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We consider two classes of natural stochastic processes on finite unlabeled graphs. These are Euclidean stochastic optimization algorithms on the adjacency matrix of weighted graphs and a modified version of the Metropolis MCMC algorithm on stochastic block models over unweighted graphs. In both cases we show that, as the size of the graph goes to infinity, the random trajectories of the stochastic processes converge to deterministic limits. These deterministic limits are curves on the space of measure-valued graphons. Measure-valued graphons, introduced by Lov\'{a}sz and Szegedy, are a refinement of the concept of graphons that can distinguish between two infinite exchangeable arrays that give rise to the same graphon limit. We introduce new metrics on this space which provide us with a natural notion of convergence for our limit theorems. This notion is equivalent to the convergence of infinite-exchangeable arrays. Under a suitable time-scaling, the Metropolis chain admits a diffusion limit as the number of vertices go to infinity. We then demonstrate that, in an appropriately formulated zero-noise limit, the stochastic process of adjacency matrices of this diffusion converge to a deterministic gradient flow curve on the space of graphons introduced in arXiv:2111.09459 [math.PR]. Under suitable assumptions, this allows us to estimate an exponential convergence rate for the Metropolis chain in a certain limiting regime. To the best of our knowledge, both the actual rate and the connection between a natural Metropolis chain commonly used in exponential random graph models and gradient flows on graphons are new in the literature.

Although some current AIs surpass human abilities in closed artificial worlds such as board games, their abilities in the real world are limited. They make strange mistakes and do not notice them. They cannot be instructed easily, fail to use common sense, and lack curiosity. They do not make good collaborators. Mainstream approaches for creating AIs are the traditional manually-constructed symbolic AI approach and generative and deep learning AI approaches including large language models (LLMs). These systems are not well suited for creating robust and trustworthy AIs. Although it is outside of the mainstream, the developmental bootstrapping approach has more potential. In developmental bootstrapping, AIs develop competences like human children do. They start with innate competences. They interact with the environment and learn from their interactions. They incrementally extend their innate competences with self-developed competences. They interact and learn from people and establish perceptual, cognitive, and common grounding. They acquire the competences they need through bootstrapping. However, developmental robotics has not yet produced AIs with robust adult-level competences. Projects have typically stopped at the Toddler Barrier corresponding to human infant development at about two years of age, before their speech is fluent. They also do not bridge the Reading Barrier, to skillfully and skeptically draw on the socially developed information resources that power current LLMs. The next competences in human cognitive development involve intrinsic motivation, imitation learning, imagination, coordination, and communication. This position paper lays out the logic, prospects, gaps, and challenges for extending the practice of developmental bootstrapping to acquire further competences and create robust, resilient, and human-compatible AIs.

A natural way to resolve different points of view and form opinions is through exchanging arguments and knowledge. Facing the vast amount of available information on the internet, people tend to focus on information consistent with their beliefs. Especially when the issue is controversial, information is often selected that does not challenge one's beliefs. To support a fair and unbiased opinion-building process, we propose a chatbot system that engages in a deliberative dialogue with a human. In contrast to persuasive systems, the envisioned chatbot aims to provide a diverse and representative overview - embedded in a conversation with the user. To account for a reflective and unbiased exploration of the topic, we enable the system to intervene if the user is too focused on their pre-existing opinion. Therefore we propose a model to estimate the users' reflective engagement (RUE), defined as their critical thinking and open-mindedness. We report on a user study with 58 participants to test our model and the effect of the intervention mechanism, discuss the implications of the results, and present perspectives for future work. The results show a significant effect on both user reflection and total user focus, proving our proposed approach's validity.

Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function, which is the means by which the quality of a solution is evaluated. In this paper we systematically develop the theory of loss functions for such problems from a novel perspective whose basic ingredients are convex sets with a particular structure. The loss function is defined as the subgradient of the support function of the convex set. It is consequently automatically proper (calibrated for probability estimation). This perspective provides three novel opportunities. It enables the development of a fundamental relationship between losses and (anti)-norms that appears to have not been noticed before. Second, it enables the development of a calculus of losses induced by the calculus of convex sets which allows the interpolation between different losses, and thus is a potential useful design tool for tailoring losses to particular problems. In doing this we build upon, and considerably extend existing results on $M$-sums of convex sets. Third, the perspective leads to a natural theory of ``polar'' loss functions, which are derived from the polar dual of the convex set defining the loss, and which form a natural universal substitution function for Vovk's aggregating algorithm.

This paper studies linear time series regressions with many regressors. Weak exogeneity is the most used identifying assumption in time series. Weak exogeneity requires the structural error to have zero conditional expectation given the present and past regressor values, allowing errors to correlate with future regressor realizations. We show that weak exogeneity in time series regressions with many controls may produce substantial biases and even render the least squares (OLS) estimator inconsistent. The bias arises in settings with many regressors because the normalized OLS design matrix remains asymptotically random and correlates with the regression error when only weak (but not strict) exogeneity holds. This bias's magnitude increases with the number of regressors and their average autocorrelation. To address this issue, we propose an innovative approach to bias correction that yields a new estimator with improved properties relative to OLS. We establish consistency and conditional asymptotic Gaussianity of this new estimator and provide a method for inference.

A new generalization of Reed-Solomon codes is given. This new generalization has similar information rate bound and similar distance rate bound as BCH codes. It also approaches to the Gilbert bound as Goppa codes. Nevertheless, decoding these new codes is much faster than decoding BCH codes.

The resolution of near-field beamforming is an important metric to measure how effectively users with different locations can be located. This letter identifies the condition under which the resolution of near-field beamforming is not perfect. This imperfect resolution means that one user's near-field beam can be still useful to other users, which motivates the application of non-orthogonal multiple access (NOMA). Both the analytical and simulation results are developed to demonstrate that those near-field beams preconfigured for legacy users can indeed be used to effectively serve additional NOMA users, which improves the overall connectivity and system throughput.

The probe and singular sources methods are well-known two classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. The common part of both methods is the notion of the indicator functions which are defined outside an unknown obstacle and blow up on the surface of the obstacle. However, their appearance is completely different. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated version of the probe and singular sources methods which fills the gap between their indicator functions is introduced. The main result is decomposed into three parts. First, the singular sources method combined with the probe method and notion of the Carleman function is formulated. Second, the indicator functions of both methods can be obtained as a result of decomposing a third indicator function into two ways. The third indicator function blows up on both the outer and obstacle surfaces. Third, the probe and singular sources methods are reformulated and it is shown that the indicator functions on which both reformulated methods based, completely coincide with each other. As a byproduct, it turns out that the reformulated singular sources method has also the Side B of the probe method, which is a characterization of the unknown obstacle by means of the blowing up property of an indicator sequence.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.