Current Retrieval-Augmented Generation systems use uniform processing, causing inefficiency as simple queries consume resources similar to complex multi-hop tasks. We present SymRAG, a framework that introduces adaptive query routing via real-time complexity and load assessment to select symbolic, neural, or hybrid pathways. SymRAG's neuro-symbolic approach adjusts computational pathways based on both query characteristics and system load, enabling efficient resource allocation across diverse query types. By combining linguistic and structural query properties with system load metrics, SymRAG allocates resources proportional to reasoning requirements. Evaluated on 2,000 queries across HotpotQA (multi-hop reasoning) and DROP (discrete reasoning) using Llama-3.2-3B and Mistral-7B models, SymRAG achieves competitive accuracy (97.6--100.0% exact match) with efficient resource utilization (3.6--6.2% CPU utilization, 0.985--3.165s processing). Disabling adaptive routing increases processing time by 169--1151%, showing its significance for complex models. These results suggest adaptive computation strategies are more sustainable and scalable for hybrid AI systems that use dynamic routing and neuro-symbolic frameworks.

To minimize the average of a set of log-convex functions, the stochastic Newton method iteratively updates its estimate using subsampled versions of the full objective's gradient and Hessian. We contextualize this optimization problem as sequential Bayesian inference on a latent state-space model with a discriminatively-specified observation process. Applying Bayesian filtering then yields a novel optimization algorithm that considers the entire history of gradients and Hessians when forming an update. We establish matrix-based conditions under which the effect of older observations diminishes over time, in a manner analogous to Polyak's heavy ball momentum. We illustrate various aspects of our approach with an example and review other relevant innovations for the stochastic Newton method.

The extensive use of smartphones in our everyday lives has created new modes of appropriation and behavior in public spaces. Recognition of these are essential for urban design and planning practices which help us to improve the relationship between humans, technologies, and urban environment. This study aims to research smartphone users in public space by observing their altering visual attention and walking behavior, and, in this way, to reveal the emergent new figures. For this purpose, Korenmarkt square in Ghent, Belgium, was observed for seven days in 10-min time intervals. The gaze and walking behavior of smartphone users were encoded as geo-located and temporal data, analyzed and mapped using statistical and spatial analysis methods. Developing and implementing new methods for identifying the characteristics of smartphone users, this study resulted in a nuanced characterization of novel spatial appropriations. The findings led to a better understanding and knowledge of the different behavior patterns of emergent figures such as post-flaneurs and smartphone zombies while uncovering their altering visual interactions with and movements in the public space. The results evoked questions on how researchers and designers can make use of spatial analysis methods and rethink the public space of the future as a hybrid construct integrating the virtual and the physical.

Recent results in nonparametric regression show that deep learning, i.e., neural networks estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in these results is that they are not fully connected. In this paper we show that we can get similar results also for fully connected multilayer feedforward neural networks with ReLU activation functions, provided the number of neurons per hidden layer is fixed and the number of hidden layers tends to infinity for sample size tending to infinity. The proof is based on new approximation results concerning fully connected deep neural networks.

We present a new technique for time series analysis based on dynamic probabilistic networks. In this approach, the observed data are modeled in terms of unobserved, mutually independent factors, as in the recently introduced technique of Independent Factor Analysis (IFA). However, unlike in IFA, the factors are not Li.d.; each factor has its own temporal statistical characteristics. We derive a family of EM algorithms that learn the structure of the underlying factors and their relation to the data. These algorithms perform source separation and noise reduction in an integrated manner, and demonstrate superior performance compared to IFA. 1 Introduction The technique of independent factor analysis (IFA) introduced in [1] provides a tool for modeling L'-dim data in terms of L unobserved factors. These factors are mutually independent and combine linearly with added noise to produce the observed data.

We present a new technique for time series analysis based on dynamic probabilistic networks. In this approach, the observed data are modeled in terms of unobserved, mutually independent factors, as in the recently introduced technique of Independent Factor Analysis (IFA). However, unlike in IFA, the factors are not Li.d.; each factor has its own temporal statistical characteristics. We derive a family of EM algorithms that learn the structure of the underlying factors and their relation to the data. These algorithms perform source separation and noise reduction in an integrated manner, and demonstrate superior performance compared to IFA. 1 Introduction The technique of independent factor analysis (IFA) introduced in [1] provides a tool for modeling L'-dim data in terms of L unobserved factors. These factors are mutually independent and combine linearly with added noise to produce the observed data.

We present a new technique for time series analysis based on dynamic probabilisticnetworks. In this approach, the observed data are modeled in terms of unobserved, mutually independent factors, as in the recently introduced technique of Independent Factor Analysis (IFA).However, unlike in IFA, the factors are not Li.d.; each factor has its own temporal statistical characteristics. We derive a family of EM algorithms that learn the structure of the underlying factors and their relation to the data. These algorithms perform source separation and noise reduction in an integrated manner, and demonstrate superior performance compared to IFA. 1 Introduction The technique of independent factor analysis (IFA) introduced in [1] provides a tool for modeling L'-dim data in terms of L unobserved factors. These factors are mutually independent and combine linearly with added noise to produce the observed data.