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General Machine Learning · Transfer, Multitask and Meta-learning

Jing Xu, Jiazheng Li, Jingzhao Zhang

Model merging offers an effective way to integrate the capabilities of multiple fine-tuned models. However, the performance degradation of the merged model remains a challenge, particularly when none or few data are available. This paper first highlights the necessity of domain-specific data for model merging by proving that data-agnostic algorithms can have arbitrarily bad worst-case performances. Building on this theoretical insight, we explore the relationship between model merging and distillation, introducing a novel few-shot merging algorithm, ProDistill (Progressive Layer-wise Distillation). Unlike common belief that layer-wise training hurts performance, we show that layer-wise teacher-student distillation not only enhances the scalability but also improves model merging performance. We conduct extensive experiments to show that compared to existing few-shot merging methods,ProDistill achieves state-of-the-art performance, with up to 6.14\% and 6.61\% improvements in vision and NLU tasks. Furthermore, we extend the experiments to models with over 10B parameters, showcasing the exceptional scalability of ProDistill.

Deep Learning · Robustness

Thibaut Boissin, Franck Mamalet, Thomas Fel, Agustin Picard, Thomas Massena, Mathieu Serrurier

Orthogonal convolutional layers are valuable components in multiple areas of machine learning, such as adversarial robustness, normalizing flows, GANs, and Lipschitz-constrained models. Their ability to preserve norms and ensure stable gradient propagation makes them valuable for a large range of problems. Despite their promise, the deployment of orthogonal convolution in large-scale applications is a significant challenge due to computational overhead and limited support for modern features like strides, dilations, group convolutions, and transposed convolutions. In this paper, we introduce **AOC** (Adaptive Orthogonal Convolution), a scalable method that extends a previous method (BCOP), effectively overcoming existing limitations in the construction of orthogonal convolutions. This advancement unlocks the construction of architectures that were previously considered impractical. We demonstrate through our experiments that our method produces expressive models that become increasingly efficient as they scale. To foster further advancement, we provide an open-source python package implementing this method, called **Orthogonium**.

General Machine Learning · Representation Learning

Philippe Chlenski, Quentin Chu, Raiyan Khan, Kaizhu Du, Antonio Moretti, Itsik Pe'er

Decision trees (DTs) and their random forest (RF) extensions are workhorses of classification and regression in Euclidean spaces. However, algorithms for learning in non-Euclidean spaces are still limited. We extend DT and RF algorithms to product manifolds: Cartesian products of several hyperbolic, hyperspherical, or Euclidean components. Such manifolds handle heterogeneous curvature while still factorizing neatly into simpler components, making them compelling embedding spaces for complex datasets. Our novel angular reformulation respects manifold geometry while preserving the algorithmic properties that make decision trees effective. In the special cases of single-component manifolds, our method simplifies to its Euclidean or hyperbolic counterparts, or introduces hyperspherical DT algorithms, depending on the curvature. In benchmarks on a diverse suite of 57 classification, regression, and link prediction tasks, our product RFs ranked first on 29 tasks and came in the top 2 for 41. This highlights the value of product RFs as straightforward yet powerful new tools for data analysis in product manifolds. Code for our method is available at https://github.com/pchlenski/manify.

Applications

Zhongming Yu, Hejia Zhang, Yujie Zhao, Hanxian Huang, Matrix Yao, Ke Ding, Jishen Zhao

Recent developments in Large Language Model (LLM) agents are revolutionizing Autonomous Software Engineering (ASE), enabling automated coding, problem fixes, and feature improvements. However, localization -- precisely identifying software problems by navigating to relevant code sections -- remains a significant challenge. Current approaches often yield suboptimal results due to a lack of effective integration between LLM agents and precise code search mechanisms. This paper introduces OrcaLoca, an LLM agent framework that improves accuracy for software issue localization by integrating priority-based scheduling for LLM-guided action, action decomposition with relevance scoring, and distance-aware context pruning. Experimental results demonstrate that OrcaLoca becomes the new open-source state-of-the-art (SOTA) in function match rate (65.33%) on SWE-bench Lite. It also improves the final resolved rate of an open-source framework by 6.33 percentage points through its patch generation integration.

