Large pretrained models can be privately fine-tuned to achieve performance approaching that of non-private models. A common theme in these results is the surprising observation that high-dimensional models can achieve favorable privacy-utility trade-offs. This seemingly contradicts known results on the model-size dependence of differentially private convex learning and raises the following research question: When does the performance of differentially private learning not degrade with increasing model size? We identify that the magnitudes of gradients projected onto subspaces is a key factor that determines performance. To precisely characterize this for private convex learning, we introduce a condition on the objective that we term \emph{restricted Lipschitz continuity} and derive improved bounds for the excess empirical and population risks that are dimension-independent under additional conditions. We empirically show that in private fine-tuning of large language models, gradients obtained during fine-tuning are mostly controlled by a few principal components. This behavior is similar to conditions under which we obtain dimension-independent bounds in convex settings. Our theoretical and empirical results together provide a possible explanation for recent successes in large-scale private fine-tuning. Code to reproduce our results can be found at \url{https://github.com/lxuechen/private-transformers/tree/main/examples/classification/spectral_analysis}.

In this paper, we examine the use of data from multiple sensing modes, i.e., accelerometry and global navigation satellite system (GNSS), for classifying animal behavior. We extract three new features from the GNSS data, namely, distance from water point, median speed, and median estimated horizontal position error. We combine the information available from the accelerometry and GNSS data via two approaches. The first approach is based on concatenating the features extracted from both sensor data and feeding the concatenated feature vector into a multi-layer perceptron (MLP) classifier. The second approach is based on fusing the posterior probabilities predicted by two MLP classifiers. The input to each classifier is the features extracted from the data of one sensing mode. We evaluate the performance of the developed multimodal animal behavior classification algorithms using two real-world datasets collected via smart cattle collar tags and ear tags. The leave-one-animal-out cross-validation results show that both approaches improve the classification performance appreciably compared with using data of only one sensing mode. This is more notable for the infrequent but important behaviors of walking and drinking. The algorithms developed based on both approaches require little computational and memory resources hence are suitable for implementation on embedded systems of our collar tags and ear tags. However, the multimodal animal behavior classification algorithm based on posterior probability fusion is preferable to the one based on feature concatenation as it delivers better classification accuracy, has less computational and memory complexity, is more robust to sensor data failure, and enjoys better modularity.

We study the generation of dependent random numbers in a distributed fashion in order to enable privatized distributed learning by networked agents. We propose a method that we refer to as local graph-homomorphic processing; it relies on the construction of particular noises over the edges to ensure a certain level of differential privacy. We show that the added noise does not affect the performance of the learned model. This is a significant improvement to previous works on differential privacy for distributed algorithms, where the noise was added in a less structured manner without respecting the graph topology and has often led to performance deterioration. We illustrate the theoretical results by considering a linear regression problem over a network of agents.

Nowadays, differential privacy (DP) has become a well-accepted standard for privacy protection, and deep neural networks (DNN) have been immensely successful in machine learning. The combination of these two techniques, i.e., deep learning with differential privacy, promises the privacy-preserving release of high-utility models trained with sensitive data such as medical records. A classic mechanism for this purpose is DP-SGD, which is a differentially private version of the stochastic gradient descent (SGD) optimizer commonly used for DNN training. Subsequent approaches have improved various aspects of the model training process, including noise decay schedule, model architecture, feature engineering, and hyperparameter tuning. However, the core mechanism for enforcing DP in the SGD optimizer remains unchanged ever since the original DP-SGD algorithm, which has increasingly become a fundamental barrier limiting the performance of DP-compliant machine learning solutions. Motivated by this, we propose DPIS, a novel mechanism for differentially private SGD training that can be used as a drop-in replacement of the core optimizer of DP-SGD, with consistent and significant accuracy gains over the latter. The main idea is to employ importance sampling (IS) in each SGD iteration for mini-batch selection, which reduces both sampling variance and the amount of random noise injected to the gradients that is required to satisfy DP. Integrating IS into the complex mathematical machinery of DP-SGD is highly non-trivial. DPIS addresses the challenge through novel mechanism designs, fine-grained privacy analysis, efficiency enhancements, and an adaptive gradient clipping optimization. Extensive experiments on four benchmark datasets, namely MNIST, FMNIST, CIFAR-10 and IMDb, demonstrate the superior effectiveness of DPIS over existing solutions for deep learning with differential privacy.

