Miracle-dz/UniFAR-FTUs huggingface dataset:
An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization

This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the gradient in conjunction with inexact solutions to the SQP subproblems. Under reasonable assumptions on the quality of the employed gradient approximations and the accuracy of the solutions to the SQP subproblems, we establish global convergence results for the proposed method. Motivated by these results, the second part of the paper describes a practical adaptive inexact stochastic sequential quadratic programming (PAIS-SQP) method. We propose criteria for controlling the sample size and the accuracy in the solutions of the SQP subproblems based on estimates of the variance in the stochastic gradient approximations obtained as the optimization progresses. Finally, we demonstrate the performance of the practical method on a subset of the CUTE problems and constrained classification tasks.
ORC: Network Group-based Knowledge Distillation using Online Role Change

In knowledge distillation, since a single, omnipotent teacher network cannot solve all problems, multiple teacher-based knowledge distillations have been studied recently. However, sometimes their improvements are not as good as expected because some immature teachers may transfer the false knowledge to the student. In this paper, to overcome this limitation and take the efficacy of the multiple networks, we divide the multiple networks into teacher and student groups, respectively. That is, the student group is a set of immature networks that require learning the teacher’s knowledge, while the teacher group consists of the selected networks that are capable of teaching successfully. We propose our online role change strategy where the top-ranked networks in the student group are able to promote to the teacher group at every iteration. After training the teacher group using the error samples of the student group to refine the teacher group’s knowledge, we transfer the collaborative knowledge from the teacher group to the student group successfully. We verify the superiority of the proposed method on CIFAR-10, CIFAR-100, and ImageNet which achieves high performance. We further show the generality of our method with various backbone architectures such as ResNet, WRN, VGG, Mobilenet, and Shufflenet.1
The contact process on dynamical scale-free networks

: We investigate the contact process on four diﬀerent types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent vertices. Depending on the type of graph, the tail exponent of the degree distribution and the updating rate, we ﬁnd parameter regimes of fast and slow extinction and in the latter case identify metastable exponents that undergo ﬁrst order phase transitions. R´esum´e: Nous ´etudions le processus de contact sur quatre types diﬀ´erents de graphes al´eatoires inhomog`enes invariants d’´echelle ´evoluant selon une dynamique stationnaire, o`u chaque arˆete potentielle est rafraˆıchie `a un taux d´ependant de la force des sommets adjacents. En fonction du type de graphe, de l’exposant de la queue de distribution des degr´es et du taux de rafraˆıchissement, nous trouvons des r´egimes d’extinction rapide ou lente et, dans ce dernier cas, nous identiﬁons des exposants m´etastables qui subissent des transitions de phase de premier ordre.
A general criterion for the P\'{o}lya-Carlson dichotomy and application

We prove a general criterion for an irrational power series f ( z ) = ∞ X n =0 a n z n with coeﬃcients in a number ﬁeld K to admit the unit circle as a natural boundary. As an application, let F be a ﬁnite ﬁeld, let d be a positive integer, let A ∈ M d ( F [ t ]) be a d × d -matrix with entries in F [ t ], and let ζ A ( z ) be the Artin-Mazur zeta function associated to the multiplication-by- A map on the compact abelian group F ((1 /t )) d /F [ t ] d . We provide a complete characterization of when ζ A ( z ) is algebraic and prove that it admits the circle of convergence as a natural boundary in the transcendence case. This is in stark contrast to the case of linear endomorphisms on R d / Z d in which Baake, Lau, and Paskunas prove that the zeta function is always rational. Some connections to earlier work of Bell, Byszewski, Cornelissen, Miles, Royals, and Ward are discussed. Our method uses a similar technique in recent work of Bell, Nguyen, and Zannier together with certain patching arguments involving linear recurrence sequences.
Know Your Boundaries: The Necessity of Explicit Behavioral Cloning in Offline RL

We introduce an offline reinforcement learning (RL) algorithm that explicitly clones a behavior policy to constrain value learning. In offline RL, it is often important to prevent a policy from selecting unobserved actions, since the consequence of these actions cannot be presumed without additional information about the environment. One straightforward way to implement such a constraint is to explicitly model a given data distribution via behavior cloning and directly force a policy not to select uncertain actions. However, many offline RL methods instantiate the constraint indirectly -- for example, pessimistic value estimation -- due to a concern about errors when modeling a potentially complex behavior policy. In this work, we argue that it is not only viable but beneficial to explicitly model the behavior policy for offline RL because the constraint can be realized in a stable way with the trained model. We first suggest a theoretical framework that allows us to incorporate behavior-cloned models into value-based offline RL methods, enjoying the strength of both explicit behavior cloning and value learning. Then, we propose a practical method utilizing a score-based generative model for behavior cloning. With the proposed method, we show state-of-the-art performance on several datasets within the D4RL and Robomimic benchmarks and achieve competitive performance across all datasets tested.
Is Mapping Necessary for Realistic PointGoal Navigation?