Deep Learning · Theory

Ruiqi Zhang, Jingfeng Wu, Peter Bartlett

We analyze the convergence of gradient descent (GD) with large, adaptive stepsizes for logistic regression on linearly separable data. The stepsize adapts to the current risk, scaled by a fixed base stepsize \eta. We prove that once the number of iterates t surpasses a margin-dependent threshold, the averaged GD iterate achieves a risk upper bound of \exp(-\Theta(\eta t)), where \eta can be chosen arbitrarily large. This implies that GD attains \emph{arbitrarily fast} convergence rates via large stepsizes, although the risk evolution might not be monotonic. In contrast, prior adaptive stepsize GD analyses require a monotonic risk decrease, limiting their rates to \exp(-\Theta(t)). We further establish a margin-dependent lower bound on the iteration complexity for any first-order method to attain a small risk, justifying the necessity of the burn-in phase in our analysis. Our results generalize to a broad class of loss functions and two-layer networks under additional assumptions.

Theory · Deep Learning

Alvaro Rodriguez Abella, João Pedro Silvestre, Paulo Tabuada

A key component of transformers is the attention mechanism orchestrating how each token influences the propagation of every other token along the layers of a transformer. In this paper we provide a rigorous, mathematical analysis of the asymptotic properties of attention in transformers. Although we present several results based on different assumptions, all of them point to the same conclusion, all tokens asymptotically converge to each other, a phenomenon that has been empirically reported in the literature. Our findings are carefully compared with existing theoretical results and illustrated by simulations and experimental studies using the GPT-2 model.

Deep Learning · Self-Supervised Learning

EMANUELE SANSONE, Tim Lebailly, Tinne Tuytelaars

We present a principled and simplified design of the projector and loss function for non-contrastive self-supervised learning based on hyperdimensional computing. We theoretically demonstrate that this design introduces an inductive bias that encourages representations to be simultaneously decorrelated and clustered, without explicitly enforcing these properties. This bias provably enhances generalization and suffices to avoid known training failure modes, such as representation, dimensional, cluster, and intracluster collapses. We validate our theoretical findings on image datasets, including SVHN, CIFAR-10, CIFAR-100, and ImageNet-100. Our approach effectively combines the strengths of feature decorrelation and cluster-based self-supervised learning methods, overcoming training failure modes while achieving strong generalization in clustering and linear classification tasks.

Optimization · Stochastic

Qiang Li, Michal Yemini, Hoi To Wai

This paper studies the convergence of clipped stochastic gradient descent (SGD) algorithms with decision-dependent data distribution. Our setting is motivated by privacy preserving optimization algorithms that interact with performative data where the prediction models can influence future outcomes. This challenging setting involves the non-smooth clipping operator and non-gradient dynamics due to distribution shifts. We make two contributions in pursuit for a performative stable solution with these algorithms. First, we characterize the stochastic bias with projected clipped SGD (PCSGD) algorithm which is caused by the clipping operator that prevents PCSGD from reaching a stable solution. When the loss function is strongly convex, we quantify the lower and upper bounds for this stochastic bias and demonstrate a bias amplification phenomenon with the sensitivity of data distribution. When the loss function is non-convex, we bound the magnitude of stationarity bias. Second, we propose remedies to mitigate the bias either by utilizing an optimal step size design for PCSGD, or to apply the recent DiceSGD algorithm [Zhang et al., 2024]. Our analysis is also extended to show that the latter algorithm is free from stochastic bias in the performative setting. Numerical experiments verify our findings.

