We present a fully polynomial-time approximation scheme (FPTAS) for computing equilibria in congestion games, under \emph{smoothed} running-time analysis. More precisely, we prove that if the resource costs of a congestion game are randomly perturbed by independent noises, whose density is at most $\phi$, then \emph{any} sequence of $(1+\varepsilon)$-improving dynamics will reach an $(1+\varepsilon)$-approximate pure Nash equilibrium (PNE) after an expected number of steps which is strongly polynomial in $\frac{1}{\varepsilon}$, $\phi$, and the size of the game's description. Our results establish a sharp contrast to the traditional worst-case analysis setting, where it is known that better-response dynamics take exponentially long to converge to $\alpha$-approximate PNE, for any constant factor $\alpha\geq 1$. As a matter of fact, computing $\alpha$-approximate PNE in congestion games is PLS-hard. We demonstrate how our analysis can be applied to various different models of congestion games including general, step-function, and polynomial cost, as well as fair cost-sharing games (where the resource costs are decreasing). It is important to note that our bounds do not depend explicitly on the cardinality of the players' strategy sets, and thus the smoothed FPTAS is readily applicable to network congestion games as well.
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Structural re-parameterization is a general training scheme for Convolutional Neural Networks (CNNs), which achieves performance improvement without increasing inference cost. As Vision Transformers (ViTs) are gradually surpassing CNNs in various visual tasks, one may question: if a training scheme specifically for ViTs exists that can also achieve performance improvement without increasing inference cost? Recently, Mixture-of-Experts (MoE) has attracted increasing attention, as it can efficiently scale up the capacity of Transformers at a fixed cost through sparsely activated experts. Considering that MoE can also be viewed as a multi-branch structure, can we utilize MoE to implement a ViT training scheme similar to structural re-parameterization? In this paper, we affirmatively answer these questions, with a new general training strategy for ViTs. Specifically, we decouple the training and inference phases of ViTs. During training, we replace some Feed-Forward Networks (FFNs) of the ViT with specially designed, more efficient MoEs that assign tokens to experts by random uniform partition, and perform Experts Weights Averaging (EWA) on these MoEs at the end of each iteration. After training, we convert each MoE into an FFN by averaging the experts, transforming the model back into original ViT for inference. We further provide a theoretical analysis to show why and how it works. Comprehensive experiments across various 2D and 3D visual tasks, ViT architectures, and datasets validate the effectiveness and generalizability of the proposed training scheme. Besides, our training scheme can also be applied to improve performance when fine-tuning ViTs. Lastly, but equally important, the proposed EWA technique can significantly improve the effectiveness of naive MoE in various 2D visual small datasets and 3D visual tasks.
Denoising Diffusion Models (DDM) are emerging as the cutting-edge technology in the realm of deep generative modeling, challenging the dominance of Generative Adversarial Networks. However, effectively exploring the latent space's semantics and identifying compelling trajectories for manipulating and editing important attributes of the generated samples remains challenging, primarily due to the high-dimensional nature of the latent space. In this study, we specifically concentrate on face rotation, which is known to be one of the most intricate editing operations. By leveraging a recent embedding technique for Denoising Diffusion Implicit Models (DDIM), we achieve, in many cases, noteworthy manipulations encompassing a wide rotation angle of $\pm 30^o$, preserving the distinct characteristics of the individual. Our methodology exploits the computation of trajectories approximating clouds of latent representations of dataset samples with different yaw rotations through linear regression. Specific trajectories are obtained by restricting the analysis to subsets of data sharing significant attributes with the source image. One of these attributes is the light provenance: a byproduct of our research is a labeling of CelebA, categorizing images into three major groups based on the illumination direction: left, center, and right.
We present VERF, a collection of two methods (VERF-PnP and VERF-Light) for providing runtime assurance on the correctness of a camera pose estimate of a monocular camera without relying on direct depth measurements. We leverage the ability of NeRF (Neural Radiance Fields) to render novel RGB perspectives of a scene. We only require as input the camera image whose pose is being estimated, an estimate of the camera pose we want to monitor, and a NeRF model containing the scene pictured by the camera. We can then predict if the pose estimate is within a desired distance from the ground truth and justify our prediction with a level of confidence. VERF-Light does this by rendering a viewpoint with NeRF at the estimated pose and estimating its relative offset to the sensor image up to scale. Since scene scale is unknown, the approach renders another auxiliary image and reasons over the consistency of the optical flows across the three images. VERF-PnP takes a different approach by rendering a stereo pair of images with NeRF and utilizing the Perspective-n-Point (PnP) algorithm. We evaluate both methods on the LLFF dataset, on data from a Unitree A1 quadruped robot, and on data collected from Blue Origin's sub-orbital New Shepard rocket to demonstrate the effectiveness of the proposed pose monitoring method across a range of scene scales. We also show monitoring can be completed in under half a second on a 3090 GPU.
