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Chris Sestito, Co-founder and CEO, HiddenLayer, pitches at the RSAC 2023 Innovation Sandbox Contest.For 17 years, cybersecurity&#x27;s boldest new innovators have...

HiddenLayer — RSA Conference 2023 Innovation Sandbox - YouTube

/PRNewswire/ -- HiddenLayer, a Gartner recognized AI Application Security company, is proud to announce a strategic collaboration with Intel Corporation to...

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Authors:
(1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch);
(2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch);
(3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.2 Anchor Regression 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation B Experiments 4.2 Housing nonlinear regression We extend the results from the previous section to the California and Boston housing data and compare ADA to C-Mixup [49]. We repeat the same experiments on three different regression datasets. Results are provided in Appendix B.2 and also show the superiority of ADA over C-Mixup for data augmentation in the implemented experimental setup. Data: We use the California housing dataset [19] and the Boston housing dataset [14]. The training dataset contains up to n = 406 samples, and the remaining samples are for validation. We report the results as a function of the number of training points. Models and comparisons: We fit a ridge regression model (baseline) and train a MLP with one hidden layer with a varying number of hidden units with sigmoid activation. The baseline models only use only the original data. We train the same models using C-Mixup with a Gaussian kernel and bandwidth of 1.75. We compare the previous approaches to models fitted on ADA augmented data. We generate 20 different augmentations per original observation using different values for γ controlled via α = 4 similar to what was described in Section 4.1. The Anchor matrix is constructed using k-means clustering with q = 10. Results: We report the results in Figure 3. First, we observe that the MLPs outperform Ridge regression suggesting a nonlinear data structure. Second, when the number of training samples is low, applying ADA improves the performance of all models compared to C-Mixup and the baseline. The performance gap decreases as the number of samples increases. When comparing C-Mixup and ADA, we see that using sufficiently many samples both methods achieve similar performance. While on the Boston data, the performance gap between the baseline and ADA persists, on California housing, the non-augmented model fit performs better than the augmented one when data availability increases. This suggests that there is a sweet spot where the addition of original data samples is required for better generalization, and augmented samples cannot contribute any further. This paper is available on arxiv under CC0 1.0 DEED license. Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Authors: Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.1 Data Augmentation 2.2 Anchor Regression 2.2 Anchor Regression 3 Anchor Data Augmentation 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation A Additional information for Anchor Data Augmentation B Experiments B Experiments 4.2 Housing nonlinear regression We extend the results from the previous section to the California and Boston housing data and compare ADA to C-Mixup [49]. We repeat the same experiments on three different regression datasets. Results are provided in Appendix B.2 and also show the superiority of ADA over C-Mixup for data augmentation in the implemented experimental setup. Data : We use the California housing dataset [19] and the Boston housing dataset [14]. The training dataset contains up to n = 406 samples, and the remaining samples are for validation. We report the results as a function of the number of training points. Data Models and comparisons: We fit a ridge regression model (baseline) and train a MLP with one hidden layer with a varying number of hidden units with sigmoid activation. The baseline models only use only the original data. We train the same models using C-Mixup with a Gaussian kernel and bandwidth of 1.75. We compare the previous approaches to models fitted on ADA augmented data. We generate 20 different augmentations per original observation using different values for γ controlled via α = 4 similar to what was described in Section 4.1. The Anchor matrix is constructed using k-means clustering with q = 10. Models and comparisons: Results : We report the results in Figure 3. First, we observe that the MLPs outperform Ridge regression suggesting a nonlinear data structure. Second, when the number of training samples is low, applying ADA improves the performance of all models compared to C-Mixup and the baseline. The performance gap decreases as the number of samples increases. When comparing C-Mixup and ADA, we see that using sufficiently many samples both methods achieve similar performance. While on the Boston data, the performance gap between the baseline and ADA persists, on California housing, the non-augmented model fit performs better than the augmented one when data availability increases. This suggests that there is a sweet spot where the addition of original data samples is required for better generalization, and augmented samples cannot contribute any further. Results This paper is available on arxiv under CC0 1.0 DEED license. This paper is available on arxiv under CC0 1.0 DEED license. available on arxiv

