Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural networks optimized with stochastic gradient descent often oscillate indefinitely. To reduce this discrepancy between theory and practice, this paper focuses on the generalization of neural networks whose training dynamics do not necessarily converge to fixed points. Our main contribution is to propose a notion of statistical algorithmic stability (SAS) that extends classical algorithmic stability to non-convergent algorithms and to study its connection to generalization. This ergodic-theoretic approach leads to new insights when compared to the traditional optimization and learning theory perspectives. We prove that the stability of the time-asymptotic behavior of a learning algorithm relates to its generalization and empirically demonstrate how loss dynamics can provide clues to generalization performance. Our findings provide evidence that networks that ``train stably generalize better'' even when the training continues indefinitely and the weights do not converge.

Fast and precise Lipschitz constant estimation of neural networks is an important task for deep learning. Researchers have recently found an intrinsic trade-off between the accuracy and smoothness of neural networks, so training a network with a loose Lipschitz constant estimation imposes a strong regularization, and can hurt the model accuracy significantly. In this work, we provide a unified theoretical framework, a quantitative geometric approach, to address the Lipschitz constant estimation. By adopting this framework, we can immediately obtain several theoretical results, including the computational hardness of Lipschitz constant estimation and its approximability. We implement the algorithms induced from this quantitative geometric approach, which are based on semidefinite programming (SDP). Our empirical evaluation demonstrates that they are more scalable and precise than existing tools on Lipschitz constant estimation for $\ell_\infty$-perturbations. Furthermore, we also show their intricate relations with other recent SDP-based techniques, both theoretically and empirically. We believe that this unified quantitative geometric perspective can bring new insights and theoretical tools to the investigation of neural-network smoothness and robustness.

The emergence of XNOR networks seek to reduce the model size and computational cost of neural networks for their deployment on specialized hardware requiring real-time processes with limited hardware resources. In XNOR networks, both weights and activations are binary, bringing great benefits to specialized hardware by replacing expensive multiplications with simple XNOR operations. Although XNOR convolutional and fully-connected neural networks have been successfully developed during the past few years, there is no XNOR network implementing commonly-used variants of recurrent neural networks such as long short-term memories (LSTMs). The main computational core of LSTMs involves vector-matrix multiplications followed by a set of non-linear functions and element-wise multiplications to obtain the gate activations and state vectors, respectively. Several previous attempts on quantization of LSTMs only focused on quantization of the vector-matrix multiplications in LSTMs while retaining the element-wise multiplications in full precision. In this paper, we propose a method that converts all the multiplications in LSTMs to XNOR operations using stochastic computing. To this end, we introduce a weighted finite-state machine and its synthesis method to approximate the non-linear functions used in LSTMs on stochastic bit streams. Experimental results show that the proposed XNOR LSTMs reduce the computational complexity of their quantized counterparts by a factor of 86x without any sacrifice on latency while achieving a better accuracy across various temporal tasks.

Deep learning models have shown their vulnerability when dealing with adversarial attacks. Existing attacks almost perform on low-level instances, such as pixels and super-pixels, and rarely exploit semantic clues. For face recognition attacks, existing methods typically generate the l_p-norm perturbations on pixels, however, resulting in low attack transferability and high vulnerability to denoising defense models. In this work, instead of performing perturbations on the low-level pixels, we propose to generate attacks through perturbing on the high-level semantics to improve attack transferability. Specifically, a unified flexible framework, Adversarial Attributes (Adv-Attribute), is designed to generate inconspicuous and transferable attacks on face recognition, which crafts the adversarial noise and adds it into different attributes based on the guidance of the difference in face recognition features from the target. Moreover, the importance-aware attribute selection and the multi-objective optimization strategy are introduced to further ensure the balance of stealthiness and attacking strength. Extensive experiments on the FFHQ and CelebA-HQ datasets show that the proposed Adv-Attribute method achieves the state-of-the-art attacking success rates while maintaining better visual effects against recent attack methods.

Blind image denoising is an important yet very challenging problem in computer vision due to the complicated acquisition process of real images. In this work we propose a new variational inference method, which integrates both noise estimation and image denoising into a unique Bayesian framework, for blind image denoising. Specifically, an approximate posterior, parameterized by deep neural networks, is presented by taking the intrinsic clean image and noise variances as latent variables conditioned on the input noisy image. This posterior provides explicit parametric forms for all its involved hyper-parameters, and thus can be easily implemented for blind image denoising with automatic noise estimation for the test noisy image. On one hand, as other data-driven deep learning methods, our method, namely variational denoising network (VDN), can perform denoising efficiently due to its explicit form of posterior expression. On the other hand, VDN inherits the advantages of traditional model-driven approaches, especially the good generalization capability of generative models. VDN has good interpretability and can be flexibly utilized to estimate and remove complicated non-i.i.d.