Can an autonomous agent navigate in a new environment without building an explicit map? For the task of PointGoal navigation ('Go to Δx, Δy’) under idealized settings (no RGB-D and actuation noise, perfect GPS+Compass), the answer is a clear ‘yes' - mapless neural models composed of task-agnostic components (CNNs and RNNs) trained with large-scale reinforcement learning achieve 100% Success on a standard dataset (Gibson [24] ). However, for PointNav in a realistic setting (RGB-D and actuation noise, no GPS+Compass), this is an open question; one we tackle in this paper. The strongest published result for this task is 71.7% Success [39]. 11According to Habitat Challenge 2020 PointNav benchmark held annually. A concurrent as-yet-unpublished result has reported 91% Success on 2021's benchmark, but we are unable to comment on the details because an associated report is not available.First, we identify the main (perhaps, only) cause of the drop in performance: absence of GPS+Compass. An agent with perfect GPS+Compass faced with RGB-D sensing and actuation noise achieves 99.8% Success (Gibson- v2 val). This suggests that (to paraphrase a meme) robust visual odometry is all we need for realistic PointNav; if we can achieve that, we can ignore the sensing and actuation noise. With that as our operating hypothesis, we scale dataset size, model size, and develop human-annotation-free dataaugmentation techniques to train neural models for visual odometry. We advance state of the art on the Habitat Realistic PointNav Challenge - SPL by 40% (relative), 53 to 74, and Success by 31% (relative), 71 to 94. While our approach does not saturate or ‘solve’ this dataset, this strong improvement combined with promising zero-shot sim2real transfer (to a LoCoBot robot) provides evidence consistent with the hypothesis that explicit mapping may not be necessary for navigation, even in a realistic setting.
Hard Negative Sampling Strategies for Contrastive Representation Learning

One of the challenges in contrastive learning is the selection of appropriate \textit{hard negative} examples, in the absence of label information. Random sampling or importance sampling methods based on feature similarity often lead to sub-optimal performance. In this work, we introduce UnReMix, a hard negative sampling strategy that takes into account anchor similarity, model uncertainty and representativeness. Experimental results on several benchmarks show that UnReMix improves negative sample selection, and subsequently downstream performance when compared to state-of-the-art contrastive learning methods.
Age of Information in Reservation Multi-Access Networks With Stochastic Arrivals: Analysis and Optimization

This paper analyzes and optimizes the average Age of Information (AAoI) of Frame Slotted ALOHA with Reservation and Data slots (FSA-RD) in a multi-access network, where multiple users transmit their randomly generated status updates to a common access point in a framed manner. Each frame consists of one reservation slot and several data slots. The reservation slot is further split into several mini-slots. In each reservation slot, users that want to transmit a status update will randomly send short reservation packets in one of the mini-slots to contend for data slots of the current frame. The reservation is successful only if one reservation packet is sent in a mini-slot. The data slots are then allocated to those users that succeed in the reservation slot. In the considered FSA-RD scheme, one user with a status update for transmission, termed active user, may need to perform multiple reservation attempts before successfully delivering it. As such, the number of active user(s) in different frames are dependent and thus the probability of making a successful reservation varies from frame to frame, making the AAoI analysis non-trivial. We manage to derive an analytical expression of AAoI for FSA-RD by characterizing the evolution of the number of active user(s) in each frame as a discrete-time Markov chain. We then consider the FSA-RD scheme with one reservation attempt per status update, termed FSA-RD-One. Thanks to the independent frame behaviors of FSA-RD-One, we attain a closed-form expression for its AAoI, which is further used to find the near-optimal reservation probability. Our analysis reveals the impact of key protocol parameters, such as frame size and reservation probability, on the AAoI. Simulation results validate our analysis and show that the optimized FSA-RD outperforms the optimized slotted ALOHA.
Adaptive Sampling-based Motion Planning with Control Barrier Functions