Theory · Deep Learning

Jingfeng Wu, Peter Bartlett, Matus Telgarsky, Bin Yu

In overparameterized logistic regression, gradient descent (GD) iterates diverge in norm while converging in direction to the maximum $\ell_2$-margin solution---a phenomenon known as the implicit bias of GD. This work investigates additional regularization effects induced by early stopping in well-specified high-dimensional logistic regression. We first demonstrate that the excess logistic risk vanishes for early stopped GD but diverges to infinity for GD iterates at convergence. This suggests that early stopped GD is well-calibrated, whereas asymptotic GD is statistically inconsistent. Second, we show that to attain a small excess zero-one risk, polynomially many samples are sufficient for early stopped GD, while exponentially many samples are necessary for any interpolating estimator, including asymptotic GD. This separation underscores the statistical benefits of early stopping in the overparameterized regime. Finally, we establish nonasymptotic bounds on the norm and angular differences between early stopped GD and $\ell_2$-regularized empirical risk minimizer, thereby connecting the implicit regularization of GD with explicit $\ell_2$-regularization.

Deep Learning · Generative Models and Autoencoders

Zhaoyu Zhang, Yang Hua, Guanxiong Sun, Hui Wang, Seán McLoone

Diffusion-based generative models (diffusion models) often require a large amount of data to train a score-based model that learns the score function of the data distribution through denoising score matching. However, collecting and cleaning such data can be expensive, time-consuming, and even infeasible. In this paper, we present a novel theoretical insight for diffusion models that two factors, i.e., the denoiser function hypothesis space and the number of training samples, can affect the denoising score matching error of all training samples. Based on this theoretical insight, it is evident that minimizing the total denoising score matching error is challenging within the denoiser function hypothesis space in existing methods, when training diffusion models with limited data. To address this, we propose a new diffusion model called Limited Data Diffusion (LD-Diffusion), which consists of two main components: a compressing model and a novel mixed augmentation with fixed probability (MAFP) strategy. Specifically, the compressing model can constrain the complexity of the denoiser function hypothesis space and MAFP can effectively increase the training samples by providing more informative guidance than existing data augmentation methods in the compressed hypothesis space. Extensive experiments on several datasets demonstrate that LD-Diffusion can achieve better performance compared to other diffusion models. Codes are available at https://github.com/zzhang05/LD-Diffusion.

Social Aspects · Privacy

Atefeh Gilani, Felipe Gomez, Shahab Asoodeh, Flavio Calmon, Oliver Kosut, Lalitha Sankar

We propose a unified optimization framework for designing continuous and discrete noise distributions that ensure differential privacy (DP) by minimizing Rényi DP, a variant of DP, under a cost constraint. Rényi DP has the advantage that by considering different values of the Rényi parameter $\alpha$, we can tailor our optimization for any number of compositions. To solve the optimization problem, we reduce it to a finite-dimensional convex formulation and perform preconditioned gradient descent. The resulting noise distributions are then compared to their Gaussian and Laplace counterparts. Numerical results demonstrate that our optimized distributions are consistently better, with significant improvements in $(\varepsilon, \delta)$-DP guarantees in the moderate composition regimes, compared to Gaussian and Laplace distributions with the same variance.

Probabilistic Methods · Bayesian Models and Methods

Stefano Cortinovis, Francois Caron

Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate estimates and tighter confidence intervals than traditional methods. In this paper, we propose to inform the PPI framework with prior knowledge on the quality of the predictions. The resulting method, which we call frequentist, assisted by Bayes, PPI (FAB-PPI), improves over PPI when the observed prediction quality is likely under the prior, while maintaining its frequentist guarantees. Furthermore, when using heavy-tailed priors, FAB-PPI adaptively reverts to standard PPI in low prior probability regions. We demonstrate the benefits of FAB-PPI in real and synthetic examples.

