using the sliced Wasserstein (SW) distance. Regression functions, which map predictors' supports to the response support, and barycenter weights are inferred within a generalized Bayes framework, enabling principled uncertainty quantification without requiring a fully specified likelihood. The inference process can be seen as an instance of an inverse SWB problem. We establish theoretical guarantees, including the stability of the SWB under perturbations of marginals and barycenter weights, sample complexity of the generalized likelihood, and posterior consistency. For practical inference, we introduce a differentiable approximation of the SWB and a smooth reparameterization to handle the simplex constraint on barycenter weights, allowing efficient gradient-based MCMC sampling. We demonstrate MDDR in an application to inference for population-scale single-cell data. Posterior analysis under the MDDR model in this example includes inference on communication between multiple source/sender cell types and a target/receiver cell type. The proposed approach provides accurate fits, reliable predictions, and interpretable posterior estimates of barycenter weights, which can be used to construct sparse cell-cell communication networks.

Cauchy-Schwarz Fairness Regularizer

Group fairness in machine learning is often enforced by adding a regularizer that reduces the dependence between model predictions and sensitive attributes. However, existing regularizers are built on heterogeneous distance measures and design choices, which makes their behavior hard to reason about and their performance inconsistent across tasks. This raises a basic question: what properties make a good fairness regularizer? We address this question by first organizing existing in-process methods into three families: (i) matching prediction statistics across sensitive groups, (ii) aligning latent representations, and (iii) directly minimizing dependence between predictions and sensitive attributes. Through this lens, we identify desirable properties of the underlying distance measure, including tight generalization bounds, robustness to scale differences, and the ability to handle arbitrary prediction distributions. Motivated by these properties, we propose a Cauchy-Schwarz (CS) fairness regularizer that penalizes the empirical CS divergence between prediction distributions conditioned on sensitive groups. Under a Gaussian comparison, we show that CS divergence yields a tighter bound than Kullback-Leibler divergence, Maximum Mean Discrepancy, and the mean disparity used in Demographic Parity, and we discuss how these advantages translate to a distribution-free, kernel-based estimator that naturally extends to multiple sensitive attributes. Extensive experiments on four tabular benchmarks and one image dataset demonstrate that the proposed CS regularizer consistently improves Demographic Parity and Equal Opportunity metrics while maintaining competitive accuracy, and achieves a more stable utility-fairness trade-off across hyperparameter settings compared to prior regularizers.

Mitigating Bias in Graph Hyperdimensional Computing

Graph hyperdimensional computing (HDC) has emerged as a promising paradigm for cognitive tasks, emulating brain-like computation with high-dimensional vectors known as hypervectors. While HDC offers robustness and efficiency on graph-structured data, its fairness implications remain largely unexplored. In this paper, we study fairness in graph HDC, where biases in data representation and decision rules can lead to unequal treatment of different groups. We show how hypervector encoding and similarity-based classification can propagate or even amplify such biases, and we propose a fairness-aware training framework, FairGHDC, to mitigate them. FairGHDC introduces a bias correction term, derived from a gap-based demographic-parity regularizer, and converts it into a scalar fairness factor that scales the update of the class hypervector for the ground-truth label. This enables debiasing directly in the hypervector space without modifying the graph encoder or requiring backpropagation. Experimental results on six benchmark datasets demonstrate that FairGHDC substantially reduces demographic-parity and equal-opportunity gaps while maintaining accuracy comparable to standard GNNs and fairness-aware GNNs. At the same time, FairGHDC preserves the computational advantages of HDC, achieving up to about one order of magnitude ($\approx 10\times$) speedup in training time on GPU compared to GNN and fairness-aware GNN baselines.

Recover-to-Forget: Gradient Reconstruction from LoRA for Efficient LLM Unlearning

Unlearning in large foundation models (e.g., LLMs) is essential for enabling dynamic knowledge updates, enforcing data deletion rights, and correcting model behavior. However, existing unlearning methods often require full-model fine-tuning or access to the original training data, which limits their scalability and practicality. In this work, we introduce Recover-to-Forget (R2F), a novel framework for efficient unlearning in LLMs based on reconstructing full-model gradient directions from low-rank LoRA adapter updates. Rather than performing backpropagation through the full model, we compute gradients with respect to LoRA parameters using multiple paraphrased prompts and train a gradient decoder to approximate the corresponding full-model gradients. To ensure applicability to larger or black-box models, the decoder is trained on a proxy model and transferred to target models. We provide a theoretical analysis of cross-model generalization and demonstrate that our method achieves effective unlearning while preserving general model performance. Experimental results demonstrate that R2F offers a scalable and lightweight alternative for unlearning in pretrained LLMs without requiring full retraining or access to internal parameters.

LUNE: Efficient LLM Unlearning via LoRA Fine-Tuning with Negative Examples

Large language models (LLMs) possess vast knowledge acquired from extensive training corpora, but they often cannot remove specific pieces of information when needed, which makes it hard to handle privacy, bias mitigation, and knowledge correction. Traditional model unlearning approaches require computationally expensive fine-tuning or direct weight editing, making them impractical for real-world deployment. In this work, we introduce LoRA-based Unlearning with Negative Examples (LUNE), a lightweight framework that performs negative-only unlearning by updating only low-rank adapters while freezing the backbone, thereby localizing edits and avoiding disruptive global changes. Leveraging Low-Rank Adaptation (LoRA), LUNE targets intermediate representations to suppress (or replace) requested knowledge with an order-of-magnitude lower compute and memory than full fine-tuning or direct weight editing. Extensive experiments on multiple factual unlearning tasks show that LUNE: (I) achieves effectiveness comparable to full fine-tuning and memory-editing methods, and (II) reduces computational cost by about an order of magnitude.

