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We study gradient descent (GD) dynamics on logistic regression problems with large, constant step sizes. For linearly-separable data, it is known that GD converges to the minimizer with arbitrarily large step sizes, a property which no longer holds when the problem is not separable. In fact, the behaviour can be much more complex -- a sequence of period-doubling bifurcations begins at the critical step size $2/\lambda$, where $\lambda$ is the largest eigenvalue of the Hessian at the solution. Using a smaller-than-critical step size guarantees convergence if initialized nearby the solution: but does this suffice globally? In one dimension, we show that a step size less than $1/\lambda$ suffices for global convergence. However, for all step sizes between $1/\lambda$ and the critical step size $2/\lambda$, one can construct a dataset such that GD converges to a stable cycle. In higher dimensions, this is actually possible even for step sizes less than $1/\lambda$. Our results show that although local convergence is guaranteed for all step sizes less than the critical step size, global convergence is not, and GD may instead converge to a cycle depending on the initialization.

Model editing aims to data-efficiently correct predictive errors of large pre-trained models while ensuring generalization to neighboring failures and locality to minimize unintended effects on unrelated examples. While significant progress has been made in editing Transformer-based large language models, effective strategies for editing vision Transformers (ViTs) in computer vision remain largely untapped. In this paper, we take initial steps towards correcting predictive errors of ViTs, particularly those arising from subpopulation shifts. Taking a locate-then-edit approach, we first address the where-to-edit challenge by meta-learning a hypernetwork on CutMix-augmented data generated for editing reliability. This trained hypernetwork produces generalizable binary masks that identify a sparse subset of structured model parameters, responsive to real-world failure samples. Afterward, we solve the how-to-edit problem by simply fine-tuning the identified parameters using a variant of gradient descent to achieve successful edits. To validate our method, we construct an editing benchmark that introduces subpopulation shifts towards natural underrepresented images and AI-generated images, thereby revealing the limitations of pre-trained ViTs for object recognition. Our approach not only achieves superior performance on the proposed benchmark but also allows for adjustable trade-offs between generalization and locality. Our code is available at //github.com/hustyyq/Where-to-Edit.

Continual learning with deep neural networks presents challenges distinct from both the fixed-dataset and convex continual learning regimes. One such challenge is plasticity loss, wherein a neural network trained in an online fashion displays a degraded ability to fit new tasks. This problem has been extensively studied in both supervised learning and off-policy reinforcement learning (RL), where a number of remedies have been proposed. Still, plasticity loss has received less attention in the on-policy deep RL setting. Here we perform an extensive set of experiments examining plasticity loss and a variety of mitigation methods in on-policy deep RL. We demonstrate that plasticity loss is pervasive under domain shift in this regime, and that a number of methods developed to resolve it in other settings fail, sometimes even performing worse than applying no intervention at all. In contrast, we find that a class of ``regenerative'' methods are able to consistently mitigate plasticity loss in a variety of contexts, including in gridworld tasks and more challenging environments like Montezuma's Revenge and ProcGen.

Achieving the effective design and improvement of reward functions in reinforcement learning (RL) tasks with complex custom environments and multiple requirements presents considerable challenges. In this paper, we propose ERFSL, an efficient reward function searcher using LLMs, which enables LLMs to be effective white-box searchers and highlights their advanced semantic understanding capabilities. Specifically, we generate reward components for each numerically explicit user requirement and employ a reward critic to identify the correct code form. Then, LLMs assign weights to the reward components to balance their values and iteratively adjust the weights without ambiguity and redundant adjustments by flexibly adopting directional mutation and crossover strategies, similar to genetic algorithms, based on the context provided by the training log analyzer. We applied the framework to an underwater data collection RL task without direct human feedback or reward examples (zero-shot learning). The reward critic successfully corrects the reward code with only one feedback instance for each requirement, effectively preventing unrectifiable errors. The initialization of weights enables the acquisition of different reward functions within the Pareto solution set without the need for weight search. Even in cases where a weight is 500 times off, on average, only 5.2 iterations are needed to meet user requirements. The ERFSL also works well with most prompts utilizing GPT-4o mini, as we decompose the weight searching process to reduce the requirement for numerical and long-context understanding capabilities

