pwc-archive/papers-with-abstracts huggingface dataset:
On Local Posterior Structure in Deep Ensembles
Authors: Mikkel Jordahn, Jonas Vestergaard Jensen, Mikkel N. Schmidt, Michael Riis Andersen
Date: 2025-03-17 00:00:00
Tasks: Uncertainty Quantification

Bayesian Neural Networks (BNNs) often improve model calibration and predictive uncertainty quantification compared to point estimators such as maximum-a-posteriori (MAP). Similarly, deep ensembles (DEs) are also known to improve calibration, and therefore, it is natural to hypothesize that deep ensembles of BNNs (DE-BNNs) should provide even further improvements. In this work, we systematically investigate this across a number of datasets, neural network architectures, and BNN approximation methods and surprisingly find that when the ensembles grow large enough, DEs consistently outperform DE-BNNs on in-distribution data. To shine light on this observation, we conduct several sensitivity and ablation studies. Moreover, we show that even though DE-BNNs outperform DEs on out-of-distribution metrics, this comes at the cost of decreased in-distribution performance. As a final contribution, we open-source the large pool of trained models to facilitate further research on this topic.
Permutation Learning with Only N Parameters: From SoftSort to Self-Organizing Gaussians
Authors: Kai Uwe Barthel, Florian Barthel, Peter Eisert
Date: 2025-03-17 00:00:00

Sorting and permutation learning are key concepts in optimization and machine learning, especially when organizing high-dimensional data into meaningful spatial layouts. The Gumbel-Sinkhorn method, while effective, requires N*N parameters to determine a full permutation matrix, making it computationally expensive for large datasets. Low-rank matrix factorization approximations reduce memory requirements to 2NM (with M << N), but they still struggle with very large problems. SoftSort, by providing a continuous relaxation of the argsort operator, allows differentiable 1D sorting, but it faces challenges with multidimensional data and complex permutations. In this paper, we present a novel method for learning permutations using only N parameters, which dramatically reduces storage costs. Our method extends SoftSort by iteratively shuffling the N indices of the elements and applying a few SoftSort optimization steps per iteration. This modification significantly improves sorting quality, especially for multidimensional data and complex optimization criteria, and outperforms pure SoftSort. Our method offers improved memory efficiency and scalability compared to existing approaches, while maintaining high-quality permutation learning. Its dramatically reduced memory requirements make it particularly well-suited for large-scale optimization tasks, such as "Self-Organizing Gaussians", where efficient and scalable permutation learning is critical.
Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity
Authors: Eliot Beyler, Francis Bach
Date: 2025-03-17 00:00:00
Tasks: Denoising

Score-based generative models achieve state-of-the-art sampling performance by denoising a distribution perturbed by Gaussian noise. In this paper, we focus on a single deterministic denoising step, and compare the optimal denoiser for the quadratic loss, we name ''full-denoising'', to the alternative ''half-denoising'' introduced by Hyv{\"a}rinen (2024). We show that looking at the performances in term of distance between distribution tells a more nuanced story, with different assumptions on the data leading to very different conclusions. We prove that half-denoising is better than full-denoising for regular enough densities, while full-denoising is better for singular densities such as mixtures of Dirac measures or densities supported on a low-dimensional subspace. In the latter case, we prove that full-denoising can alleviate the curse of dimensionality under a linear manifold hypothesis.
Augmented Invertible Koopman Autoencoder for long-term time series forecasting
Authors: Anthony Frion, Lucas Drumetz, Mauro Dalla Mura, Guillaume Tochon, Abdeldjalil Aïssa-El-Bey
Date: 2025-03-17 00:00:00
Tasks: Time Series, Time Series Forecasting

Following the introduction of Dynamic Mode Decomposition and its numerous extensions, many neural autoencoder-based implementations of the Koopman operator have recently been proposed. This class of methods appears to be of interest for modeling dynamical systems, either through direct long-term prediction of the evolution of the state or as a powerful embedding for downstream methods. In particular, a recent line of work has developed invertible Koopman autoencoders (IKAEs), which provide an exact reconstruction of the input state thanks to their analytically invertible encoder, based on coupling layer normalizing flow models. We identify that the conservation of the dimension imposed by the normalizing flows is a limitation for the IKAE models, and thus we propose to augment the latent state with a second, non-invertible encoder network. This results in our new model: the Augmented Invertible Koopman AutoEncoder (AIKAE). We demonstrate the relevance of the AIKAE through a series of long-term time series forecasting experiments, on satellite image time series as well as on a benchmark involving predictions based on a large lookback window of observations.
Edgeworth Expansion for Semi-hard Triplet Loss
Authors: Masanari Kimura
Date: 2025-03-17 00:00:00
Tasks: Triplet