Social Aspects · Privacy

Erchi Wang, Yuqing Zhu, Yu-Xiang Wang

This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of $\tilde{O}\left(\frac{1}{\gamma^2\varepsilon n} + \frac{|S_{\mathrm{out}}|}{\gamma n}\right)$ where $n$ is the number of data points, $S_{\mathrm{out}}$ is an arbitrary subset of data one can remove and $\gamma$ is the margin of linear separation of the remaining data points (after $S_{\mathrm{out}}$ is removed). Here, $\tilde{O}(\cdot)$ hides only logarithmic terms. In the agnostic case, we improve the existing results when the number of outliers is small. Our algorithm is highly adaptive because it does not require knowing the margin parameter $\gamma$ or outlier subset $S_{\mathrm{out}}$. We also derive a utility bound for the advanced private hyperparameter tuning algorithm.

Applications · Robotics

Lucy Xiaoyang Shi, brian ichter, Michael Equi, Liyiming Ke, Karl Pertsch, Quan Vuong, James Tanner, Anna Walling, Haohuan Wang, Niccolo Fusai 等

Generalist robots that can perform a range of different tasks in open-world settings must be able to not only reason about the steps needed to accomplish their goals, but also process complex instructions, prompts, and even feedback during task execution. Intricate instructions (e.g., "Could you make me a vegetarian sandwich?" or "I don't like that one") require not just the ability to physically perform the individual steps, but the ability to situate complex commands and feedback in the physical world. In this work, we describe a system that uses vision-language models in a hierarchical structure, first reasoning over complex prompts and user feedback to deduce the most appropriate next step to fulfill the task, and then performing that step with low-level actions. In contrast to direct instruction following methods that can fulfill simple commands ("pick up the cup"), our system can reason through complex prompts and incorporate situated feedback during task execution ("that's not trash"). We evaluate our system across three robotic platforms, including single-arm, dual-arm, and dual-arm mobile robots, demonstrating its ability to handle tasks such as cleaning messy tables, making sandwiches, and grocery shopping.Videos are available at https://www.pi.website/research/hirobot

Deep Learning · Graph Neural Networks

Alex Vitvitskyi, João Madeira Araujo, Marc Lackenby, Petar Veličković

As implied by the plethora of literature on graph rewiring, the choice of computational graph employed by a neural network can make a significant impact on its downstream performance. Certain effects related to the computational graph, such as under-reaching and over-squashing, may even render the model incapable of learning certain functions. Most of these effects have only been thoroughly studied in the domain of undirected graphs; however, recent years have seen a significant rise in interest in feedforward computational graphs: directed graphs without any back edges. In this paper, we study the desirable properties of a feedforward computational graph, discovering two important complementary measures: fidelity and mixing time, and evaluating a few popular choices of graphs through the lens of these measures. Our study is backed by both theoretical analyses of the metrics' asymptotic behaviour for various graphs, as well as correlating these metrics to the performance of trained neural network models using the corresponding graphs.

General Machine Learning · Unsupervised and Semi-supervised Learning

Harit Vishwakarma, Yi Chen, Satya Sai Srinath Namburi GNVV, Sui Jiet Tay, Ramya Vinayak, Frederic Sala

Modern semi-supervised learning (SSL) methods rely on pseudolabeling and consistency regularization. Pseudolabeling is typically performed by comparing the model's confidence scores and a predefined threshold. While several heuristics have been proposed to improve threshold selection, the underlying issues of overconfidence and miscalibration in confidence scores remain largely unaddressed, leading to inaccurate pseudolabels, degraded test accuracy, and prolonged training. We take a first-principles approach to learn confidence scores and thresholds with an explicit knob for error. This flexible framework addresses the fundamental question of optimal scores and threshold selection in pseudolabeling. Moreover, it gives practitioners a principled way to control the quality and quantity of pseudolabels. Such control is vital in SSL, where balancing pseudolabel quality and quantity directly affects model performance and training efficiency. Our experiments show that, by integrating this framework with modern SSL methods, we achieve significant improvements in accuracy and training efficiency. In addition, we provide novel insights on the trade-offs between the choices of the error parameter and the end model's performance.

