dataesr/scientific-paragraphs-categorization huggingface dataset:
In a recent study, we have introduced a SNN as a classification model applied to event-based streams using Multinomial Logistic Regression (MLR)  [25]  which extended the HOTS model. By transforming each event in the stream as a vectorial input, our MLR classifier was able to make a decision for every single event, that is, in an online fashion. We have demonstrated on several benchmark datasets that it provides with efficient computations, resulting in ultra-fast categorization. Additionally, we made a formal bridge between this event-based MLR and a SNN, demonstrating the bio-plausibility of this method and its possible integration to neuromorphic hardware. A serie of similar algorithms are applied to real-life applications such as optical flow  [4] , depth estimation  [16] , or gesture recognition  [43].
All these findings, and more  [6] , highlight the importance of the temporal aspect of the neural code and suggest the existence of spatio-temporal spiking motifs in biological spike trains. In neuronal models, an efficient use or detection of these spatio-temporal motifs embedded in the spike train comes with the integration of heterogeneous delays  [26, 27, 71]. Notably, Izhikevich  [33]  introduced the notion of the polychronous group as a repetitive motif of spikes defined by a subset of neurons with different, yet precise, relative spiking delays. This representation has a much greater information capacity in comparison to a firing-rate based neural coding approach through the variety of configurations and the possible coexistence of multiple superposed motifs. This paper explores the possibility that prototypical spiking motifs may be a useful representation used in neurobiology and that we may transfer this hypothesis to neuromorphic algorithms.
Outline In this work, we study the emergence of spatio-temporal spiking motifs when training a single layer of spiking neurons on a semi-supervised classification task (see Fig. 3 ). The paper is organized as follows. We develop a theoretically defined SNN capable of learning heterogeneous delays from spiking motifs that we first evaluate on a synthetic event-based dataset. We first detail the methodology by defining the basic mechanism of spiking neurons that utilize heterogeneous delays. This will allow us to formalize the spike neuron used to learn the model's parameters and test its effectiveness. We aim to apply this model to a realistic motion detection task which we will first define. Then, we will show how the model can be adapted to solve the motion detection task. In the results section, we will detail the emergent structure of the model solving the task and show in particular the similarities with neurobiological observations.
Finally, the trajectory is integrated by assuming first that velocities are uniformly and independently sampled from the set of different motion-sets and second that motion is uniform during a time segment. The resulting instances yield trajectories qualitatively similar to those observed for human eye movements (see Fig. 3-(a) ). Once these eye movement trajectories are generated, we can apply them to a visual scene. For this purpose, we selected a database of 10 natural grayscale images that are commonly used to study the statistics of natural images  [48]. Note that these are pre-processed to equalize the energy in each frequency band (i. e. , whitened). This process is known to occur as early as the retinothalamic pathway  [14]. These images are 512 × 512 in size and we will extract sub-images of size 128 × 128 which will be positioned around the center of the gaze at each time step (see Fig.
Note that to remain within the framework of a causal calculation, the kernels are shifted in time such that only past information gives an answer at the present time. The output of the MLR model corresponds to an event with the highest probability class, keeping the same timing as the input event. It is important to note that we include the prior knowledge that the event-based input is spatio-temporally clustered and that these clusters are sparse. Therefore, we will only select a given proportion of the most active cells, which we set here to. 01% of all output voxels. This threshold was found using validation and future work should automate how this may be determined for various datasets. Given a stimulus input, the model thus yields a spike output in the postsynaptic address space. Since the model is fully differentiable, we can now implement a semisupervised learning rule.
By taking the logit of the probability of the output given by the model, we can therefore calculate the probability of the output. This allows one to calculate the accuracy (as the percentage of times the motion is accurately predicted) or the squared error of the velocity estimate given by the average estimate. These calculations are performed on a different input dataset than the one used in the training or validation steps. These metrics will be useful to compare our methods with other methods on our defined task. The complete code to reproduce the results of this paper is available at https://github. com/SpikeAI/pyTERtorch.