Sampling-based algorithms, such as Rapidly Exploring Random Trees (RRT) and its variants, have been used extensively for motion planning. Control barrier functions (CBFs) have been recently proposed to synthesize controllers for safety-critical systems. In this paper, we combine the effectiveness of RRT-based algorithms with the safety guarantees provided by CBFs in a method called CBF-RRT∗. CBFs are used for local trajectory planning for RRT∗, avoiding explicit collision checking of the extended paths. We prove that CBF-RRT∗ preserves the probabilistic completeness of RRT∗. Furthermore, in order to improve the sampling efficiency of the algorithm, we equip the algorithm with an adaptive sampling procedure, which is based on the cross-entropy method (CEM) for importance sampling (IS). The procedure exploits the tree of samples to focus the sampling in promising regions of the configuration space. We demonstrate the efficacy of the proposed algorithms through simulation examples.
Defense Against Gradient Leakage Attacks via Learning to Obscure Data

Federated learning is considered as an effective privacy-preserving learning mechanism that separates the client's data and model training process. However, federated learning is still under the risk of privacy leakage because of the existence of attackers who deliberately conduct gradient leakage attacks to reconstruct the client data. Recently, popular strategies such as gradient perturbation methods and input encryption methods have been proposed to defend against gradient leakage attacks. Nevertheless, these defenses can either greatly sacrifice the model performance, or be evaded by more advanced attacks. In this paper, we propose a new defense method to protect the privacy of clients' data by learning to obscure data. Our defense method can generate synthetic samples that are totally distinct from the original samples, but they can also maximally preserve their predictive features and guarantee the model performance. Furthermore, our defense strategy makes the gradient leakage attack and its variants extremely difficult to reconstruct the client data. Through extensive experiments, we show that our proposed defense method obtains better privacy protection while preserving high accuracy compared with state-of-the-art methods.
Feature Space Particle Inference for Neural Network Ensembles

Ensembles of deep neural networks demonstrate improved performance over single models. For enhancing the diversity of ensemble members while keeping their performance, particle-based inference methods offer a promising approach from a Bayesian perspective. However, the best way to apply these methods to neural networks is still unclear: seeking samples from the weight-space posterior suffers from inefficiency due to the over-parameterization issues, while seeking samples directly from the function-space posterior often results in serious underfitting. In this study, we propose optimizing particles in the feature space where the activation of a specific intermediate layer lies to address the above-mentioned difficulties. Our method encourages each member to capture distinct features, which is expected to improve ensemble prediction robustness. Extensive evaluation on real-world datasets shows that our model significantly outperforms the gold-standard Deep Ensembles on various metrics, including accuracy, calibration, and robustness. Code is available at https://github.com/DensoITLab/featurePI .
Quasinormal modes of Schwarzschild black holes on the real axis

We study the scattering of gravitational waves by a Schwarzschild black hole and its perturbed siblings to investigate influences of proposed spectral instability of quasinormal modes on the ringdown signal. Our results indicate that information of dominant ringdown signals, which are ascribed to the fundamental (i.e., least damping) quasinormal mode of unperturbed Schwarzschild black holes, is imprinted in the phase shift defined from the transmission amplitude (1/A_{in} in our notation). This approximately parallels the fact that the resonance of quantum systems is imprinted in the phase shift of the S-matrix. The phase shift around the oscillation frequency of the fundamental mode is modified only perturbatively even if the quasinormal-mode spectrum is destabilized by a perturbative bump at a distant location, signifying the stability of the ringdown signal. At the same time, the phase shift at low frequencies is modulated substantially reflecting the late-time excitation of echo signals associated with the quasinormal-mode spectrum after destabilization.
Federated Learning with a Sampling Algorithm under Isoperimetry

Federated learning uses a set of techniques to efficiently distribute the training of a machine learning algorithm across several devices, who own the training data. These techniques critically rely on reducing the communication cost -- the main bottleneck -- between the devices and a central server. Federated learning algorithms usually take an optimization approach: they are algorithms for minimizing the training loss subject to communication (and other) constraints. In this work, we instead take a Bayesian approach for the training task, and propose a communication-efficient variant of the Langevin algorithm to sample a posteriori. The latter approach is more robust and provides more knowledge of the \textit{a posteriori} distribution than its optimization counterpart. We analyze our algorithm without assuming that the target distribution is strongly log-concave. Instead, we assume the weaker log Sobolev inequality, which allows for nonconvexity.
Incorporating Explicit Uncertainty Estimates into Deep Offline Reinforcement Learning

