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Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. This paper proposes a system of neural differential equations representing first- and second-order score functions along trajectories based on deep neural networks. We reformulate the mean field control (MFC) problem with individual noises into an unconstrained optimization problem framed by the proposed neural ODE system. Additionally, we introduce a novel regularization term to enforce characteristics of viscous Hamilton--Jacobi--Bellman (HJB) equations to be satisfied based on the evolution of the second-order score function. Examples include regularized Wasserstein proximal operators (RWPOs), probability flow matching of Fokker--Planck (FP) equations, and linear quadratic (LQ) MFC problems, which demonstrate the effectiveness and accuracy of the proposed method.

The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works also demonstrate the potential for neural networks to go beyond NTK regime and perform feature learning. Recently, a line of work highlighted the feature learning capabilities of the early stages of gradient-based training. In this paper we consider another mechanism for feature learning via gradient descent through a local convergence analysis. We show that once the loss is below a certain threshold, gradient descent with a carefully regularized objective will capture ground-truth directions. We further strengthen this local convergence analysis by incorporating early-stage feature learning analysis. Our results demonstrate that feature learning not only happens at the initial gradient steps, but can also occur towards the end of training., Comment: NeurIPS 2024 camera ready version

We propose an actor-critic framework to solve the time-continuous stochastic optimal control problem. A least square temporal difference method is applied to compute the value function for the critic. The policy gradient method is implemented as policy improvement for the actor. Our key contribution lies in establishing the global convergence property of our proposed actor-critic flow, demonstrating a linear rate of convergence. Theoretical findings are further validated through numerical examples, showing the efficacy of our approach in practical applications., Comment: arXiv admin note: text overlap with arXiv:2302.05816

With a strong alignment between the training and test distributions, object relation as a context prior facilitates object detection. Yet, it turns into a harmful but inevitable training set bias upon test distributions that shift differently across space and time. Nevertheless, the existing detectors cannot incorporate deployment context prior during the test phase without parameter update. Such kind of capability requires the model to explicitly learn disentangled representations with respect to context prior. To achieve this, we introduce an additional graph input to the detector, where the graph represents the deployment context prior, and its edge values represent object relations. Then, the detector behavior is trained to bound to the graph with a modified training objective. As a result, during the test phase, any suitable deployment context prior can be injected into the detector via graph edits, hence calibrating, or "re-biasing" the detector towards the given prior at run-time without parameter update. Even if the deployment prior is unknown, the detector can self-calibrate using deployment prior approximated using its own predictions. Comprehensive experimental results on the COCO dataset, as well as cross-dataset testing on the Objects365 dataset, demonstrate the effectiveness of the run-time calibratable detector.

Adversarial robustness often comes at the cost of degraded accuracy, impeding real-life applications of robust classification models. Training-based solutions for better trade-offs are limited by incompatibilities with already-trained high-performance large models, necessitating the exploration of training-free ensemble approaches. Observing that robust models are more confident in correct predictions than in incorrect ones on clean and adversarial data alike, we speculate amplifying this "benign confidence property" can reconcile accuracy and robustness in an ensemble setting. To achieve so, we propose "MixedNUTS", a training-free method where the output logits of a robust classifier and a standard non-robust classifier are processed by nonlinear transformations with only three parameters, which are optimized through an efficient algorithm. MixedNUTS then converts the transformed logits into probabilities and mixes them as the overall output. On CIFAR-10, CIFAR-100, and ImageNet datasets, experimental results with custom strong adaptive attacks demonstrate MixedNUTS's vastly improved accuracy and near-SOTA robustness -- it boosts CIFAR-100 clean accuracy by 7.86 points, sacrificing merely 0.87 points in robust accuracy.

Recent advances in deep generative models have led to the development of methods capable of synthesizing high-quality, realistic images. These models pose threats to society due to their potential misuse. Prior research attempted to mitigate these threats by detecting generated images, but the varying traces left by different generative models make it challenging to create a universal detector capable of generalizing to new, unseen generative models. In this paper, we propose to inject a universal adversarial signature into an arbitrary pre-trained generative model, in order to make its generated contents more detectable and traceable. First, the imperceptible optimal signature for each image can be found by a signature injector through adversarial training. Subsequently, the signature can be incorporated into an arbitrary generator by fine-tuning it with the images processed by the signature injector. In this way, the detector corresponding to the signature can be reused for any fine-tuned generator for tracking the generator identity. The proposed method is validated on the FFHQ and ImageNet datasets with various state-of-the-art generative models, consistently showing a promising detection rate. Code will be made publicly available at \url{https://github.com/zengxianyu/genwm}.