We develop a higher-order asymptotic analysis for the semi-hard triplet loss using the Edgeworth expansion. It is known that this loss function enforces that embeddings of similar samples are close while those of dissimilar samples are separated by a specified margin. By refining the classical central limit theorem, our approach quantifies the impact of the margin parameter and the skewness of the underlying data distribution on the loss behavior. In particular, we derive explicit Edgeworth expansions that reveal first-order corrections in terms of the third cumulant, thereby characterizing non-Gaussian effects present in the distribution of distance differences between anchor-positive and anchor-negative pairs. Our findings provide detailed insight into the sensitivity of the semi-hard triplet loss to its parameters and offer guidance for choosing the margin to ensure training stability.
An Optimization Framework for Differentially Private Sparse Fine-Tuning
Authors: Mehdi Makni, Kayhan Behdin, Gabriel Afriat, Zheng Xu, Sergei Vassilvitskii, Natalia Ponomareva, Hussein Hazimeh, Rahul Mazumder
Date: 2025-03-17 00:00:00
Tasks: Transfer Learning

Differentially private stochastic gradient descent (DP-SGD) is broadly considered to be the gold standard for training and fine-tuning neural networks under differential privacy (DP). With the increasing availability of high-quality pre-trained model checkpoints (e.g., vision and language models), fine-tuning has become a popular strategy. However, despite recent progress in understanding and applying DP-SGD for private transfer learning tasks, significant challenges remain -- most notably, the performance gap between models fine-tuned with DP-SGD and their non-private counterparts. Sparse fine-tuning on private data has emerged as an alternative to full-model fine-tuning; recent work has shown that privately fine-tuning only a small subset of model weights and keeping the rest of the weights fixed can lead to better performance. In this work, we propose a new approach for sparse fine-tuning of neural networks under DP. Existing work on private sparse finetuning often used fixed choice of trainable weights (e.g., updating only the last layer), or relied on public model's weights to choose the subset of weights to modify. Such choice of weights remains suboptimal. In contrast, we explore an optimization-based approach, where our selection method makes use of the private gradient information, while using off the shelf privacy accounting techniques. Our numerical experiments on several computer vision models and datasets show that our selection method leads to better prediction accuracy, compared to full-model private fine-tuning or existing private sparse fine-tuning approaches.
A Multi-Power Law for Loss Curve Prediction Across Learning Rate Schedules
Authors: Kairong Luo, Haodong Wen, Shengding Hu, Zhenbo Sun, Zhiyuan Liu, Maosong Sun, Kaifeng Lyu, WenGuang Chen
Date: 2025-03-17 00:00:00

Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we present an empirical law that describes how the pretraining loss of large language models evolves under different learning rate schedules, such as constant, cosine, and step decay schedules. Our proposed law takes a multi-power form, combining a power law based on the sum of learning rates and additional power laws to account for a loss reduction effect induced by learning rate decay. We extensively validate this law on various model sizes and architectures, and demonstrate that after fitting on a few learning rate schedules, the law accurately predicts the loss curves for unseen schedules of different shapes and horizons. Moreover, by minimizing the predicted final pretraining loss across learning rate schedules, we are able to find a schedule that outperforms the widely used cosine learning rate schedule. Interestingly, this automatically discovered schedule bears some resemblance to the recently proposed Warmup-Stable-Decay (WSD) schedule (Hu et al, 2024) but achieves a slightly lower final loss. We believe these results could offer valuable insights for understanding the dynamics of pretraining and designing learning rate schedules to improve efficiency.
In-Context Linear Regression Demystified: Training Dynamics and Mechanistic Interpretability of Multi-Head Softmax Attention
Authors: Jianliang He, Xintian Pan, Siyu Chen, Zhuoran Yang
Date: 2025-03-17 00:00:00
Tasks: In-Context Learning

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns: a diagonal and homogeneous pattern in the key-query (KQ) weights, and a last-entry-only and zero-sum pattern in the output-value (OV) weights. Remarkably, these patterns consistently appear from gradient-based training starting from random initialization. Our analysis reveals that such emergent structures enable multi-head attention to approximately implement a debiased gradient descent predictor -- one that outperforms single-head attention and nearly achieves Bayesian optimality up to proportional factor. Furthermore, compared to linear transformers, the softmax attention readily generalizes to sequences longer than those seen during training. We also extend our study to scenarios with non-isotropic covariates and multi-task linear regression. In the former, multi-head attention learns to implement a form of pre-conditioned gradient descent. In the latter, we uncover an intriguing regime where the interplay between head number and task number triggers a superposition phenomenon that efficiently resolves multi-task in-context learning. Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution, paving the way for deeper understanding and broader applications of in-context learning.
Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions
Authors: Farhad Pourkamali-Anaraki
Date: 2025-03-16 00:00:00
Tasks: Prediction Intervals, regression, Uncertainty Quantification