QUILL: An Algorithm-Architecture Co-Design for Cache-Local Deformable Attention

Deformable transformers deliver state-of-the-art detection but map poorly to hardware due to irregular memory access and low arithmetic intensity. We introduce QUILL, a schedule-aware accelerator that turns deformable attention into cache-friendly, single-pass work. At its core, Distance-based Out-of-Order Querying (DOOQ) orders queries by spatial proximity; the look-ahead drives a region prefetch into an alternate buffer--forming a schedule-aware prefetch loop that overlaps memory and compute. A fused MSDeformAttn engine executes interpolation, Softmax, aggregation, and the final projection (W''m) in one pass without spilling intermediates, while small tensors are kept on-chip and surrounding dense layers run on integrated GEMMs. Implemented as RTL and evaluated end-to-end, QUILL achieves up to 7.29x higher throughput and 47.3x better energy efficiency than an RTX 4090, and exceeds prior accelerators by 3.26-9.82x in throughput and 2.01-6.07x in energy efficiency. With mixed-precision quantization, accuracy tracks FP32 within <=0.9 AP across Deformable and Sparse DETR variants. By converting sparsity into locality--and locality into utilization--QUILL delivers consistent, end-to-end speedups.

RETuning: Upgrading Inference-Time Scaling for Stock Movement Prediction with Large Language Models

Recently, large language models (LLMs) have demonstrated outstanding reasoning capabilities on mathematical and coding tasks. However, their application to financial tasks-especially the most fundamental task of stock movement prediction-remains underexplored. We study a three-class classification problem (up, hold, down) and, by analyzing existing reasoning responses, observe that: (1) LLMs follow analysts' opinions rather than exhibit a systematic, independent analytical logic (CoTs). (2) LLMs list summaries from different sources without weighing adversarial evidence, yet such counterevidence is crucial for reliable prediction. It shows that the model does not make good use of its reasoning ability to complete the task. To address this, we propose Reflective Evidence Tuning (RETuning), a cold-start method prior to reinforcement learning, to enhance prediction ability. While generating CoT, RETuning encourages dynamically constructing an analytical framework from diverse information sources, organizing and scoring evidence for price up or down based on that framework-rather than on contextual viewpoints-and finally reflecting to derive the prediction. This approach maximally aligns the model with its learned analytical framework, ensuring independent logical reasoning and reducing undue influence from context. We also build a large-scale dataset spanning all of 2024 for 5,123 A-share stocks, with long contexts (32K tokens) and over 200K samples. In addition to price and news, it incorporates analysts' opinions, quantitative reports, fundamental data, macroeconomic indicators, and similar stocks. Experiments show that RETuning successfully unlocks the model's reasoning ability in the financial domain. Inference-time scaling still works even after 6 months or on out-of-distribution stocks, since the models gain valuable insights about stock movement prediction.

Consistent causal discovery with equal error variances: a least-squares perspective

We consider the problem of recovering the true causal structure among a set of variables, generated by a linear acyclic structural equation model (SEM) with the error terms being independent and having equal variances. It is well-known that the true underlying directed acyclic graph (DAG) encoding the causal structure is uniquely identifiable under this assumption. In this work, we establish that the sum of minimum expected squared errors for every variable, while predicted by the best linear combination of its parent variables, is minimised if and only if the causal structure is represented by any supergraph of the true DAG. This property is further utilised to design a Bayesian DAG selection method that recovers the true graph consistently.

Enabling Group Fairness in Graph Unlearning via Bi-level Debiasing

Graph unlearning is a crucial approach for protecting user privacy by erasing the influence of user data on trained graph models. Recent developments in graph unlearning methods have primarily focused on maintaining model prediction performance while removing user information. However, we have observed that when user information is deleted from the model, the prediction distribution across different sensitive groups often changes. Furthermore, graph models are shown to be prone to amplifying biases, making the study of fairness in graph unlearning particularly important. This raises the question: Does graph unlearning actually introduce bias? Our findings indicate that the predictions of post-unlearning models become highly correlated with sensitive attributes, confirming the introduction of bias in the graph unlearning process. To address this issue, we propose a fair graph unlearning method, FGU. To guarantee privacy, FGU trains shard models on partitioned subgraphs, unlearns the requested data from the corresponding subgraphs, and retrains the shard models on the modified subgraphs. To ensure fairness, FGU employs a bi-level debiasing process: it first enables shard-level fairness by incorporating a fairness regularizer in the shard model retraining, and then achieves global-level fairness by aligning all shard models to minimize global disparity. Our experiments demonstrate that FGU achieves superior fairness while maintaining privacy and accuracy. Additionally, FGU is robust to diverse unlearning requests, ensuring fairness and utility performance across various data distributions.

Bayesian Density-Density Regression with Application to Cell-Cell Communications

We introduce a scalable framework for regressing multivariate distributions onto multivariate distributions, motivated by the application of inferring cell-cell communication from population-scale single-cell data. The observed data consist of pairs of multivariate distributions for ligands from one cell type and corresponding receptors from another. For each ordered pair $e=(l,r)$ of cell types $(l \neq r)$ and each sample $i = 1, \ldots, n$, we observe a pair of distributions $(F_{ei}, G_{ei})$ of gene expressions for ligands and receptors of cell types $l$ and $r$, respectively. The aim is to set up a regression of receptor distributions $G_{ei}$ given ligand distributions $F_{ei}$. A key challenge is that these distributions reside in distinct spaces of differing dimensions. We formulate the regression of multivariate densities on multivariate densities using a generalized Bayes framework with the sliced Wasserstein distance between fitted and observed distributions. Finally, we use inference under such regressions to define a directed graph for cell-cell communications.