For any given velocity, we also varied the parameters of the textures, such as the mean and variance of the orientation or spatial frequency content to provide with some naturalistic variability. This method provides a rich dataset of textured movies for which we know the ground truth for motion. We plot here main axis of interests. First, as we change the mean spatial frequency of the texture, we observe a monotonous decrease in accuracy. This comes as a similar trend as that observed in the primary visual areas  [58]. Notably, the accuracy is better for a large spatial frequency bandwidth (which qualitatively resemble a more textured stimulus) than for a grating-like stimulation, reminiscent to the behavioral response of humans' eye movements to such stimuli  [65]. Interestingly, we also see a modulation of accuracy as a function of orientation bandwidth.
Synthesis and main contributions To recap, we have introduced in this paper a spiking neural network model with heterogeneous delays that we have trained and evaluated on a complex motion detection task. The model was defined to optimally detect event-driven spatiotemporal motifs. We have shown that when the model is trained on a dataset of natural images with realistic eye movements, the model learns kernels similar to those found in the early visual cortex of humans for example. We have then shown that the model displays similarities with the responses observed in biology. We have evaluated the computational cost of this model if implemented on neuromorphic hardware, showing that the use of heterogeneous delays may be a frugal computational solution for future neuromorphic hardware, but also a key to understand why spikes represent a universal component of neuronal information processing.
Perspectives In the definition of our task, we highlighted how the generation of events depends on the spatial gradient in each image. This gradient is defined in both horizontal and vertical dimensions and its maxima are generally oriented. Taken together, these oriented edges form the contours of visual objects in the scene  [35]. Thus, there is a dependence within the event stream between motion and orientation information. It would be crucial to study this interdependence further. This could be initiated by training the model on a dataset with labels providing local orientation. Studying this dependence will allow us to dissociate these two forms of visual information and to enable us to integrate them. In particular it will allow us to consider that the definition of motion is more accurate perpendicular to an oriented contour (aka, the aperture problem), thus allowing us to implement recurrent predictive rules, such as those identified to dissociate this problem  [56].
In contrast to conventional methodologies that are used to process neurobiological data, such a event-based model would be able to answer key questions regarding the representation of information in neurobiological data. Furthermore, it would open up possibilities in the field of machine learning, especially in computer vision, to address current key concerns such as robustness to attacks, scalability, interpretability, or energy consumption. Acknowledgments. Thanks to Thomas Schatz, Rosa Cossart, Hugo Ladret, Camille Besnainou and Jean-Nicolas Jérémie for useful discussions prior to the elaboration of this work. This research was funded by the European Union ERA-NET CHIST-ERA 2018 research and innovation program under grant agreement N°ANR-19-CHR3-0008-03 ("APROVIS3D"). LP received funding from the ANR project N°ANR-20-CE23-0021 "AgileNeuroBot" and from the ANR project "PolyChronies".
Funding This research was funded by the  European Union   ERA-NET CHIST-ERA 2018 research and innovation program  under grant agreement  N°ANR-19-CHR3-0008-03 ("APROVIS3D "). LP received funding from the  ANR  project  N°ANR-20-CE23-0021  " AgileNeuroBot " and from the  ANR  project " PolyChronies ".
To do so, FuzDeMa assesses in real time the loss or the reception of a packet according to the in-situ node's environments before its transmission and decides whether to send or not the packet based on the computed reliability. To validate the proposed approach, we embed it into a dedicated underground node called the MoleNet and realized real experimentations irstly with an existing dataset and secondly, with precision-measuring equipment to estimate the energy consumption. The results revealed the possibility of prolonging the lifetime of the sensor node by saving up to 81. 7876𝜇𝐽 in a single round. Additionally, FuzDeMa shows the ability to save energy for up to 46 of additional revolutions, thus extending the life of the sensor node to 32. 85% for 140 real transmission cycles. An analytical generalization of FuzDeMa is provided regardless of a speci ic dataset or sensor node.