Most theoretically motivated work in the offline reinforcement learning setting requires precise uncertainty estimates. This requirement restricts the algorithms derived in that work to the tabular and linear settings where such estimates exist. In this work, we develop a novel method for incorporating scalable uncertainty estimates into an offline reinforcement learning algorithm called deep-SPIBB that extends the SPIBB family of algorithms to environments with larger state and action spaces. We use recent innovations in uncertainty estimation from the deep learning community to get more scalable uncertainty estimates to plug into deep-SPIBB. While these uncertainty estimates do not allow for the same theoretical guarantees as in the tabular case, we argue that the SPIBB mechanism for incorporating uncertainty is more robust and flexible than pessimistic approaches that incorporate the uncertainty as a value function penalty. We bear this out empirically, showing that deep-SPIBB outperforms pessimism based approaches with access to the same uncertainty estimates and performs at least on par with a variety of other strong baselines across several environments and datasets.
Sequential Bayesian Neural Subnetwork Ensembles

Deep neural network ensembles that appeal to model diversity have been used successfully to improve predictive performance and model robustness in several applications. Whereas, it has recently been shown that sparse subnetworks of dense models can match the performance of their dense counterparts and increase their robustness while effectively decreasing the model complexity. However, most ensembling techniques require multiple parallel and costly evaluations and have been proposed primarily with deterministic models, whereas sparsity induction has been mostly done through ad-hoc pruning. We propose sequential ensembling of dynamic Bayesian neural subnetworks that systematically reduce model complexity through sparsity-inducing priors and generate diverse ensembles in a single forward pass of the model. The ensembling strategy consists of an exploration phase that finds high-performing regions of the parameter space and multiple exploitation phases that effectively exploit the compactness of the sparse model to quickly converge to different minima in the energy landscape corresponding to high-performing subnetworks yielding diverse ensembles. We empirically demonstrate that our proposed approach surpasses the baselines of the dense frequentist and Bayesian ensemble models in prediction accuracy, uncertainty estimation, and out-of-distribution (OoD) robustness on CIFAR10, CIFAR100 datasets, and their out-of-distribution variants: CIFAR10-C, CIFAR100-C induced by corruptions. Furthermore, we found that our approach produced the most diverse ensembles compared to the approaches with a single forward pass and even compared to the approaches with multiple forward passes in some cases.
REVIVE: Regional Visual Representation Matters in Knowledge-Based Visual Question Answering

This paper revisits visual representation in knowledge-based visual question answering (VQA) and demonstrates that using regional information in a better way can significantly improve the performance. While visual representation is extensively studied in traditional VQA, it is under-explored in knowledge-based VQA even though these two tasks share the common spirit, i.e., rely on visual input to answer the question. Specifically, we observe that in most state-of-the-art knowledge-based VQA methods: 1) visual features are extracted either from the whole image or in a sliding window manner for retrieving knowledge, and the important relationship within/among object regions is neglected; 2) visual features are not well utilized in the final answering model, which is counter-intuitive to some extent. Based on these observations, we propose a new knowledge-based VQA method REVIVE, which tries to utilize the explicit information of object regions not only in the knowledge retrieval stage but also in the answering model. The key motivation is that object regions and inherent relationship are important for knowledge-based VQA. We perform extensive experiments on the standard OK-VQA dataset and achieve new state-of-the-art performance, i.e., 58.0% accuracy, surpassing previous state-of-the-art method by a large margin (+3.6%). We also conduct detailed analysis and show the necessity of regional information in different framework components for knowledge-based VQA. Code is publicly available at https://github.com/yzleroy/REVIVE.
Trajectory of Mini-Batch Momentum: Batch Size Saturation and Convergence in High Dimensions

We analyze the dynamics of large batch stochastic gradient descent with momentum (SGD+M) on the least squares problem when both the number of samples and dimensions are large. In this setting, we show that the dynamics of SGD+M converge to a deterministic discrete Volterra equation as dimension increases, which we analyze. We identify a stability measurement, the implicit conditioning ratio (ICR), which regulates the ability of SGD+M to accelerate the algorithm. When the batch size exceeds this ICR, SGD+M converges linearly at a rate of $\mathcal{O}(1/\sqrt{\kappa})$, matching optimal full-batch momentum (in particular performing as well as a full-batch but with a fraction of the size). For batch sizes smaller than the ICR, in contrast, SGD+M has rates that scale like a multiple of the single batch SGD rate. We give explicit choices for the learning rate and momentum parameter in terms of the Hessian spectra that achieve this performance.
Core-periphery Models for Hypergraphs

We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is practically linear wrt. the number of nodes in the graph after a preprocessing step that is almost linear in the number of hyperedges, as well as a scalable sampling algorithm. Our inference algorithm is capable of learning embeddings that correspond to the reputation (rank) of a node within the hypergraph. We also give theoretical bounds on the size of the core of hypergraphs generated by our model. We experiment with hypergraph data that range to ∼ 105 hyperedges mined from the Microsoft Academic Graph, Stack Exchange, and GitHub and show that our model outperforms baselines wrt. producing good fits.