Deep learning algorithms can fare poorly when the training dataset suffers from heavy class-imbalance but the testing criterion requires good generalization on less frequent classes. We design two novel methods to improve performance in such scenarios. First, we propose a theoretically-principled label-distribution-aware margin (LDAM) loss motivated by minimizing a margin-based generalization bound. This loss replaces the standard cross-entropy objective during training and can be applied with prior strategies for training with class-imbalance such as re-weighting or re-sampling. Second, we propose a simple, yet effective, training schedule that defers re-weighting until after the initial stage, allowing the model to learn an initial representation while avoiding some of the complications associated with re-weighting or re-sampling. We test our methods on several benchmark vision tasks including the real-world imbalanced dataset iNaturalist 2018. Our experiments show that either of these methods alone can already improve over existing techniques and their combination achieves even better performance gains.

We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variational evidence lower bound (ELBO) while remaining as broadly applicable. We provide a computationally efficient gradient estimator for the TVO that applies to continuous, discrete, and non-reparameterizable distributions and show that the objective functions used in variational inference, variational autoencoders, wake sleep, and inference compilation are all special cases of the TVO. We use the TVO to learn both discrete and continuous deep generative models and empirically demonstrate state of the art model and inference network learning.

The last few years have witnessed a surge in methods for symbolic regression, from advances in traditional evolutionary approaches to novel deep learning-based systems. Individual works typically focus on advancing the state-of-the-art for one particular class of solution strategies, and there have been few attempts to investigate the benefits of hybridizing or integrating multiple strategies. In this work, we identify five classes of symbolic regression solution strategies---recursive problem simplification, neural-guided search, large-scale pre-training, genetic programming, and linear models---and propose a strategy to hybridize them into a single modular, unified symbolic regression framework. Based on empirical evaluation using SRBench, a new community tool for benchmarking symbolic regression methods, our unified framework achieves state-of-the-art performance in its ability to (1) symbolically recover analytical expressions, (2) fit datasets with high accuracy, and (3) balance accuracy-complexity trade-offs, across 252 ground-truth and black-box benchmark problems, in both noiseless settings and across various noise levels. Finally, we provide practical use case-based guidance for constructing hybrid symbolic regression algorithms, supported by extensive, combinatorial ablation studies.

Conversational generative AI has demonstrated remarkable promise for empowering biomedical practitioners, but current investigations focus on unimodal text. Multimodal conversational AI has seen rapid progress by leveraging billions of image-text pairs from the public web, but such general-domain vision-language models still lack sophistication in understanding and conversing about biomedical images. In this paper, we propose a cost-efficient approach for training a vision-language conversational assistant that can answer open-ended research questions of biomedical images. The key idea is to leverage a large-scale, broad-coverage biomedical figure-caption dataset extracted from PubMed Central, use GPT-4 to self-instruct open-ended instruction-following data from the captions, and then fine-tune a large general-domain vision-language model using a novel curriculum learning method. Specifically, the model first learns to align biomedical vocabulary using the figure-caption pairs as is, then learns to master open-ended conversational semantics using GPT-4 generated instruction-following data, broadly mimicking how a layperson gradually acquires biomedical knowledge. This enables us to train a Large Language and Vision Assistant for BioMedicine (LLaVA-Med) in less than 15 hours (with eight A100s). LLaVA-Med exhibits excellent multimodal conversational capability and can follow open-ended instruction to assist with inquiries about a biomedical image. On three standard biomedical visual question answering datasets, LLaVA-Med outperforms previous supervised state-of-the-art on certain metrics. To facilitate biomedical multimodal research, we will release our instruction-following data and the LLaVA-Med model.

The advent of deep learning algorithms for mobile devices and sensors has led to a dramatic expansion in the availability and number of systems trained on a wide range of machine learning tasks, creating a host of opportunities and challenges in the realm of transfer learning. Currently, most transfer learning methods require some kind of control over the systems learned, either by enforcing constraints during the source training, or through the use of a joint optimization objective between tasks that requires all data be co-located for training. However, for practical, privacy, or other reasons, in a variety of applications we may have no control over the individual source task training, nor access to source training samples. Instead we only have access to features pre-trained on such data as the output of black-boxes.'' For such scenarios, we consider the multi-source learning problem of training a classifier using an ensemble of pre-trained neural networks for a set of classes that have not been observed by any of the source networks, and for which we have very few training samples. We show that by using these distributed networks as feature extractors, we can train an effective classifier in a computationally-efficient manner using tools from (nonlinear) maximal correlation analysis. In particular, we develop a method we refer to as maximal correlation weighting (MCW) to build the required target classifier from an appropriate weighting of the feature functions from the source networks. We illustrate the effectiveness of the resulting classifier on datasets derived from the CIFAR-100, Stanford Dogs, and Tiny ImageNet datasets, and, in addition, use the methodology to characterize the relative value of different source tasks in learning a target task.