For that, this latter evaluates the reception probability of sending the data based on its environment parameters. If the reception probability is low, the node keeps the data locally and avoids a useless transmission, thus saving energy. The results show that FuzDeMa can save up to 81. 7876𝜇𝐽 per round in a real and dedicated underground sensor node called the MoleNet. Furthermore, the energy evaluation through a real dataset reveals that FuzDeMa can extend the lifetime of the sensor to up to 32. 85% without losing information at the sink (for 140 different measurements. The main contributions of this paper are as follows: • A new lightweight decision-making approach based on Sugeno's fuzzy inference system that accurately estimates packet loss before transmission. • The evaluation of the performance of the proposed FuzDeMa according to a real dataset.
FuzDeMa has been compared to a recent and accurate path loss model. • The implementation of FuzDeMa on a real and dedicated sensor node used for underground applications such as precision agricultural and ecological monitoring. • The evaluation of the energy behaviour of FuzDeMa when operating within real sensor nodes according to different scenarios. • The energy consumption of FuzDeMa was intensively evaluated using precision-measuring equipment. • The analytical generalization of FuzDeMa is performed in order to give the energy break-even point of the proposal regardless of the sensor node used. The rest of this paper is organised as follows: Background and related work are presented in Section 2; Section 3 presents the main motivation of this work and states the problem of the paper. The fuzzy-based solution for decision-making during transmission is described in Section 4; Section 5 presents the performance evaluation of FuzDeMa on a real dataset.
To achieve this, the authors designed and compared their approach based on Mamdani and Sugeno FIS. This is similar to Jassbi et al. [22]. The output set describes the satisfaction and the bene it gained from the application and is made up of ive membership functions. From the experimentations and comparisons, the authors show that the Sugeno FIS gives better results than Mamdani in their application. Like the previous proposals, SinglaSingla2015 uses the two existing FIS to design a decision-making tool for diabetes diagnosis. As input data, the author considers 11 parameters needed to diagnose different types of diabetes. The output of his proposal consists of four variables corresponding to the different types of diabetes. To validate the tool, the author considered a dataset consisting of 150 different cases of diagnosed patients and compared the results obtained with Mamdani and Sugeno FIS.
Almadi et al. [26]  proposed a novel framework based on the fuzzy logic to identify the behaviour of drivers. The resulting approach is based on the Mamdani FIS and the authors considered as inputs speed limits, the weather and road conditions. The different possible behaviours of the drivers are considered as output set. To validate the decision-making approach, the authors considered a dataset made up of 100 people grouped in ive different age categories. The fuzzy logic is also used for Non-deterministic Polynomial (NP) hard optimization problem in wireless sensor networks. These optimization problems include the clustering that is widely used in several approaches based either on Mamdani or Sugeno FIS  [27, 5, 28, 29]. Bayrakdar  [9]  proposed a fuzzy-based solution for loss-less data transmission in WUSN.
These results are possible because of its simplicity, which allows its rapid conception, adaptability to the uncertainty of incomplete information and the small dataset required for its implementation. Furthermore, as shown in  [30] , the computational cost for fuzzy-based systems can be constant, thus, no additional computation is needed regardless of the number of inputs. The present paper improve our previous work  [30]  that discussed the possible use of fuzzy logic for reliable wireless underground communications. However, the validation of this type of solution needs more experimentations and must be integrated in real devices to verify its feasibility. In addition, the computational cost (energy consumption) should be carried out to verify its applicability in real applications. Thus, by addressing these issues, the present study is a novel contribution in the ields of wireless underground communications and fuzzy logic for WUSN.
