We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such approximate tensorization results immediately imply as corollaries many important structural properties of the associated Gibbs distribution, in particular rapid mixing of the Glauber dynamics for sampling. We prove approximate tensorization by recursively establishing block factorization of variance and entropy with a small balanced separator of the graph. Our approach goes beyond the classical canonical path method for variance and the recent spectral independence approach, and allows us to obtain new rapid mixing results. As applications of our approach, we show that: 1. On graphs of treewidth $t$, the mixing time of the Glauber dynamics is $n^{O(t)}$, which recovers the recent results of Eppstein and Frishberg with improved exponents and simpler proofs; 2. On bounded-degree planar graphs, strong spatial mixing implies $\tilde{O}(n)$ mixing time of the Glauber dynamics, which gives a faster algorithm than the previous deterministic counting algorithm by Yin and Zhang.
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A recent empirical observation of activation sparsity in MLP layers offers an opportunity to drastically reduce computation costs for free. Despite several works attributing it to training dynamics, the theoretical explanation of activation sparsity's emergence is restricted to shallow networks, small training steps well as modified training, even though the sparsity has been found in deep models trained by vanilla protocols for large steps. To fill the three gaps, we propose the notion of gradient sparsity as the source of activation sparsity and a theoretical explanation based on it that explains gradient sparsity and then activation sparsity as necessary steps to adversarial robustness w.r.t. hidden features and parameters, which is approximately the flatness of minima for well-learned models. The theory applies to standardly trained LayerNorm-ed pure MLPs, and further to Transformers or other architectures if noises are added to weights during training. To eliminate other sources of flatness when arguing sparsities' necessity, we discover the phenomenon of spectral concentration, i.e., the ratio between the largest and the smallest non-zero singular values of weight matrices is small. We utilize random matrix theory (RMT) as a powerful theoretical tool to analyze stochastic gradient noises and discuss the emergence of spectral concentration. With these insights, we propose two plug-and-play modules for both training from scratch and sparsity finetuning, as well as one radical modification that only applies to from-scratch training. Another under-testing module for both sparsity and flatness is also immediate from our theories. Validational experiments are conducted to verify our explanation. Experiments for productivity demonstrate modifications' improvement in sparsity, indicating further theoretical cost reduction in both training and inference.
Theory and application of stochastic approximation (SA) has grown within the control systems community since the earliest days of adaptive control. This paper takes a new look at the topic, motivated by recent results establishing remarkable performance of SA with (sufficiently small) constant step-size $\alpha>0$. If averaging is implemented to obtain the final parameter estimate, then the estimates are asymptotically unbiased with nearly optimal asymptotic covariance. These results have been obtained for random linear SA recursions with i.i.d.\ coefficients. This paper obtains very different conclusions in the more common case of geometrically ergodic Markovian disturbance: (i) The \textit{target bias} is identified, even in the case of non-linear SA, and is in general non-zero. The remaining results are established for linear SA recursions: (ii) the bivariate parameter-disturbance process is geometrically ergodic in a topological sense; (iii) the representation for bias has a simpler form in this case, and cannot be expected to be zero if there is multiplicative noise; (iv) the asymptotic covariance of the averaged parameters is within $O(\alpha)$ of optimal. The error term is identified, and may be massive if mean dynamics are not well conditioned. The theory is illustrated with application to TD-learning.
The aim of latent variable disentanglement is to infer the multiple informative latent representations that lie behind a data generation process and is a key factor in controllable data generation. In this paper, we propose a deep neural network-based self-supervised learning method to infer the disentangled rhythmic and harmonic representations behind music audio generation. We train a variational autoencoder that generates an audio mel-spectrogram from two latent features representing the rhythmic and harmonic content. In the training phase, the variational autoencoder is trained to reconstruct the input mel-spectrogram given its pitch-shifted version. At each forward computation in the training phase, a vector rotation operation is applied to one of the latent features, assuming that the dimensions of the feature vectors are related to pitch intervals. Therefore, in the trained variational autoencoder, the rotated latent feature represents the pitch-related information of the mel-spectrogram, and the unrotated latent feature represents the pitch-invariant information, i.e., the rhythmic content. The proposed method was evaluated using a predictor-based disentanglement metric on the learned features. Furthermore, we demonstrate its application to the automatic generation of music remixes.
