Before defining our algorithm at each iterationt we first lighten our notation with a shorthandba(X) = b(ˆp(t 1)(X),a) (at different iterationt, ba denotes different functions), andb(X) is the vector of (b1(X),,bK(X)). For the intuition of the algorithm, consider the t-th iteration where the current prediction function is ˆp(t 1). Thestatement of the theorem is identical; the proof is also essentially the same except for the use of some new technicaltools. Conversely, if ˆp is LB decision calibrated, then kE[p (X) ˆp(X)|U]k1 = 0 almost surely (because if the expectation of a non-negative random variable is zero, the random variable must be zero almost surely), which implies thatˆp is distributioncalibrated. For BKa we use the VC dimension approach.

Deep learning has been proven to be a powerful tool for addressing the most significant issues in cognitive radio networks, such as spectrum sensing, spectrum sharing, resource allocation, and security attacks. The utilization of deep learning techniques in cognitive radio networks can significantly enhance the network's capability to adapt to changing environments and improve the overall system's efficiency and reliability. As the demand for higher data rates and connectivity increases, B5G/6G wireless networks are expected to enable new services and applications significantly. Therefore, the significance of deep learning in addressing cognitive radio network challenges cannot be overstated. This review article provides valuable insights into potential solutions that can serve as a foundation for the development of future B5G/6G services. By leveraging the power of deep learning, cognitive radio networks can pave the way for the next generation of wireless networks capable of meeting the ever-increasing demands for higher data rates, improved reliability, and security.

The remarkable ability of single-celled organisms to sense and react to the dynamic changes in their environment is a testament to the adaptive capabilities of their internal biochemical circuitry. One of the goals of synthetic biology is to develop biochemical analogues of such systems to autonomously monitor and control biochemical processes. Such systems may have impactful applications in fields such as molecular diagnostics, smart therapeutics, and in vivo nanomedicine. So far, the attempts to create such systems have been focused on functionally replicating the behavior of traditional feedforward networks in abstract and DNA-based synthetic chemistries. However, the inherent incompatibility between digital and chemical modes of computation introduces several nonidealities into these implementations, making it challenging to realize them in practice. In this work, we present NeuralCRNs, a novel supervised learning framework constructed as a collection of deterministic chemical reaction networks (CRNs). Unlike prior works, the NeuralCRNs framework is founded on dynamical system-based learning implementations and, thus, results in chemically compatible computations. First, we show the construction and training of a supervised learning classifier for linear classification. We then extend this framework to support nonlinear classification. We then demonstrate the validity of our constructions by training and evaluating them first on several binary and multi-class classification datasets with complex class separation boundaries. Finally, we detail several considerations regarding the NeuralCRNs framework and elaborate on the pros and cons of our methodology compared to the existing works.

Counterfactual estimation from observations represents a critical endeavor in numerous application fields, such as healthcare and finance, with the primary challenge being the mitigation of treatment bias. The balancing strategy aimed at reducing covariate disparities between different treatment groups serves as a universal solution. However, when it comes to the time series data, the effectiveness of balancing strategies remains an open question, with a thorough analysis of the robustness and applicability of balancing strategies still lacking. This paper revisits counterfactual estimation in the temporal setting and provides a brief overview of recent advancements in balancing strategies. More importantly, we conduct a critical empirical examination for the effectiveness of the balancing strategies within the realm of temporal counterfactual estimation in various settings on multiple datasets. Our findings could be of significant interest to researchers and practitioners and call for a reexamination of the balancing strategy in time series settings.