Traditional neural network regression models provide only point estimates, failing to capture predictive uncertainty. Probabilistic neural networks (PNNs) address this limitation by producing output distributions, enabling the construction of prediction intervals. However, the common assumption of Gaussian output distributions often results in overly wide intervals, particularly in the presence of outliers or deviations from normality. To enhance the adaptability of PNNs, we propose t-Distributed Neural Networks (TDistNNs), which generate t-distributed outputs, parameterized by location, scale, and degrees of freedom. The degrees of freedom parameter allows TDistNNs to model heavy-tailed predictive distributions, improving robustness to non-Gaussian data and enabling more adaptive uncertainty quantification. We develop a novel loss function tailored for the t-distribution and derive efficient gradient computations for seamless integration into deep learning frameworks. Empirical evaluations on synthetic and real-world data demonstrate that TDistNNs improve the balance between coverage and interval width. Notably, for identical architectures, TDistNNs consistently produce narrower prediction intervals than Gaussian-based PNNs while maintaining proper coverage. This work contributes a flexible framework for uncertainty estimation in neural networks tasked with regression, particularly suited to settings involving complex output distributions.
Support Collapse of Deep Gaussian Processes with Polynomial Kernels for a Wide Regime of Hyperparameters
Authors: Daryna Chernobrovkina, Steffen Grünewälder
Date: 2025-03-15 00:00:00
Tasks: Gaussian Processes

We analyze the prior that a Deep Gaussian Process with polynomial kernels induces. We observe that, even for relatively small depths, averaging effects occur within such a Deep Gaussian Process and that the prior can be analyzed and approximated effectively by means of the Berry-Esseen Theorem. One of the key findings of this analysis is that, in the absence of careful hyper-parameter tuning, the prior of a Deep Gaussian Process either collapses rapidly towards zero as the depth increases or places negligible mass on low norm functions. This aligns well with experimental findings and mirrors known results for convolution based Deep Gaussian Processes.
Evaluation-Time Policy Switching for Offline Reinforcement Learning
Authors: Natinael Solomon Neggatu, Jeremie Houssineau, Giovanni Montana
Date: 2025-03-15 00:00:00
Tasks: Behavioural cloning, Offline RL, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

Offline reinforcement learning (RL) looks at learning how to optimally solve tasks using a fixed dataset of interactions from the environment. Many off-policy algorithms developed for online learning struggle in the offline setting as they tend to over-estimate the behaviour of out of distributions actions. Existing offline RL algorithms adapt off-policy algorithms, employing techniques such as constraining the policy or modifying the value function to achieve good performance on individual datasets but struggle to adapt to different tasks or datasets of different qualities without tuning hyper-parameters. We introduce a policy switching technique that dynamically combines the behaviour of a pure off-policy RL agent, for improving behaviour, and a behavioural cloning (BC) agent, for staying close to the data. We achieve this by using a combination of epistemic uncertainty, quantified by our RL model, and a metric for aleatoric uncertainty extracted from the dataset. We show empirically that our policy switching technique can outperform not only the individual algorithms used in the switching process but also compete with state-of-the-art methods on numerous benchmarks. Our use of epistemic uncertainty for policy switching also allows us to naturally extend our method to the domain of offline to online fine-tuning allowing our model to adapt quickly and safely from online data, either matching or exceeding the performance of current methods that typically require additional modification or hyper-parameter fine-tuning.
Variance-Dependent Regret Lower Bounds for Contextual Bandits
Authors: Jiafan He, Quanquan Gu
Date: 2025-03-15 00:00:00
Tasks: Multi-Armed Bandits

Variance-dependent regret bounds for linear contextual bandits, which improve upon the classical $\tilde{O}(d\sqrt{K})$ regret bound to $\tilde{O}(d\sqrt{\sum_{k=1}^K\sigma_k^2})$, where $d$ is the context dimension, $K$ is the number of rounds, and $\sigma^2_k$ is the noise variance in round $k$, has been widely studied in recent years. However, most existing works focus on the regret upper bounds instead of lower bounds. To our knowledge, the only lower bound is from Jia et al. (2024), which proved that for any eluder dimension $d_{\textbf{elu}}$ and total variance budget $\Lambda$, there exists an instance with $\sum_{k=1}^K\sigma_k^2\leq \Lambda$ for which any algorithm incurs a variance-dependent lower bound of $\Omega(\sqrt{d_{\textbf{elu}}\Lambda})$. However, this lower bound has a $\sqrt{d}$ gap with existing upper bounds. Moreover, it only considers a fixed total variance budget $\Lambda$ and does not apply to a general variance sequence $\{\sigma_1^2,\ldots,\sigma_K^2\}$. In this paper, to overcome the limitations of Jia et al. (2024), we consider the general variance sequence under two settings. For a prefixed sequence, where the entire variance sequence is revealed to the learner at the beginning of the learning process, we establish a variance-dependent lower bound of $\Omega(d \sqrt{\sum_{k=1}^K\sigma_k^2 }/\log K)$ for linear contextual bandits. For an adaptive sequence, where an adversary can generate the variance $\sigma_k^2$ in each round $k$ based on historical observations, we show that when the adversary must generate $\sigma_k^2$ before observing the decision set $\mathcal{D}_k$, a similar lower bound of $\Omega(d\sqrt{ \sum_{k=1}^K\sigma_k^2} /\log^6(dK))$ holds. In both settings, our results match the upper bounds of the SAVE algorithm (Zhao et al., 2023) up to logarithmic factors.
Test-Time Training Provably Improves Transformers as In-context Learners
Authors: Halil Alperen Gozeten, M. Emrullah Ildiz, Xuechen Zhang, Mahdi Soltanolkotabi, Marco Mondelli, Samet Oymak
Date: 2025-03-14 00:00:00
Tasks: In-Context Learning, Language Modeling, Language Modelling, tabular-classification

Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify this success, we investigate a gradient-based TTT algorithm for in-context learning, where we train a transformer model on the in-context demonstrations provided in the test prompt. Specifically, we provide a comprehensive theoretical characterization of linear transformers when the update rule is a single gradient step. Our theory (i) delineates the role of alignment between pretraining distribution and target task, (ii) demystifies how TTT can alleviate distribution shift, and (iii) quantifies the sample complexity of TTT including how it can significantly reduce the eventual sample size required for in-context learning. As our empirical contribution, we study the benefits of TTT for TabPFN, a tabular foundation model. In line with our theory, we demonstrate that TTT significantly reduces the required sample size for tabular classification (3 to 5 times fewer) unlocking substantial inference efficiency with a negligible training cost.
Rethinking Diffusion Model in High Dimension
Authors: Zhenxin Zheng, Zhenjie Zheng
Date: 2025-03-11 00:00:00
Tasks: model

Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that they can learn the statistical properties of the underlying probability distribution, enabling sampling from this distribution to generate realistic samples. But is this really how they work? To address this question, this paper conducts a detailed analysis of the objective function and inference methods of diffusion models, leading to several important conclusions that help answer the above question: 1) In high-dimensional sparse scenarios, the target of the objective function fitting degrades from a weighted sum of multiple samples to a single sample. 2) The mainstream inference methods can all be represented within a simple unified framework, without requiring statistical concepts such as Markov chains and SDE, while aligning with the degraded objective function. 3) Guided by this simple framework, more efficient inference methods can be discovered.
Spectral-factorized Positive-definite Curvature Learning for NN Training
Authors: Wu Lin, Felix Dangel, Runa Eschenhagen, Juhan Bae, Richard E. Turner, Roger B. Grosse
Date: 2025-02-10 00:00:00
Tasks: Riemannian optimization

Many training methods, such as Adam(W) and Shampoo, learn a positive-definite curvature matrix and apply an inverse root before preconditioning. Recently, non-diagonal training methods, such as Shampoo, have gained significant attention; however, they remain computationally inefficient and are limited to specific types of curvature information due to the costly matrix root computation via matrix decomposition. To address this, we propose a Riemannian optimization approach that dynamically adapts spectral-factorized positive-definite curvature estimates, enabling the efficient application of arbitrary matrix roots and generic curvature learning. We demonstrate the efficacy and versatility of our approach in positive-definite matrix optimization and covariance adaptation for gradient-free optimization, as well as its efficiency in curvature learning for neural net training.
CombiGCN: An effective GCN model for Recommender System
Authors: Loc Tan Nguyen, Tin T. Tran
Date: 2025-03-27 00:00:00
Tasks: Collaborative Filtering, Recommendation Systems

Graph Neural Networks (GNNs) have opened up a potential line of research for collaborative filtering (CF). The key power of GNNs is based on injecting collaborative signal into user and item embeddings which will contain information about user-item interactions after that. However, there are still some unsatisfactory points for a CF model that GNNs could have done better. The way in which the collaborative signal are extracted through an implicit feedback matrix that is essentially built on top of the message-passing architecture of GNNs, and it only helps to update the embedding based on the value of the items (or users) embeddings neighboring. By identifying the similarity weight of users through their interaction history, a key concept of CF, we endeavor to build a user-user weighted connection graph based on their similarity weight. In this study, we propose a recommendation framework, CombiGCN, in which item embeddings are only linearly propagated on the user-item interaction graph, while user embeddings are propagated simultaneously on both the user-user weighted connection graph and user-item interaction graph graphs with Light Graph Convolution (LGC) and combined in a simpler method by using the weighted sum of the embeddings for each layer. We also conducted experiments comparing CombiGCN with several state-of-the-art models on three real-world datasets.