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different approaches to leverage the subspace containing the history of solutions computed at previous time steps in order to generate a good initial guess for the iterative solver. In particular, we propose a novel combination of reduced-order projection with randomized linear algebra techniques, which drastically reduces the number of iterations needed for convergence. We analyze the accuracy of the initial guess produced by the reduced-order projection when the coefficients of the linear system depend analytically on time. Extending extrapolation results by Demanet and Townsend to a vector-valued setting, we show that the accuracy improves rapidly as the size of the history increases, a theoretical result confirmed by our numerical observations. In particular, we apply the developed method to the simulation of plasma turbulence in the boundary of a fusion device, showing that the time needed for solving the linear systems is significantly reduced.
We investigate the complexity of several manipulation and control problems under numerous prevalent approval-based multiwinner voting rules. Particularly, the rules we study include approval voting (AV), satisfaction approval voting (SAV), net-satisfaction approval voting (NSAV), proportional approval voting (PAV), approval-based Chamberlin-Courant voting (ABCCV), minimax approval voting (MAV), etc. We show that these rules generally resist the strategic types scrutinized in the paper, with only a few exceptions. In addition, we also obtain many fixed-parameter tractability results for these problems with respect to several natural parameters, and derive polynomial-time algorithms for certain special cases.
Microservices are increasingly used in modern applications, leading to a growing need for effective service integration solutions. However, we argue that traditional API-centric integration mechanisms (e.g., RPC, REST, and Pub/Sub) hamper the modularity of microservices. These mechanisms introduce rigid code-level coupling, scatter integration logic, and hinder visibility into cross-service state exchanges. Ultimately, these limitations complicate the maintenance and evolution of microservice-based applications. In response, we propose a rethinking of service integration and present Knactor, a new state-centric integration framework to restore the modularity that microservices were intended to offer. Knactor decouples service integration from service development, allowing integration to be implemented as explicit state exchanges among multiple services. Our initial case study suggests that Knactor simplifies service integration and creates new opportunities for optimizations.
We describe a newly-developed, free, browser-based application, for the interactive exploration of the dynamic geometry of Poncelet families of triangles. The main focus is on responsive display of the beauteous loci of centers of such families, refreshing them smoothly upon any changes in simulation parameters. The app informs the user when curves swept are conics and reports if certain metric quantities are conserved. Live simulations can be easily shared via a URL. A list of more than 400 pre-made experiments is included which can be regarded as conjectures and/or exercises. Millions of experiment combinations are possible.
The integration of vision-based frameworks to achieve lunar robot applications faces numerous challenges such as terrain configuration or extreme lighting conditions. This paper presents a generic task pipeline using object detection, instance segmentation and grasp detection, that can be used for various applications by using the results of these vision-based systems in a different way. We achieve a rock stacking task on a non-flat surface in difficult lighting conditions with a very good success rate of 92%. Eventually, we present an experiment to assemble 3D printed robot components to initiate more complex tasks in the future.
Deep Learning (DL) frameworks are now widely used, simplifying the creation of complex models as well as their integration to various applications even to non DL experts. However, like any other programs, they are prone to bugs. This paper deals with the subcategory of bugs named silent bugs: they lead to wrong behavior but they do not cause system crashes or hangs, nor show an error message to the user. Such bugs are even more dangerous in DL applications and frameworks due to the "black-box" and stochastic nature of the systems (the end user can not understand how the model makes decisions). This paper presents the first empirical study of Keras and TensorFlow silent bugs, and their impact on users' programs. We extracted closed issues related to Keras from the TensorFlow GitHub repository. Out of the 1,168 issues that we gathered, 77 were reproducible silent bugs affecting users' programs. We categorized the bugs based on the effects on the users' programs and the components where the issues occurred, using information from the issue reports. We then derived a threat level for each of the issues, based on the impact they had on the users' programs. To assess the relevance of identified categories and the impact scale, we conducted an online survey with 103 DL developers. The participants generally agreed with the significant impact of silent bugs in DL libraries and acknowledged our findings (i.e., categories of silent bugs and the proposed impact scale). Finally, leveraging our analysis, we provide a set of guidelines to facilitate safeguarding against such bugs in DL frameworks.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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