Vertical federated learning (VFL), where data features are stored in multiple parties distributively, is an important area in machine learning. However, the communication complexity for VFL is typically very high. In this paper, we propose a unified framework by constructing coresets in a distributed fashion for communication-efficient VFL. We study two important learning tasks in the VFL setting: regularized linear regression and $k$-means clustering, and apply our coreset framework to both problems. We theoretically show that using coresets can drastically alleviate the communication complexity, while nearly maintain the solution quality. Numerical experiments are conducted to corroborate our theoretical findings.

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the iterative optimization process. To accelerate such a procedure, we apply a numerical pipeline that involves artificial neural networks to parametrize the boundary conditions of the problem in hand, compress the dimensionality of the (full-order) snapshots, and approximate the parametric solution manifold. It derives a general framework capable to provide an ad-hoc parametrization of the inlet boundary and quickly converges to the optimal solution thanks to model order reduction. We present in this contribution the results obtained by applying such methods to two different CFD test cases.

We consider the problem of finding the matching map between two sets of $d$ dimensional vectors from noisy observations, where the second set contains outliers. The matching map is then an injection, which can be consistently estimated only if the vectors of the second set are well separated. The main result shows that, in the high-dimensional setting, a detection region of unknown injection can be characterized by the sets of vectors for which the inlier-inlier distance is of order at least $d^{1/4}$ and the inlier-outlier distance is of order at least $d^{1/2}$. These rates are achieved using the estimated matching minimizing the sum of logarithms of distances between matched pairs of points. We also prove lower bounds establishing optimality of these rates. Finally, we report results of numerical experiments on both synthetic and real world data that illustrate our theoretical results and provide further insight into the properties of the estimators studied in this work.

Despite recent progress in understanding the double descend phenomena [1, 2, 3, 4] we still do not have a complete theory of generalisation in over-parameterised models. Two recent empirical observations, neural collapse [5] and grokking (generalisation beyond over-fitting) [6], can help us understand the training and generalisation properties of over-parameterised models. Neural collapse occurs in the terminal phase of training, i.e. the phase with zero train error. It refers to the collapse of the N dimensional, last-layer features (input to the last/classification layer) [5] to a (C 1)- dimensional equiangular tight frame (ETF) structure, where C is the number of classes. The feature vectors converge towards the vertices of the ETF structure such that features for each class are close to one vertex.

Domain generalization (DG) is a branch of transfer learning that aims to train the learning models on several seen domains and subsequently apply these pre-trained models to other unseen (unknown but related) domains. To deal with challenging settings in DG where both data and label of the unseen domain are not available at training time, the most common approach is to design the classifiers based on the domain-invariant representation features, i.e., the latent representations that are unchanged and transferable between domains. Contrary to popular belief, we show that designing classifiers based on invariant representation features alone is necessary but insufficient in DG. Our analysis indicates the necessity of imposing a constraint on the reconstruction loss induced by representation functions to preserve most of the relevant information about the label in the latent space. More importantly, we point out the trade-off between minimizing the reconstruction loss and achieving domain alignment in DG. Our theoretical results motivate a new DG framework that jointly optimizes the reconstruction loss and the domain discrepancy. Both theoretical and numerical results are provided to justify our approach.

Instance-level image retrieval in fashion is a challenging issue owing to its increasing importance in real-scenario visual fashion search. Cross-domain fashion retrieval aims to match the unconstrained customer images as queries for photographs provided by retailers; however, it is a difficult task due to a wide range of consumer-to-shop (C2S) domain discrepancies and also considering that clothing image is vulnerable to various non-rigid deformations. To this end, we propose a novel multi-scale and multi-granularity feature learning network (MMFL-Net), which can jointly learn global-local aggregation feature representations of clothing images in a unified framework, aiming to train a cross-domain model for C2S fashion visual similarity. First, a new semantic-spatial feature fusion part is designed to bridge the semantic-spatial gap by applying top-down and bottom-up bidirectional multi-scale feature fusion. Next, a multi-branch deep network architecture is introduced to capture global salient, part-informed, and local detailed information, and extracting robust and discrimination feature embedding by integrating the similarity learning of coarse-to-fine embedding with the multiple granularities. Finally, the improved trihard loss, center loss, and multi-task classification loss are adopted for our MMFL-Net, which can jointly optimize intra-class and inter-class distance and thus explicitly improve intra-class compactness and inter-class discriminability between its visual representations for feature learning. Furthermore, our proposed model also combines the multi-task attribute recognition and classification module with multi-label semantic attributes and product ID labels. Experimental results demonstrate that our proposed MMFL-Net achieves significant improvement over the state-of-the-art methods on the two datasets, DeepFashion-C2S and Street2Shop. Specifically, our approach exceeds the current best method by a large margin of +4.2% and +11.4% for mAP and Acc@1, respectively, on the most challenging dataset DeepFashion-C2S.