Probabilistic Methods · Variational Inference

Ngoc Quan Pham, Tuan Truong, Quyen Tran, Tan Nguyen, Dinh Phung, Trung Le

We introduce Interactive Bayesian Distributional Robustness (IBDR), a novel Bayesian inference framework that allows modeling the interactions between particles, thereby enhancing ensemble quality through increased particle diversity. IBDR is grounded in a generalized theoretical framework that connects the distributional population loss with the approximate posterior, motivating a practical dual optimization procedure that enforces distributional robustness while fostering particle diversity. We evaluate IBDR's performance against various baseline methods using the VTAB-1K benchmark and the common reasoning language task. The results consistently show that IBDR outperforms these baselines, underscoring its effectiveness in real-world applications.

Deep Learning · Large Language Models

Linxi Zhao, Yihe Deng, Weitong Zhang, Quanquan Gu

The advancement of Large Vision-Language Models (LVLMs) has increasingly highlighted the critical issue of their tendency to hallucinate non-existing objects in the images. To address this issue, previous works focused on using specially curated datasets or powerful LLMs to rectify the outputs of LVLMs. However, these approaches require either costly training or fine-tuning, or API access to proprietary LLMs for post-generation correction. In response to these limitations, we propose Mitigating hallucinAtion via image-gRounded guIdaNcE (MARINE), a framework that is both training-free and API-free. MARINE effectively and efficiently reduces object hallucinations during inference by introducing image-grounded guidance to LVLMs. This is achieved by leveraging open-source vision models to extract object-level information, thereby enhancing the precision of LVLM-generated content. Our framework's flexibility further allows for the integration of multiple vision models, enabling more reliable and robust object-level guidance. Through comprehensive evaluations across 5 popular LVLMs with diverse evaluation metrics and benchmarks, we demonstrate the effectiveness of MARINE, which even outperforms existing fine-tuning-based methods. Remarkably, it reduces hallucinations consistently in GPT-4V-assisted evaluation while maintaining the detailedness of LVLMs' generations. We release our code at https://github.com/Linxi-ZHAO/MARINE.

Deep Learning · Large Language Models

Sreyan Ghosh, Zhifeng Kong, Sonal Kumar, S Sakshi, Jaehyeon Kim, Wei Ping, Rafael Valle, Dinesh Manocha, Bryan Catanzaro

Understanding and reasoning over non-speech sounds and music are crucial for both humans and AI agents to interact effectively with their environments. In this paper, we introduce Audio Flamingo 2 (AF2), an Audio-Language Model (ALM) with advanced audio understanding and reasoning capabilities. AF2 leverages (i) a custom CLAP model, (ii) synthetic Audio QA data for fine-grained audio reasoning, and (iii) a multi-stage curriculum learning strategy. AF2 achieves state-of-the-art performance with only a 3B parameter small language model, surpassing large open-source and proprietary models across over 20 benchmarks. Next, for the first time, we extend audio understanding to long audio segments (30 secs to 5 mins) and propose LongAudio, a large and novel dataset for training ALMs on long audio captioning and question-answering tasks. Fine-tuning AF2 on LongAudio leads to exceptional performance on our proposed LongAudioBench, an expert-annotated benchmark for evaluating ALMs on long audio understanding capabilities. We conduct extensive ablation studies to confirm the efficacy of our approach.

Deep Learning · Robustness

Maximilian Müller, Matthias Hein

Detecting out-of-distribution (OOD) examples is an important task for deploying reliable machine learning models in safety-critial applications. While post-hoc methods based on the Mahalanobis distance applied to pre-logit features are among the most effective for ImageNet-scale OOD detection, their performance varies significantly across models. We connect this inconsistency to strong variations in feature norms, indicating severe violations of the Gaussian assumption underlying the Mahalanobis distance estimation. We show that simple $\ell_2$-normalization of the features mitigates this problem effectively, aligning better with the premise of normally distributed data with shared covariance matrix. Extensive experiments on 44 models across diverse architectures and pretraining schemes show that $\ell_2$-normalization improves the conventional Mahalanobis distance-based approaches significantly and consistently, and outperforms other recently proposed OOD detection methods.