Autonomous driving requires an accurate and fast 3D perception system that includes 3D object detection, tracking, and segmentation. Although recent low-cost camera-based approaches have shown promising results, they are susceptible to poor illumination or bad weather conditions and have a large localization error. Hence, fusing camera with low-cost radar, which provides precise long-range measurement and operates reliably in all environments, is promising but has not yet been thoroughly investigated. In this paper, we propose Camera Radar Net (CRN), a novel camera-radar fusion framework that generates a semantically rich and spatially accurate bird's-eye-view (BEV) feature map for various tasks. To overcome the lack of spatial information in an image, we transform perspective view image features to BEV with the help of sparse but accurate radar points. We further aggregate image and radar feature maps in BEV using multi-modal deformable attention designed to tackle the spatial misalignment between inputs. CRN with real-time setting operates at 20 FPS while achieving comparable performance to LiDAR detectors on nuScenes, and even outperforms at a far distance on 100m setting. Moreover, CRN with offline setting yields 62.4% NDS, 57.5% mAP on nuScenes test set and ranks first among all camera and camera-radar 3D object detectors.

Information processing relying on biochemical interactions in the cellular environment is essential for biological organisms. The implementation of molecular computational systems holds significant interest and potential in the fields of synthetic biology and molecular computation. This two-part article aims to introduce a programmable biochemical reaction network (BCRN) system endowed with mass action kinetics that realizes the fully connected neural network (FCNN) and has the potential to act automatically in vivo. In part I, the feedforward propagation computation, the backpropagation component, and all bridging processes of FCNN are ingeniously designed as specific BCRN modules based on their dynamics. This approach addresses a design gap in the biochemical assignment module and judgment termination module and provides a novel precise and robust realization of bi-molecular reactions for the learning process. Through equilibrium approaching, we demonstrate that the designed BCRN system achieves FCNN functionality with exponential convergence to target computational results, thereby enhancing the theoretical support for such work. Finally, the performance of this construction is further evaluated on two typical logic classification problems.

Can a micron sized sack of interacting molecules autonomously learn an internal model of a complex and fluctuating environment? We draw insights from control theory, machine learning theory, chemical reaction network theory, and statistical physics to develop a general architecture whereby a broad class of chemical systems can autonomously learn complex distributions. Our construction takes the form of a chemical implementation of machine learning's optimization workhorse: gradient descent on the relative entropy cost function. We show how this method can be applied to optimize any detailed balanced chemical reaction network and that the construction is capable of using hidden units to learn complex distributions. This result is then recast as a form of integral feedback control. Finally, due to our use of an explicit physical model of learning, we are able to derive thermodynamic costs and trade-offs associated to this process.

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.

Inferring chemical reaction networks (CRN) from concentration time series is a challenge encouragedby the growing availability of quantitative temporal data at the cellular level. This motivates thedesign of algorithms to infer the preponderant reactions between the molecular species observed ina given biochemical process, and build CRN structure and kinetics models. Existing ODE-basedinference methods such as SINDy resort to least square regression combined with sparsity-enforcingpenalization, such as Lasso. However, we observe that these methods fail to learn sparse modelswhen the input time series are only available in wild type conditions, i.e. without the possibility toplay with combinations of zeroes in the initial conditions. We present a CRN inference algorithmwhich enforces sparsity by inferring reactions in a sequential fashion within a search tree of boundeddepth, ranking the inferred reaction candidates according to the variance of their kinetics on theirsupporting transitions, and re-optimizing the kinetic parameters of the CRN candidates on the wholetrace in a final pass. We show that Reactmine succeeds both on simulation data by retrievinghidden CRNs where SINDy fails, and on two real datasets, one of fluorescence videomicroscopyof cell cycle and circadian clock markers, the other one of biomedical measurements of systemiccircadian biomarkers possibly acting on clock gene expression in peripheral organs, by inferringpreponderant regulations in agreement with previous model-based analyses. The code is available athttps://gitlab.inria.fr/julmarti/crninf/ together with introductory notebooks.

We present a differentiable formulation of abstract chemical reaction networks (CRNs) that can be trained to solve a variety of computational tasks. Chemical reaction networks are one of the most fundamental computational substrates used by nature. We study well-mixed single-chamber systems, as well as systems with multiple chambers separated by membranes, under mass-action kinetics. We demonstrate that differentiable optimisation, combined with proper regularisation, can discover non-trivial sparse reaction networks that can implement various sorts of oscillators and other chemical computing devices.