While deep neural networks can achieve good performance on in-distribution samples, their generalization ability significantly degrades under unknown test shifts. We study the problem of out-of-distribution (OOD) generalization capability of models by exploring the relationship between generalization error and training set size. Previous empirical evidence suggests that error falls off as a power of training set size and that lower errors indicate better model generalization. However, in the case of OOD samples, this is not true from our observations. Counterintuitively, increasing training data size does not always lead to a decrease in test generalization error. Such a non-decreasing phenomenon is formally investigated under a linear setting with empirical verification across varying visual benchmarks. To investigate the above results, we redefine OOD data as data located outside the convex hull of the data mixture in training and prove a new generalization error bound. Together our observations highlight that the effectiveness of well-trained models can be guaranteed on data within the convex hull of the training mixture. For OOD data beyond this coverage, the capability of models may be unassured. To achieve better generalization without knowledge of target environments, we demonstrate multiple strategies including data augmentation and pre-training. We also employ a novel data selection algorithm that outperforms baselines.

The rapid progress of Large Models (LMs) has recently revolutionized various fields of deep learning with remarkable grades, ranging from Natural Language Processing (NLP) to Computer Vision (CV). However, LMs are increasingly challenged and criticized by academia and industry due to their powerful performance but untrustworthy behavior, which urgently needs to be alleviated by reliable methods. Despite the abundance of literature on trustworthy LMs in NLP, a systematic survey specifically delving into the trustworthiness of LMs in CV remains absent. In order to mitigate this gap, we summarize four relevant concerns that obstruct the trustworthy usage in vision of LMs in this survey, including 1) human misuse, 2) vulnerability, 3) inherent issue and 4) interpretability. By highlighting corresponding challenge, countermeasures, and discussion in each topic, we hope this survey will facilitate readers' understanding of this field, promote alignment of LMs with human expectations and enable trustworthy LMs to serve as welfare rather than disaster for human society.

In deep learning, stochastic gradient descent (SGD) and its momentum-based variants are widely used in optimization algorithms, they usually face the problem of slow convergence. Meanwhile, existing adaptive learning rate optimizers accelerate convergence but often at the expense of generalization ability. We demonstrate that the adaptive learning rate property impairs generalization. To address this contradiction, we propose a novel optimization method that aims to accelerate the convergence rate of SGD without loss of generalization. This approach is based on the idea of reducing the variance of the historical gradient, enhancing the first-order moment estimation of the SGD by applying Wiener filtering theory, and introducing a time-varying adaptive weight. Experimental results show that SGDF achieves a trade-off between convergence and generalization compared to state-of-the-art optimizers.

Since the objective functions of reinforcement learning problems are typically highly nonconvex, it is desirable that policy gradient, the most popular algorithm, escapes saddle points and arrives at second-order stationary points. Existing results only consider vanilla policy gradient algorithms with unbiased gradient estimators, but practical implementations under the infinite-horizon discounted reward setting are biased due to finite-horizon sampling. Moreover, actor-critic methods, whose second-order convergence has not yet been established, are also biased due to the critic approximation of the value function. We provide a novel second-order analysis of biased policy gradient methods, including the vanilla gradient estimator computed from Monte-Carlo sampling of trajectories as well as the double-loop actor-critic algorithm, where in the inner loop the critic improves the approximation of the value function via TD(0) learning. Separately, we also establish the convergence of TD(0) on Markov chains irrespective of initial state distribution.

Recently, due to the popularity of deep neural networks and other methods whose training typically relies on the optimization of an objective function, and due to concerns for data privacy, there is a lot of interest in differentially private gradient descent methods. To achieve differential privacy guarantees with a minimum amount of noise, it is important to be able to bound precisely the sensitivity of the information which the participants will observe. In this study, we present a novel approach that mitigates the bias arising from traditional gradient clipping. By leveraging a public upper bound of the Lipschitz value of the current model and its current location within the search domain, we can achieve refined noise level adjustments. We present a new algorithm with improved differential privacy guarantees and a systematic empirical evaluation, showing that our new approach outperforms existing approaches also in practice.

