We would like to thank the reviewers for the insightful remarks and comments. In our experiment, we show that FGNN outperforms the Max-Product algorithm. MRF whose length ranges from 15 to 45 (the potentials are generated using the same protocol as Dataset3). This also further addresses the overfitting issue raised by R1. Factor without trivial representation of fixed dimension: R3.

Numerous studies have demonstrated that the cognitive processes of the human brain can be modeled using the Bayes theorem for probabilistic inference of the external world. Spiking neural networks (SNNs), capable of performing Bayesian computation with greater physiological interpretability, offer a novel approach to distributed information processing in the cortex. However, applying these models to real-world scenarios to harness the advantages of brain-like computation remains a challenge. Recently, bio-inspired sensors with high dynamic range and ultra-high temporal resolution have been widely used in extreme vision scenarios. Event streams, generated by various types of motion, represent spatiotemporal data.

A.1 Inverted Pendulum Model and Controller The inverted pendulum system is modeled using state s =[,!] where is the angle of the pendulum from the vertical, and! is its angular velocity. We clip! such that the magnitude of the angular velocity does not exceed 8 rad/s, and we clip the control inputs so that the maximum torque magnitude does not exceed 2 N m. We derive a simple rule-based policy to balance the pendulum according to the following two equations! The second equation performs proportional control using this quantity and the current angular velocity. This controller is able to keep the pendulum upright under perfect perception.

Modern autonomous systems rely on perception modules to process complex sensor measurements into state estimates. These estimates are then passed to a controller, which uses them to make safety-critical decisions. It is therefore important that we design perception systems to minimize errors that reduce the overall safety of the system. We develop a risk-driven approach to designing perception systems that accounts for the effect of perceptual errors on the performance of the fullyintegrated, closed-loop system. We formulate a risk function to quantify the effect of a given perceptual error on overall safety, and show how we can use it to design safer perception systems by including a risk-dependent term in the loss function and generating training data in risk-sensitive regions. We evaluate our techniques on a realistic vision-based aircraft detect and avoid application and show that risk-driven design reduces collision risk by 37 % over a baseline system.

In this work, we propose a training-free method to inject visual prompts into Multimodal Large Language Models (MLLMs) through learnable latent variable optimization. We observe that attention, as the core module of MLLMs, connects text prompt tokens and visual tokens, ultimately determining the final results. Our approach involves adjusting visual tokens from the MLP output during inference, controlling the attention response to ensure text prompt tokens attend to visual tokens in referring regions. We optimize a learnable latent variable based on an energy function, enhancing the strength of referring regions in the attention map. This enables detailed region description and reasoning without the need for substantial training costs or model retraining. Our method offers a promising direction for integrating referring abilities into MLLMs, and supports referring with box, mask, scribble and point. The results demonstrate that our method exhibits out-of-domain generalization and interpretability.

Tabular data - structured, heterogeneous, spreadsheet-style data with rows and columns - is widely used in practice across many domains. However, while recent foundation models have reduced the need for developing task-specific datasets and predictors in domains such as language modeling and computer vision, this transfer learning paradigm has not had similar impact in the tabular domain.

Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over time. Previous studies primarily adopt stationarization to attenuate the nonstationarity of original series for better predictability. But the stationarized series deprived of inherent non-stationarity can be less instructive for real-world bursty events forecasting. This problem, termed over-stationarization in this paper, leads Transformers to generate indistinguishable temporal attentions for different series and impedes the predictive capability of deep models. To tackle the dilemma between series predictability and model capability, we propose Non-stationary Transformers as a generic framework with two interdependent modules: Series Stationarization and De-stationary Attention. Concretely, Series Stationarization unifies the statistics of each input and converts the output with restored statistics for better predictability. To address the over-stationarization problem, Destationary Attention is devised to recover the intrinsic non-stationary information into temporal dependencies by approximating distinguishable attentions learned from raw series. Our Non-stationary Transformers framework consistently boosts mainstream Transformers by a large margin, which reduces MSE by 49.43% on Transformer, 47.34% on Informer, and 46.89% on Reformer, making them the state-of-the-art in time series forecasting.

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel optimization method that locally approximates the solution set of the lower-level problem using a cutting plane approach and employs an accelerated gradient-based update to reduce the upper-level objective function over the approximated solution set. We measure the performance of our method in terms of suboptimality and infeasibility errors and provide non-asymptotic convergence guarantees for both error criteria.

Based on a sample of size n, we consider estimating the number of symbols that appear at least µ times in an independent sample of size a n, where a is a given parameter. This formulation includes, as a special case, the well-known problem of inferring the number of unseen species introduced by [Fisher et al.] in 1943 and considered by many others. Of considerable interest in this line of works is the largest a for which the quantity can be accurately predicted. We completely resolve this problem by determining the limit of estimation to be a (log n)/µ, with both lower and upper bounds matching up to constant factors. For the particular case of µ = 1, this implies the recent result by [Orlitsky et al.] on the unseen species problem. Experimental evaluations show that the proposed estimator performs exceptionally well in practice. Furthermore, the estimator is a linear combination of symbols' empirical counts, and hence linear-time computable.

Interpretable and explainable machine learning has seen a recent surge of interest. We focus on safety as a key motivation behind the surge and make the relationship between interpretability and safety more quantitative. Toward assessing safety, we introduce the concept of maximum deviation via an optimization problem to find the largest deviation of a supervised learning model from a reference model regarded as safe. We then show how interpretability facilitates this safety assessment. For models including decision trees, generalized linear and additive models, the maximum deviation can be computed exactly and efficiently. For tree ensembles, which are not regarded as interpretable, discrete optimization techniques can still provide informative bounds. For a broader class of piecewise Lipschitz functions, we leverage the multi-armed bandit literature to show that interpretability produces tighter (regret) bounds on the maximum deviation. We present case studies, including one on mortgage approval, to illustrate our methods and the insights about models that may be obtained from deviation maximization.