Ehrenfeucht-Fra\"iss\'e games provide a fundamental method for proving elementary equivalence (and equivalence up to a certain quantifier rank) of relational structures. We investigate the soundness and completeness of this method in the more general context of semiring semantics. Motivated originally by provenance analysis of database queries, semiring semantics evaluates logical statements not just by true or false, but by values in some commutative semiring; this can provide much more detailed information, for instance concerning the combinations of atomic facts that imply the truth of a statement, or practical information about evaluation costs, confidence scores, access levels or the number of successful evaluation strategies. There is a wide variety of different semirings that are relevant for provenance analysis, and the applicability of classical logical methods in semiring semantics may strongly depend on the algebraic properties of the underlying semiring. While Ehrenfeucht-Fra\"iss\'e games are sound and complete for logical equivalences in classical semantics, and thus on the Boolean semiring, this is in general not the case for other semirings. We provide a detailed analysis of the soundness and completeness of model comparison games on specific semirings, not just for classical Ehrenfeucht-Fra\"iss\'e games but also for other variants based on bijections or counting. Finally we propose a new kind of games, called homomorphism games, which are based on the fact that there exist certain rather simple semiring interpretations that are locally very different and can be separated even in a one-move game, but which can be proved to be elementarily equivalent via separating sets of homomorphisms into the Boolean semiring. We prove that these homomorphism games provide a sound and complete method for logical equivalences on finite and infinite lattice semirings.
This paper focuses on the impact of leveraging autonomous offensive approaches in Deep Reinforcement Learning (DRL) to train more robust agents by exploring the impact of applying adversarial learning to DRL for autonomous security in Software Defined Networks (SDN). Two algorithms, Double Deep Q-Networks (DDQN) and Neural Episodic Control to Deep Q-Network (NEC2DQN or N2D), are compared. NEC2DQN was proposed in 2018 and is a new member of the deep q-network (DQN) family of algorithms. The attacker has full observability of the environment and access to a causative attack that uses state manipulation in an attempt to poison the learning process. The implementation of the attack is done under a white-box setting, in which the attacker has access to the defender's model and experiences. Two games are played; in the first game, DDQN is a defender and N2D is an attacker, and in second game, the roles are reversed. The games are played twice; first, without an active causative attack and secondly, with an active causative attack. For execution, three sets of game results are recorded in which a single set consists of 10 game runs. The before and after results are then compared in order to see if there was actually an improvement or degradation. The results show that with minute parameter changes made to the algorithms, there was growth in the attacker's role, since it is able to win games. Implementation of the adversarial learning by the introduction of the causative attack showed the algorithms are still able to defend the network according to their strengths.
This study proposes a simple method for multi-object tracking (MOT) of players in a badminton court. We leverage two off-the-shelf cameras, one on the top of the court and the other on the side of the court. The one on the top is to track players' trajectories, while the one on the side is to analyze the pixel features of players. By computing the correlations between adjacent frames and engaging the information of the two cameras, MOT of badminton players is obtained. This two-camera approach addresses the challenge of player occlusion and overlapping in a badminton court, providing player trajectory tracking and multi-angle analysis. The presented system offers insights into the positions and movements of badminton players, thus serving as a coaching or self-training tool for badminton players to improve their gaming strategies.
Emotion recognition in conversation (ERC) aims to detect the emotion label for each utterance. Motivated by recent studies which have proven that feeding training examples in a meaningful order rather than considering them randomly can boost the performance of models, we propose an ERC-oriented hybrid curriculum learning framework. Our framework consists of two curricula: (1) conversation-level curriculum (CC); and (2) utterance-level curriculum (UC). In CC, we construct a difficulty measurer based on "emotion shift" frequency within a conversation, then the conversations are scheduled in an "easy to hard" schema according to the difficulty score returned by the difficulty measurer. For UC, it is implemented from an emotion-similarity perspective, which progressively strengthens the model's ability in identifying the confusing emotions. With the proposed model-agnostic hybrid curriculum learning strategy, we observe significant performance boosts over a wide range of existing ERC models and we are able to achieve new state-of-the-art results on four public ERC datasets.
Image-level weakly supervised semantic segmentation (WSSS) is a fundamental yet challenging computer vision task facilitating scene understanding and automatic driving. Most existing methods resort to classification-based Class Activation Maps (CAMs) to play as the initial pseudo labels, which tend to focus on the discriminative image regions and lack customized characteristics for the segmentation task. To alleviate this issue, we propose a novel activation modulation and recalibration (AMR) scheme, which leverages a spotlight branch and a compensation branch to obtain weighted CAMs that can provide recalibration supervision and task-specific concepts. Specifically, an attention modulation module (AMM) is employed to rearrange the distribution of feature importance from the channel-spatial sequential perspective, which helps to explicitly model channel-wise interdependencies and spatial encodings to adaptively modulate segmentation-oriented activation responses. Furthermore, we introduce a cross pseudo supervision for dual branches, which can be regarded as a semantic similar regularization to mutually refine two branches. Extensive experiments show that AMR establishes a new state-of-the-art performance on the PASCAL VOC 2012 dataset, surpassing not only current methods trained with the image-level of supervision but also some methods relying on stronger supervision, such as saliency label. Experiments also reveal that our scheme is plug-and-play and can be incorporated with other approaches to boost their performance.
Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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