Diffusion-based imitation learning improves Behavioral Cloning (BC) on multimodal decision-making, but comes at the cost of significantly slower inference due to the recursion in the diffusion process. It urges us to design efficient policy generators while keeping the ability to generate diverse actions. To address this challenge, we propose AdaFlow, an imitation learning framework based on flowbased generative modeling. AdaFlow represents the policy with state-conditioned ordinary differential equations (ODEs), which are known as probability flows. We reveal an intriguing connection between the conditional variance of their training loss and the discretization error of the ODEs. With this insight, we propose a variance-adaptive ODE solver that can adjust its step size in the inference stage, making AdaFlow an adaptive decision-maker, offering rapid inference without sacrificing diversity. Interestingly, it automatically reduces to a one-step generator when the action distribution is uni-modal. Our comprehensive empirical evaluation shows that AdaFlow achieves high performance with fast inference speed.

An implication of the bounds is that the network is biased to learn the top eigenfunctions of the Neural Tangent Kernel not just on the training set but over the entire input space. This bias depends on the model architecture and input distribution alone and thus does not depend on the target function which does not need to be in the RKHS of the kernel. The result is valid for deep architectures with fully connected, convolutional, and residual layers. Furthermore the width does not need to grow polynomially with the number of samples in order to obtain high probability bounds up to a stopping time. The proof exploits the low-effective-rank property of the Fisher Information Matrix at initialization, which implies a low effective dimension of the model (far smaller than the number of parameters). We conclude that local capacity control from the low effective rank of the Fisher Information Matrix is still underexplored theoretically.

Performing eigendecomposition during neural network training is essential for tasks such as dimensionality reduction, network compression, image denoising, and graph learning. However, eigendecomposition is computationally expensive as it is orders of magnitude slower than other neural network operations. To address this challenge, we propose a novel approach called "amortized eigendecomposition" that relaxes the exact eigendecomposition by introducing an additional loss term called eigen loss. Our approach offers significant speed improvements by replacing the computationally expensive eigendecomposition with a more affordable QR decomposition at each iteration. Theoretical analysis guarantees that the desired eigenpair is attained as optima of the eigen loss. Empirical studies on nuclear norm regularization, latent-space principal component analysis, and graphs adversarial learning demonstrate significant improvements in training efficiency while producing nearly identical outcomes to conventional approaches. This novel methodology promises to integrate eigendecomposition efficiently into neural network training, overcoming existing computational challenges and unlocking new potential for advanced deep learning applications.

Coreset is a small set that provides a data summary for a large dataset, such that training solely on the small set achieves competitive performance compared with a large dataset. In rehearsal-based continual learning, the coreset is typically used in the memory replay buffer to stand for representative samples in previous tasks, and the coreset selection procedure is typically formulated as a bilevel problem. However, the typical bilevel formulation for coreset selection explicitly performs optimization over discrete decision variables with greedy search, which is computationally expensive. Several works consider other formulations to address this issue, but they ignore the nested nature of bilevel optimization problems and may not solve the bilevel coreset selection problem accurately. To address these issues, we propose a new bilevel formulation, where the inner problem tries to find a model which minimizes the expected training error sampled from a given probability distribution, and the outer problem aims to learn the probability distribution with approximately K (coreset size) nonzero entries such that learned model in the inner problem minimizes the training error over the whole data. To ensure the learned probability has approximately K nonzero entries, we introduce a novel regularizer based on the smoothed top-K loss in the upper problem.

We present variational inference with sequential sample-average approximations (VISA), a method for approximate inference in computationally intensive models, such as those based on numerical simulations. VISA extends importance-weighted forward-KL variational inference (IWFVI) by employing a sequence of sampleaverage approximations, which are considered valid inside a trust region. This makes it possible to reuse model evaluations across multiple gradient steps, thereby reducing computational cost. We perform experiments on high-dimensional Gaussians, Lotka-Volterra dynamics, and a Pickover attractor. We demonstrate that VISA can achieve comparable approximation accuracy to standard importanceweighted forward-KL variational inference while requirering significantly fewer samples for conservatively chosen learning rates.

The Segmentation Anything Model (SAM) requires labor-intensive data labeling. We present Unsupervised SAM (UnSAM) for promptable and automatic wholeimage segmentation that does not require human annotations. UnSAM utilizes a divide-and-conquer strategy to "discover" the hierarchical structure of visual scenes.

Advances in generative models have made it possible for AI-generated text, code, and images to mirror human-generated content in many applications. Watermarking, a technique that aims to embed information in the output of a model to verify its source, is useful for mitigating the misuse of such AI-generated content. However, we show that common design choices in LLM watermarking schemes make the resulting systems surprisingly susceptible to attack--leading to fundamental trade-offs in robustness, utility, and usability. To navigate these trade-offs, we rigorously study a set of simple yet effective attacks on common watermarking systems, and propose guidelines and defenses for LLM watermarking in practice.

Equation (8) uses the linearity of expectation. Includes 100 synthetic 2D graphs, regular tiling of the 2D plane with equilateral triangles, with 100 |V | < 400 [47]. Includes 100 synthetic graphs with 10 |V | 100. Includes 100 synthetic 2D graphs, regular tiling of the 2D plane with equilateral squares, with 100 |V | < 400 [47]. Figure 5: Each dataset is split into train, validation and test sets.