Deep perception networks in autonomous driving traditionally rely on data-intensive training regimes and post-hoc anomaly detection, often disregarding fundamental information-theoretic constraints governing stable information processing. We reconceptualize deep neural encoders as hierarchical communication chains that incrementally compress raw sensory inputs into task-relevant latent features. Within this framework, we establish two theoretically justified design principles for robust perception: (D1) smooth variation of mutual information between consecutive layers, and (D2) monotonic decay of latent entropy with network depth. Our analysis shows that, under realistic architectural assumptions, particularly blocks comprising repeated layers of similar capacity, enforcing smooth information flow (D1) naturally encourages entropy decay (D2), thus ensuring stable compression. Guided by these insights, we propose Eloss, a novel entropy-based regularizer designed as a lightweight, plug-and-play training objective. Rather than marginal accuracy improvements, this approach represents a conceptual shift: it unifies information-theoretic stability with standard perception tasks, enabling explicit, principled detection of anomalous sensor inputs through entropy deviations. Experimental validation on large-scale 3D object detection benchmarks (KITTI and nuScenes) demonstrates that incorporating Eloss consistently achieves competitive or improved accuracy while dramatically enhancing sensitivity to anomalies, amplifying distribution-shift signals by up to two orders of magnitude. This stable information-compression perspective not only improves interpretability but also establishes a solid theoretical foundation for safer, more robust autonomous driving perception systems.

Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the complexities of numerical derivatives into the training process of these models. In this study, we propose modifying the structure of the traditional RNN to enable the prediction of each block over a time interval, making it possible to calculate the derivative of the output with respect to time using the backpropagation algorithm. To achieve this, the time intervals of these blocks are overlapped, defining a mutual loss function between them. Additionally, the employment of conditional hidden states enables us to achieve a unique solution for each block. The forget factor is utilized to control the influence of the conditional hidden state on the prediction of the subsequent block. This new model, termed the Mutual Interval RNN (MI-RNN), is applied to solve three different benchmarks: the Burgers equation, unsteady heat conduction in an irregular domain, and the Green vortex problem. Our results demonstrate that MI-RNN can find the exact solution more accurately compared to existing RNN models. For instance, in the second problem, MI-RNN achieved one order of magnitude less relative error compared to the RNN model with numerical derivatives.

Over the last three decades, researchers have intensively explored various clustering tools for categorical data analysis. Despite the proposal of various clustering algorithms, the classical k-modes algorithm remains a popular choice for unsupervised learning of categorical data. Surprisingly, our first insight is that in a natural generative block model, the k-modes algorithm performs poorly for a large range of parameters. We remedy this issue by proposing a soft rounding variant of the k-modes algorithm (SoftModes) and theoretically prove that our variant addresses the drawbacks of the k-modes algorithm in the generative model. Finally, we empirically verify that SoftModes performs well on both synthetic and real-world datasets.

The improvement of air-quality in urban areas is one of the main concerns of public government bodies. This concern emerges from the evidence between the air quality and the public health. Major efforts from government bodies in this area include monitoring and forecasting systems, banning more pollutant motor vehicles, and traffic limitations during the periods of low-quality air. In this work, a proposal for dynamic prices in regulated parking services is presented. The dynamic prices in parking service must discourage motor vehicles parking when low-quality episodes are predicted. For this purpose, diverse deep learning strategies are evaluated. They have in common the use of collective air-quality measurements for forecasting labels about air quality in the city. The proposal is evaluated by using economic parameters and deep learning quality criteria at Madrid (Spain).

Several authors have recently suggested that a possible approach to planning in uncertain domains is to analyze all possible situations beforehand and then store information about what to do in each. The result is that a system can simply use its sensors to examine its domain and then decide what to do by finding its current situation in some sort of a table. The purpose of this article is to argue that even if the compile-time costs of the analysis are ignored, the size of the table must, in general, grow exponentially with the complexity of the domain. This growth makes it unlikely that this approach to planning will be able to deal with problems of an interesting size; one really needs the ability to do some amount of inference at run time. In other words, an effective approach to acting in uncertain domains cannot be to look and then leap; it must always be to look, to think, and only then to leap.