Contrary to the previous parameters, the moisture level in the soil is evaluated through three triangular membership functions: low, average and high (Fig. 3b ). We chose triangular functions here because of the direct impact of the soil moisture in the quality of underground communications. Based on calibration measurements carried out using the dataset  [31] , we observe that the impact of soil moisture on communication becomes more signi icant at 40% moisture regardless of the location of the nodes. The soil moisture varies from dry soil (nearly 0% moisture) to free water (close to 100% moisture). • The distance between the transmitter and receiver (LD): This consists of three triangular membership functions: close, medium and far (Fig. 3c ). Similar to the soil moisture, the direct distance between the transmitter and the receiver has a direct impact on the communication quality.
For example, we have observed that when the linear distance between nodes is small (less than 7m), underground communications are reliable with very few lost packets. The range value of the distance between the transmitter and receiver (up to 30m) depends on our previous results  [3, 30]  and the dataset  [31]. During the fuzzi ication process, the membership degree of each input parameter 𝑥 of the proposed FIS is evaluated according to Table  2. The probability used for decisionmaking (defuzzi ication) in the fuzzy-based approach is the average weight of the 36 rules of the inference system given in  (16). Having only two classes (reception or not reception), our proposed decision-making system divides the probability of reception into two equal parts. Thus, when the calculated probability is less than or equal to 0.
PERFORMANCE EVALUATION OF FUZDEMA To evaluate the performance of the proposed FuzDeMa, we consider the dataset of  [31]  also used to design and validate our previous work  [3]. From this dataset, 140 different scenarios were evaluated in two different con igurations of the soil: dry and moist. For each scenario, we evaluate the performance of the FuzDeMa by considering the following metrics (17) -(  21 ) that depend on the values of True Positive (TP); True Negative (TN), False Positive (FP) and False Negative: • The Threat Score (TS): This is also known as the Critical Success Index (CSI) and given in (  17 ) is a performance metric used to measure the success of an initiative (reception or loss of a packet). • The Fowlkes-Mallows Index (FMI): This is an index used to determine the similarity between two different classes (reception or not reception).
Its formula is de ined in  (18). • The Matthews Correlation Coef icient (MCC): This is also known as the Phi-coef icient applied in two classes helps to measure the correlation differences between the real observation and the predicted values  (19). • The balanced Accuracy (bACC) : This is a metric used for evaluating how good a binary classi ier is when the classes are imbalanced (size of the positive class is higher than the size of the negative class). Its formula is given in  (20). • The F1-Score : This metric is similar to the bACC but is applied when the size of the negative class is higher than the size of the positive class  (21). • The Root Mean Square Deviation (RMSD) : This is the square root of errors between the predicted and the observed values  (22). It gives the magnitudes of the errors in predictions for varied datasets.
Dry soil con igurations The 80 measurements of the dry con iguration occurred when the soil moisture was close to 0%. From the experimental dataset, 68 and 12 observations are obtained for the positive and negative classes (reception rcv. and loss of packets not rcv. ), respectively. The resulting confusion matrix in dry soil con igurations is given in Table  3. We observe that for dry soil, the proposed FuzDeMa achieves perfect predictions (𝑇 𝑆 = 𝐹 𝑀 𝐼 = 𝑀 𝐶𝐶 = 1 and 𝑏𝐴𝐶𝐶 = 100%) regardless of the different scenarios of the dataset used (with a 68. 57% prevalence).
Moist soil con igurations When the soil moisture level has a difference of 0%, the soil is assumed to be wet. From the considered dataset, 60 measurements for wet soils are recorded (Table  4 ). Contrary to the dry con iguration, here, the number of negative cases is higher than the number of positive cases (32 and 28, respectively). Furthermore, due to the inequity between the size of the sets, the F1-Score is more suitable than the balanced accuracy. The performance evaluation of FuzDeMa is given in Table  5. The results show that FuzDeMa gets a positive correlation between the prediction (reception or loss) and the actual scenarios of the dataset used when the soil is wet. Indeed, the value of the MCC de ines a high correlation between the prediction and the observation with an accuracy of 80.
675% (F1-Score). In short, over the 140 measurements of the used dataset  [31] , the miss-rate (or False Negative Rate FNR) probability and the False Discovery Rate (FDR) de ined in  (23)  of FuzDeMa are 3. 125% and 8. 824% respectively. These low values demonstrate the high feasibility of FuzDeMa to address the problem of reliable communications in WUSN.