Diffusion Probabilistic Field (DPF) models the distribution of continuous functions defined over metric spaces. While DPF shows great potential for unifying data generation of various modalities including images, videos, and 3D geometry, it does not scale to a higher data resolution. This can be attributed to the ``scaling property'', where it is difficult for the model to capture local structures through uniform sampling. To this end, we propose a new model comprising of a view-wise sampling algorithm to focus on local structure learning, and incorporating additional guidance, e.g., text description, to complement the global geometry. The model can be scaled to generate high-resolution data while unifying multiple modalities. Experimental results on data generation in various modalities demonstrate the effectiveness of our model, as well as its potential as a foundation framework for scalable modality-unified visual content generation., Comment: for project page, see https://t1-diffusion-model.github.io

Depth separation -- why a deeper network is more powerful than a shallower one -- has been a major problem in deep learning theory. Previous results often focus on representation power. For example, arXiv:1904.06984 constructed a function that is easy to approximate using a 3-layer network but not approximable by any 2-layer network. In this paper, we show that this separation is in fact algorithmic: one can learn the function constructed by arXiv:1904.06984 using an overparameterized network with polynomially many neurons efficiently. Our result relies on a new way of extending the mean-field limit to multilayer networks, and a decomposition of loss that factors out the error introduced by the discretization of infinite-width mean-field networks., Comment: ICLR 2023

We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global convergence of the gradient flow and establish a convergence rate under some regularity assumptions. The main novelty in the analysis is the notion of local optimal control function, which is introduced to characterize the local optimality of the iterate., Comment: 53 pages

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem $y = \beta^{*\top} x +\xi$ with sparse $\beta^*$, neither minimum $\ell_1$ or $\ell_2$ norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of $\ell_1$ and $\ell_2$ interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization., Comment: ICML 2023 camera ready version

We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the object. One of the standard approaches for solving this problem is to reformulate it as an optimization problem: finding the boundary of the domain that minimizes the $L^2$ distance between computed values of the scattered field and the given measurement data. The optimization problem is computationally challenging since the local set of convexity shrinks with increasing frequency and results in an increasing number of local minima in the vicinity of the true solution. In many practical experimental settings, low frequency measurements are unavailable due to limitations of the experimental setup or the sensors used for measurement. Thus, obtaining a good initial guess for the optimization problem plays a vital role in this environment. We present a neural network warm-start approach for solving the inverse scattering problem, where an initial guess for the optimization problem is obtained using a trained neural network. We demonstrate the effectiveness of our method with several numerical examples. For high frequency problems, this approach outperforms traditional iterative methods such as Gauss-Newton initialized without any prior (i.e., initialized using a unit circle), or initialized using the solution of a direct method such as the linear sampling method. The algorithm remains robust to noise in the scattered field measurements and also converges to the true solution for limited aperture data. However, the number of training samples required to train the neural network scales exponentially in frequency and the complexity of the obstacles considered. We conclude with a discussion of this phenomenon and potential directions for future research.

Recently, researchers observed that gradient descent for deep neural networks operates in an ``edge-of-stability'' (EoS) regime: the sharpness (maximum eigenvalue of the Hessian) is often larger than stability threshold $2/\eta$ (where $\eta$ is the step size). Despite this, the loss oscillates and converges in the long run, and the sharpness at the end is just slightly below $2/\eta$. While many other well-understood nonconvex objectives such as matrix factorization or two-layer networks can also converge despite large sharpness, there is often a larger gap between sharpness of the endpoint and $2/\eta$. In this paper, we study EoS phenomenon by constructing a simple function that has the same behavior. We give rigorous analysis for its training dynamics in a large local region and explain why the final converging point has sharpness close to $2/\eta$. Globally we observe that the training dynamics for our example has an interesting bifurcating behavior, which was also observed in the training of neural nets., Comment: 53 pages, 19 figures

Monotonic linear interpolation (MLI) - on the line connecting a random initialization with the minimizer it converges to, the loss and accuracy are monotonic - is a phenomenon that is commonly observed in the training of neural networks. Such a phenomenon may seem to suggest that optimization of neural networks is easy. In this paper, we show that the MLI property is not necessarily related to the hardness of optimization problems, and empirical observations on MLI for deep neural networks depend heavily on biases. In particular, we show that interpolating both weights and biases linearly leads to very different influences on the final output, and when different classes have different last-layer biases on a deep network, there will be a long plateau in both the loss and accuracy interpolation (which existing theory of MLI cannot explain). We also show how the last-layer biases for different classes can be different even on a perfectly balanced dataset using a simple model. Empirically we demonstrate that similar intuitions hold on practical networks and realistic datasets., Comment: ICLR 2023

By simulating the X-ray paths and the Chapman Model of a flat multi-channel plate and a curved multi-channel plate in the MATLAB, the field of view, local reflection efficiency, spherical aberration, point-spread function, collection efficiency of incident X-ray and peak-to-background ratio on the focal plane of the two devices were compared. At the same time, the advantages and disadvantages of the flat multi-channel plate and the curved multi-channel plate were compared.

