Inversionoflinearsystems As mentioned in Corollary(1), for the Lasso, when computing the gradient off, one can either invert an nlinear system or anm mlinear system.

Video-based dialogue systems, such as education assistants, have compelling application value, thereby garnering growing interest. However, the current video-based dialogue systems are limited by their reliance on a single dialogue type, which hinders their versatility in practical applications across a range of scenarios, including question-answering, emotional dialog, etc. In this paper, we identify this challenge as how to generate video-driven multilingual mixed-type dialogues. To mitigate this challenge, we propose a novel task and create a human-to-human video-driven multilingual mixed-type dialogue corpus, termed KwaiChat, containing a total of 93,209 videos and 246,080 dialogues, across 4 dialogue types, 30 domains, 4 languages, and 13 topics. Additionally, we establish baseline models on KwaiChat. An extensive analysis of 7 distinct LLMs on KwaiChat reveals that GPT-4o achieves the best performance but still cannot perform well in this situation even with the help of in-context learning and fine-tuning, which indicates that the task is not trivial and needs further research.

Efficient and reliable probabilistic prediction of intraday electricity prices is essential to manage market uncertainties and support robust trading strategies. However, current methods often suffer from parameter inefficiencies, as they fail to fully exploit the potential of modeling interdependencies between bids and offers in the orderbook, requiring a large number of parameters for representation learning. Furthermore, these methods face the quantile crossing issue, where upper quantiles fall below the lower quantiles, resulting in unreliable probabilistic predictions. To address these two challenges, we propose an encoding method called OrderFusion and design a hierarchical multi-quantile head. The OrderFusion encodes the orderbook into a 2.5D representation, which is processed by a tailored jump cross-attention backbone to capture the interdependencies of bids and offers, enabling parameter-efficient learning. The head sets the median quantile as an anchor and predicts multiple quantiles hierarchically, ensuring reliability by enforcing monotonicity between quantiles through non-negative functions. Extensive experiments and ablation studies are conducted on four price indices: 60-min ID3, 60-min ID1, 15-min ID3, and 15-min ID1 using the German orderbook over three years to ensure a fair evaluation. The results confirm that our design choices improve overall performance, offering a parameter-efficient and reliable solution for probabilistic intraday price prediction.

We prove deep neural network (DNN for short) expressivity rate bounds for solution sets of a model class of singularly perturbed, elliptic two-point boundary value problems, in Sobolev norms, on the bounded interval $(-1,1)$. We assume that the given source term and reaction coefficient are analytic in $[-1,1]$. We establish expression rate bounds in Sobolev norms in terms of the NN size which are uniform with respect to the singular perturbation parameter for several classes of DNN architectures. In particular, ReLU NNs, spiking NNs, and $\tanh$- and sigmoid-activated NNs. The latter activations can represent ``exponential boundary layer solution features'' explicitly, in the last hidden layer of the DNN, i.e. in a shallow subnetwork, and afford improved robust expression rate bounds in terms of the NN size. We prove that all DNN architectures allow robust exponential solution expression in so-called `energy' as well as in `balanced' Sobolev norms, for analytic input data.

Automated vehicles (AV) heavily depend on robust perception systems. Current methods for evaluating vision systems focus mainly on frame-by-frame performance. Such evaluation methods appear to be inadequate in assessing the performance of a perception subsystem when used within an AV. In this paper, we present a logic -- referred to as Spatio-Temporal Perception Logic (STPL) -- which utilizes both spatial and temporal modalities. STPL enables reasoning over perception data using spatial and temporal operators. One major advantage of STPL is that it facilitates basic sanity checks on the functional performance of the perception system, even without ground-truth data in some cases. We identify a fragment of STPL which is efficiently monitorable offline in polynomial time. Finally, we present a range of specifications for AV perception systems to highlight the types of requirements that can be expressed and analyzed through offline monitoring with STPL.