We present a maximum entropy inverse reinforcement learning (IRL) approach for improving the sample quality of diffusion generative models, especially when the number of generation time steps is small. Similar to how IRL trains a policy based on the reward function learned from expert demonstrations, we train (or fine-tune) a diffusion model using the log probability density estimated from training data. Since we employ an energy-based model (EBM) to represent the log density, our approach boils down to the joint training of a diffusion model and an EBM. Our IRL formulation, named Diffusion by Maximum Entropy IRL (DxMI), is a minimax problem that reaches equilibrium when both models converge to the data distribution. The entropy maximization plays a key role in DxMI, facilitating the exploration of the diffusion model and ensuring the convergence of the EBM. We also propose Diffusion by Dynamic Programming (DxDP), a novel reinforcement learning algorithm for diffusion models, as a subroutine in DxMI. DxDP makes the diffusion model update in DxMI efficient by transforming the original problem into an optimal control formulation where value functions replace back-propagation in time. Our empirical studies show that diffusion models fine-tuned using DxMI can generate high-quality samples in as few as 4 and 10 steps. Additionally, DxMI enables the training of an EBM without MCMC, stabilizing EBM training dynamics and enhancing anomaly detection performance.

We study reinforcement learning with multinomial logistic (MNL) function approximation where the underlying transition probability kernel of the Markov decision processes (MDPs) is parametrized by an unknown transition core with features of state and action. For the finite horizon episodic setting with inhomogeneous state transitions, we propose provably efficient algorithms with randomized exploration having frequentist regret guarantees. For our first algorithm, $\texttt{RRL-MNL}$, we adapt optimistic sampling to ensure the optimism of the estimated value function with sufficient frequency. We establish that $\texttt{RRL-MNL}$ achieves a $\tilde{O}(\kappa^{-1} d^{\frac{3}{2}} H^{\frac{3}{2}} \sqrt{T})$ frequentist regret bound with constant-time computational cost per episode. Here, $d$ is the dimension of the transition core, $H$ is the horizon length, $T$ is the total number of steps, and $\kappa$ is a problem-dependent constant. Despite the simplicity and practicality of $\texttt{RRL-MNL}$, its regret bound scales with $\kappa^{-1}$, which is potentially large in the worst case. To improve the dependence on $\kappa^{-1}$, we propose $\texttt{ORRL-MNL}$, which estimates the value function using the local gradient information of the MNL transition model. We show that its frequentist regret bound is $\tilde{O}(d^{\frac{3}{2}} H^{\frac{3}{2}} \sqrt{T} + \kappa^{-1} d^2 H^2)$. To the best of our knowledge, these are the first randomized RL algorithms for the MNL transition model that achieve statistical guarantees with constant-time computational cost per episode. Numerical experiments demonstrate the superior performance of the proposed algorithms.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Conventional methods for object detection typically require a substantial amount of training data and preparing such high-quality training data is very labor-intensive. In this paper, we propose a novel few-shot object detection network that aims at detecting objects of unseen categories with only a few annotated examples. Central to our method are our Attention-RPN, Multi-Relation Detector and Contrastive Training strategy, which exploit the similarity between the few shot support set and query set to detect novel objects while suppressing false detection in the background. To train our network, we contribute a new dataset that contains 1000 categories of various objects with high-quality annotations. To the best of our knowledge, this is one of the first datasets specifically designed for few-shot object detection. Once our few-shot network is trained, it can detect objects of unseen categories without further training or fine-tuning. Our method is general and has a wide range of potential applications. We produce a new state-of-the-art performance on different datasets in the few-shot setting. The dataset link is //github.com/fanq15/Few-Shot-Object-Detection-Dataset.

We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.