Adversarial attacks pose safety and security concerns to deep learning applications, but their characteristics are under-explored. Yet largely imperceptible, a strong trace could have been left by PGD-like attacks in an adversarial example. Recall that PGD-like attacks trigger the ``local linearity'' of a network, which implies different extents of linearity for benign or adversarial examples. Inspired by this, we construct an Adversarial Response Characteristics (ARC) feature to reflect the model's gradient consistency around the input to indicate the extent of linearity. Under certain conditions, it qualitatively shows a gradually varying pattern from benign example to adversarial example, as the latter leads to Sequel Attack Effect (SAE). To quantitatively evaluate the effectiveness of ARC, we conduct experiments on CIFAR-10 and ImageNet for attack detection and attack type recognition in a challenging setting. The results suggest that SAE is an effective and unique trace of PGD-like attacks reflected through the ARC feature. The ARC feature is intuitive, light-weighted, non-intrusive, and data-undemanding.

The x-ray polycapillary lens is an optical device with good optic performance. Similar to the traditional X-ray polycapillary lens, square polycapillary slice lens was regulated on X-ray based on the full reflection principle of X-ray in the capillaries surfaces. According to its geometrical structure model and the X-ray tracing principle, a set of X-ray transmission procedures was established. A complete square polycapillary slice lens with quadratic curve was produced and the optical performance was tested

Blind or low vision (BLV) people were recently reported to be live streamers on the online platforms that employed content curation algorithms. Recent research uncovered algorithm biases suppressing the content created by marginalized populations. However, little is known about the effects of the algorithms adopted by live streaming platforms on BLV streamers and how they, as a marginalized population, perceive the effects of the algorithms. We interviewed BLV streamers (N=19) of Douyin -- a popular live stream platform in China -- to understand their perceptions of algorithms, perceived challenges, and mitigation strategies. Our findings show the perceived factors contributing to disadvantages under algorithmic evaluation of BLV streamers' content (e.g., issues with filming and timely interaction with viewers) and perceived algorithmic suppression (e.g., content not amplified to sighted users but suppressed within the BLV community). Their mitigation strategies (e.g., not watching other BLV streamers' shows) tended to be passive. We discuss design considerations to design a more inclusive and fair live streaming platform., Comment: DIS '22: ACM SIGCHI Conference on Designing Interactive Systems (DIS), June 13--June 17, 2022, Online

Higher neutron current densities can provide convenience for neutron experiments. Using neutron optical focusing elements, large flux beams transported to sample can be achieved. As one kind of focusing elements, polycapillary lens is very suitable for neutron absorption experiments such as PGAA and NDP technology. At present, a Neutron Physics and Application Spectrometer was in construction in CSNS, which is the first pulsed neutron source in China. To provide some suggestions and ideas for the following design of enhanced PGAA or NDP instrument with polycapillary lens in CSNS, a first neutron focusing experiment using polycapillary lens in CSNS was conducted. For 0.5-12.6 polychromatic beam, a focal spot with FWHM of 800 was obtained. As the value of wavelength increased, the beam size, transmission efficiency and gain increased. For cold neutron, the gain maintained in a level of 7., Comment: 12 pages, 13 figures, 12 references

Owing to security implications of adversarial vulnerability, adversarial robustness of deep metric learning models has to be improved. In order to avoid model collapse due to excessively hard examples, the existing defenses dismiss the min-max adversarial training, but instead learn from a weak adversary inefficiently. Conversely, we propose Hardness Manipulation to efficiently perturb the training triplet till a specified level of hardness for adversarial training, according to a harder benign triplet or a pseudo-hardness function. It is flexible since regular training and min-max adversarial training are its boundary cases. Besides, Gradual Adversary, a family of pseudo-hardness functions is proposed to gradually increase the specified hardness level during training for a better balance between performance and robustness. Additionally, an Intra-Class Structure loss term among benign and adversarial examples further improves model robustness and efficiency. Comprehensive experimental results suggest that the proposed method, although simple in its form, overwhelmingly outperforms the state-of-the-art defenses in terms of robustness, training efficiency, as well as performance on benign examples., Comment: Accepted by CVPR2022

Self-supervised learning has significantly improved the performance of many NLP tasks. However, how can self-supervised learning discover useful representations, and why is it better than traditional approaches such as probabilistic models are still largely unknown. In this paper, we focus on the context of topic modeling and highlight a key advantage of self-supervised learning - when applied to data generated by topic models, self-supervised learning can be oblivious to the specific model, and hence is less susceptible to model misspecification. In particular, we prove that commonly used self-supervised objectives based on reconstruction or contrastive samples can both recover useful posterior information for general topic models. Empirically, we show that the same objectives can perform on par with posterior inference using the correct model, while outperforming posterior inference using misspecified models., Comment: Accepted at ICLR 2023. Camera ready version

We propose a single time-scale actor-critic algorithm to solve the linear quadratic regulator (LQR) problem. A least squares temporal difference (LSTD) method is applied to the critic and a natural policy gradient method is used for the actor. We give a proof of convergence with sample complexity $\mathcal{O}(\varepsilon^{-1} \log(\varepsilon^{-1})^2)$. The method in the proof is applicable to general single time-scale bilevel optimization problem. We also numerically validate our theoretical results on the convergence., Comment: 4 figures