Pearl's do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this problem is NP-hard, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial-time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.

Perception algorithms in autonomous vehicles are vital for the vehicle to understand the semantics of its surroundings, including detection and tracking of objects in the environment. The outputs of these algorithms are in turn used for decision-making in safety-critical scenarios like collision avoidance, and automated emergency braking. Thus, it is crucial to monitor such perception systems at runtime. However, due to the high-level, complex representations of the outputs of perception systems, it is a challenge to test and verify these systems, especially at runtime. In this paper, we present a runtime monitoring tool, PerceMon that can monitor arbitrary specifications in Timed Quality Temporal Logic (TQTL) and its extensions with spatial operators. We integrate the tool with the CARLA autonomous vehicle simulation environment and the ROS middleware platform while monitoring properties on state-of-the-art object detection and tracking algorithms.

The problem of managing spatio-temporal data arises in many applications, such as location-based services, environmental monitoring, geographic information systems, and many others. Often spatio-temporal data arising from such applications turn out to be inconsistent, i.e., representing an impossible situation in the real world. Though several inconsistency measures have been proposed to quantify in a principled way inconsistency in propositional knowledge bases, little effort has been done so far on inconsistency measures tailored for the spatio-temporal setting. In this paper, we define and investigate new measures that are particularly suitable for dealing with inconsistent spatio-temporal information, because they explicitly take into account the spatial and temporal dimensions, as well as the dimension concerning the identifiers of the monitored objects. Specifically, we first define natural measures that look at individual dimensions (time, space, and objects), and then propose measures based on the notion of a repair. We then analyze their behavior w.r.t. common postulates defined for classical propositional knowledge bases, and find that the latter are not suitable for spatio-temporal databases, in that the proposed inconsistency measures do not often satisfy them. In light of this, we argue that also postulates should explicitly take into account the spatial, temporal, and object dimensions and thus define “dimension-aware” counterparts of common postulates, which are indeed often satisfied by the new inconsistency measures. Finally, we study the complexity of the proposed inconsistency measures.

The Sentential Decision Diagram (SDD) is a tractable representation of Boolean functions that subsumes the famous Ordered Binary Decision Diagram (OBDD) as a strict subset. SDDs are attracting much attention because they are more succinct than OBDDs, as well as having canonical forms and supporting many useful queries and transformations such as model counting and Apply operation. In this paper, we propose a more succinct variant of SDD named Variable Shift SDD (VS-SDD). The key idea is to create a unique representation for Boolean functions that are equivalent under a specific variable substitution. We show that VS-SDDs are never larger than SDDs and there are cases in which the size of a VS-SDD is exponentially smaller than that of an SDD. Moreover, despite such succinctness, we show that numerous basic operations that are supported in polytime with SDD are also supported in polytime with VS-SDD. Experiments confirm that VS-SDDs are significantly more succinct than SDDs when applied to classical planning instances, where inherent symmetry exists.

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding parameters with the maximum likelihood is NP-hard even in very simple settings. In recent years, provably efficient algorithms were nevertheless developed for models with linear structures: topic models, mixture models, hidden markov models, etc. These algorithms use matrix or tensor decomposition, and make some reasonable assumptions about the parameters of the underlying model. But matrix or tensor decomposition seems of little use when the latent variable model has nonlinearities. The current paper shows how to make progress: tensor decomposition is applied for learning the single-layer {\em noisy or} network, which is a textbook example of a Bayes net, and used for example in the classic QMR-DT software for diagnosing which disease(s) a patient may have by observing the symptoms he/she exhibits. The technical novelty here, which should be useful in other settings in future, is analysis of tensor decomposition in presence of systematic error (i.e., where the noise/error is correlated with the signal, and doesn't decrease as number of samples goes to infinity). This requires rethinking all steps of tensor decomposition methods from the ground up. For simplicity our analysis is stated assuming that the network parameters were chosen from a probability distribution but the method seems more generally applicable.