Decision Transformer (DT), which employs expressive sequence modeling techniques to perform action generation, has emerged as a promising approach to offline policy optimization. However, DT generates actions conditioned on a desired future return, which is known to bear some weaknesses such as the susceptibility to environmental stochasticity. To overcome DT's weaknesses, we propose to empower DT with dynamic programming. Our method comprises three steps. First, we employ in-sample value iteration to obtain approximated value functions, which involves dynamic programming over the MDP structure. Second, we evaluate action quality in context with estimated advantages. We introduce two types of advantage estimators, IAE and GAE, which are suitable for different tasks. Third, we train an Advantage-Conditioned Transformer (ACT) to generate actions conditioned on the estimated advantages. Finally, during testing, ACT generates actions conditioned on a desired advantage. Our evaluation results validate that, by leveraging the power of dynamic programming, ACT demonstrates effective trajectory stitching and robust action generation in spite of the environmental stochasticity, outperforming baseline methods across various benchmarks. Additionally, we conduct an in-depth analysis of ACT's various design choices through ablation studies. Our code is available at https://github.com/LAMDA-RL/ACT.

Personalized learner modeling using cognitive diagnosis (CD), which aims to model learners' cognitive states by diagnosing learner traits from behavioral data, is a fundamental yet significant task in many web learning services. Existing cognitive diagnosis models (CDMs) follow the proficiency-response paradigm that views learner traits and question parameters as trainable embeddings and learns them through learner performance prediction. However, we notice that this paradigm leads to the inevitable non-identifiability and explainability overfitting problem, which is harmful to the quantification of learners' cognitive states and the quality of web learning services. To address these problems, we propose an identifiable cognitive diagnosis framework (ID-CDF) based on a novel response-proficiency-response paradigm inspired by encoder-decoder models. Specifically, we first devise the diagnostic module of ID-CDF, which leverages inductive learning to eliminate randomness in optimization to guarantee identifiability and captures the monotonicity between overall response data distribution and cognitive states to prevent explainability overfitting. Next, we propose a flexible predictive module for ID-CDF to ensure diagnosis preciseness. We further present an implementation of ID-CDF, i.e., ID-CDM, to illustrate its usability. Extensive experiments on four real-world datasets with different characteristics demonstrate that ID-CDF can effectively address the problems without loss of diagnosis preciseness.

While stochastic gradient descent (SGD) can use various learning rates, such as constant or diminishing rates, the previous numerical results showed that SGD performs better than other deep learning optimizers using when it uses learning rates given by line search methods. In this paper, we perform a convergence analysis on SGD with a learning rate given by an Armijo line search for nonconvex optimization indicating that the upper bound of the expectation of the squared norm of the full gradient becomes small when the number of steps and the batch size are large. Next, we show that, for SGD with the Armijo-line-search learning rate, the number of steps needed for nonconvex optimization is a monotone decreasing convex function of the batch size; that is, the number of steps needed for nonconvex optimization decreases as the batch size increases. Furthermore, we show that the stochastic first-order oracle (SFO) complexity, which is the stochastic gradient computation cost, is a convex function of the batch size; that is, there exists a critical batch size that minimizes the SFO complexity. Finally, we provide numerical results that support our theoretical results. The numerical results indicate that the number of steps needed for training deep neural networks decreases as the batch size increases and that there exist the critical batch sizes that can be estimated from the theoretical results.

Extended Vision techniques are ubiquitous in physics. However, the data cubes steaming from such analysis often pose a challenge in their interpretation, due to the intrinsic difficulty in discerning the relevant information from the spectra composing the data cube. Furthermore, the huge dimensionality of data cube spectra poses a complex task in its statistical interpretation; nevertheless, this complexity contains a massive amount of statistical information that can be exploited in an unsupervised manner to outline some essential properties of the case study at hand, e.g.~it is possible to obtain an image segmentation via (deep) clustering of data-cube's spectra, performed in a suitably defined low-dimensional embedding space. To tackle this topic, we explore the possibility of applying unsupervised clustering methods in encoded space, i.e. perform deep clustering on the spectral properties of datacube pixels. A statistical dimensional reduction is performed by an ad hoc trained (Variational) AutoEncoder, in charge of mapping spectra into lower dimensional metric spaces, while the clustering process is performed by a (learnable) iterative K-Means clustering algorithm. We apply this technique to two different use cases, of different physical origins: a set of Macro mapping X-Ray Fluorescence (MA-XRF) synthetic data on pictorial artworks, and a dataset of simulated astrophysical observations.

We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks is well known, while the spectral bias dependence on the choice of training algorithm is less studied. Our experiments demonstrate that an adaptive random Fourier features algorithm (ARFF) can yield a spectral bias closer to zero compared to the stochastic gradient descent optimizer (SGD). Additionally, we train two identically structured classifiers, employing SGD and ARFF, to the same accuracy levels and empirically assess their robustness against adversarial noise attacks.