𝐹 𝑁 𝑅 = 𝐹 𝑁 𝐹 𝑁 + 𝑇 𝑃 ; 𝑃 𝐷𝑅 = 𝐹 𝑃 𝐹 𝑃 + 𝑇 𝑃 (23) To validate the performance of FuzDeMa in predicting the reception or the loss of packet before transmission, we consider the performance metrics of (  17 ) -  (21). For each of these parameters, we compare our proposal with WUSN-PLM that obtained the best results compared to the existing path loss models (Table  1 ). Table  6  summarizes the overall performance comparison of FuzDeMa and WUSN-PLM. We observe that the proposed decisionmaking tool outperforms WUSN-PLM with higher bACC, MCC, TS and FMI. The comparison table reveals that FuzDeMa has a lower error than WUSN-PLM in the same dataset. Additionally, to evaluate the proposed approach independently of the ixed threshold (0. 50) and the insensibility to class distribution, the Receiver Operating Characteristic (ROC) curve is considered (Fig.
CONCLUSION In this paper, we proposed and evaluated a novel portable fuzzy-based approach for decision-making during transmission in WUSN to avoid energy waste called FuzDeMa. The main idea of our proposed solution is to allow a sensor node to send data only when it is "sure" of its reception according to a calculated reception probability. The output of the fuzzy inference system used is the reliability of data reception which depends on the soil moisture level, the distance between nodes and the burial depths of the transmitter and receiver. Evaluation of the energy consumed during different scenarios (TN, TN, FP, FN) reveals that the approach can save up to 81. 7876𝜇𝐽 per transmission cycle. Moreover, the validation of FuzDeMa is based on a real dataset made up of 140 different measurements in two different con igurations (dry and moist soils).
Problem P1 has been already addressed in the literature, notably by  Biane and Delaplace (2019)  with the ActoNet method and by  Moon, Lee, Chopra, and Kwon (2022) , based on bilevel integer programming. To our knowledge, none of the other problems have been addressed completely in the literature. The software BoNesis (https://github. com/bnediction/bonesis) provides a generic environment for the automated construction of BNs with MP update mode from specified structural and dynamical properties. The properties are translated into a logic satisfiability problem, expressed in Answer-Set Programming (ASP). Initially, BoNesis has been designed for performing BN synthesis  (Chevalier, Froidevaux, Paulevé, and Zinovyev, 2019) : solutions of the logic model correspond to BNs that possess the specified structural and dynamical properties.
Leveraging this generic declarative specification of properties, BoNesis is a versatile tool for reasoning on BNs in general, with the MP update mode: besides synthesis, it can be used to do model checking, identify fixed points and attractors in ensemble of BNs, and identifying reprogramming strategies. In this paper, we show how the software BoNesis can be employed to solve P1, P2, P3, and P4 in the scope of locally-monotone BNs, where each local function is unate (https://en. wikipedia. org/ wiki/Unate_function), i. e. , where each local function never depends on both positively and negatively from a same component. Locally-monotone BNs cover all the models where it assumed that a node cannot be both an activator and inhibitor of a same other node, which is a common assumption when modeling biological system.
The Results section details how the different reprogramming problems P1-P4 can be addressed using BoNesis and shows some experiments to assess their scalability. Finally, the Discussion section sketches possible extensions of the addressed problems and underlines current challenges for their resolution. This paper is executable: it contains snippets of Python code employing BoNesis to demonstrate its usage on small examples, including command line usage. Instructions for its execution are given at the beginning of the Results section. It can be visualized online (https://nbviewer. org/ Loïc Paulevé github/bnediction/reprogramming-with-bonesis/blob/release/paper. ipynb) and interactively executed either online (https://mybinder. org/v2/gh/bnediction/reprogramming-with-bonesis/release?urlpath=tree/paper.