ADA vs C-Mixup: Performance on California and Boston Housing Datasets

Authors:
(1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch);
(2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch);
(3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.2 Anchor Regression 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation B Experiments 4 Experiments We experimentally investigate and compare the performance of ADA. First, we use ADA in an in-distribution setting for a linear regression problem (Section 4.1), in which we show that even in this case, ADA provides improved performance in the low data regime. Second, in Section 4.2, we apply ADA and C-Mixup to the California and Boston Housing datasets as we increase the number of training samples. In the last two subsections, we replicate the in-distribution generalization (Section 4.3) and the out-of-distribution Robustness (Section 4.4) from the C-Mixup paper [49]. In [49] the authors further assess a task generalization experiment. However, the corresponding code was not publicly provided, and a comparison could not be easily made. 4.1 Linear synthetic data Using synthetic linear data, we investigate if ADA can improve model performance in an overparameterized setting compared to C-Mixup, vanilla augmentation, or classical expected risk minimization (ERM). Additionally, we analyze the sensitivity of our approach to the choice of γ and the number of augmentations. Data: The generated data follows a standard linear structure Models and Comparisons: We investigate and compare the impact of ADA using two different models with varying complexity: a linear Ridge regression and a multilayer perceptron (MLP) with one hidden layer and 10 units with ReLU activation. Using an MLP with more hidden layers shows similar results (see Appendix B.1 for details). For the Ridge regression model, we increase the dataset by a factor of 10 by sampling from the respective augmentation methods and subsequently compute the regression estimators. In contrast, for the MLP, we implement the augmentation methods on a minibatch level. Specifically, we incorporate vanilla augmentation by adding Gaussian noise to each batch, apply C-Mixup after sampling from the beta distribution in each batch, and finally, apply ADA after sampling from the defined gamma values in each batch. In summary, even in the simplest of cases, in which we should not expect gains from ADA (or C-Mixup), these data augmentation strategies provide gains in performance when the number of training examples is not sufficient to achieve the error floor. This paper is available on arxiv under CC0 1.0 DEED license. Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Authors: Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.1 Data Augmentation 2.2 Anchor Regression 2.2 Anchor Regression 3 Anchor Data Augmentation 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation A Additional information for Anchor Data Augmentation B Experiments B Experiments 4 Experiments We experimentally investigate and compare the performance of ADA. First, we use ADA in an in-distribution setting for a linear regression problem (Section 4.1), in which we show that even in this case, ADA provides improved performance in the low data regime. Second, in Section 4.2, we apply ADA and C-Mixup to the California and Boston Housing datasets as we increase the number of training samples. In the last two subsections, we replicate the in-distribution generalization (Section 4.3) and the out-of-distribution Robustness (Section 4.4) from the C-Mixup paper [49]. In [49] the authors further assess a task generalization experiment. However, the corresponding code was not publicly provided, and a comparison could not be easily made. 4.1 Linear synthetic data Using synthetic linear data, we investigate if ADA can improve model performance in an overparameterized setting compared to C-Mixup, vanilla augmentation, or classical expected risk minimization (ERM). Additionally, we analyze the sensitivity of our approach to the choice of γ and the number of augmentations. Data : The generated data follows a standard linear structure Data Models and Comparisons: We investigate and compare the impact of ADA using two different models with varying complexity: a linear Ridge regression and a multilayer perceptron (MLP) with one hidden layer and 10 units with ReLU activation. Using an MLP with more hidden layers shows similar results (see Appendix B.1 for details). Models and Comparisons: For the Ridge regression model, we increase the dataset by a factor of 10 by sampling from the respective augmentation methods and subsequently compute the regression estimators. In contrast, for the MLP, we implement the augmentation methods on a minibatch level. Specifically, we incorporate vanilla augmentation by adding Gaussian noise to each batch, apply C-Mixup after sampling from the beta distribution in each batch, and finally, apply ADA after sampling from the defined gamma values in each batch. In summary, even in the simplest of cases, in which we should not expect gains from ADA (or C-Mixup), these data augmentation strategies provide gains in performance when the number of training examples is not sufficient to achieve the error floor. This paper is available on arxiv under CC0 1.0 DEED license. This paper is available on arxiv under CC0 1.0 DEED license. available on arxiv

Evaluating ADA: Experimental Results on Linear and Housing Datasets

Table of Links Abstract and 1 Introduction 2 Preliminaries 3 End-to-End Adaptive Local Learning 3.1 Loss-Driven Mixture-of-Experts 3.2 Synchronized Learning via Adaptive Weight 4 Debiasing Experiments and 4.1 Experimental Setup 4.2 Debiasing Performance 4.3 Ablation Study 4.4 Effect of the Adaptive Weight Module and 4.5 Hyper-parameter Study 5 Related Work 6 Conclusion, Acknowledgements, and References 4 Debiasing Experiments In this section, we present a comprehensive set of experiments to highlight the strong debiasing performance of the proposed method, validate the effectiveness of various model components, assess the impact of the proposed adaptive weight module, and examine the impact of hyperparameters. 4.1 Experimental Setup Considering the Rawlsian Max-Min fairness principle [29], the goal of debiasing is to promote the average NDCG@20 for subgroups with low mainstream scores while preserving or even improving the utility for subgroups with high mainstream scores at the same time. Hence, we also anticipate an increase in the overall NDCG@20 of the model. Baselines. In the experiments, we compare the proposed TALL with MultVAE and four state-of-art debiasing methods: (1) MultVAE [26] is the widely used vanilla recommendation model without debiasing. (2) WL [39] is a global method designed to assign more weights to niche users in the training loss of MultVAE. (3) LOCA [12] is a local learning model that trains multiple anchor models corresponding to identified anchor users and aggregates the outputs from anchor models based on the similarity between the target user and anchor users. (4) LFT [39] is the SOTA local learning model that first trains a global model with all data and then fine-tunes a customized local model for each user using their local data for the target user. (5) EnLFT [39] is the ensembled version of LFT, which is similar to LOCA but trains the anchor models by the approach of LFT. To fairly compare the performance of different baselines and our proposed model, for all four debiasing baselines and our proposed TALL, we adopt the MultVAE as the base model (or the expert model in TALL). LOCA, EnLFT, and TALL have the same complexity with a fixed number of MultVAE in them. And owing to the end-to-end training paradigm, TALL takes less training time than other local learning baselines. Last, LFT has the largest complexity, which has an independent MultVAE for each user. Reproducibility. All models are implemented in PyTorch and optimized by the Adam algorithm [20]. For the baseline MultVAE and the MultVAE component in other models, we set one hidden layer of size 100. And we maintain the number of local models at 100 for LOCA, EnLFT, and TALL for all datasets to ensure a fair comparison. All other hyper-parameters are grid searched by the validation sets. All code and data can be found at https:// github.com/ JP-25/ end-To-end-Adaptive-Local-Leanring-TALL-. Authors:
(1) Jinhao Pan [0009 −0006 −1574 −6376], Texas A&M University, College Station, TX, USA;
(2) Ziwei Zhu [0000 −0002 −3990 −4774], George Mason University, Fairfax, VA, USA;
(3) Jianling Wang [0000 −0001 −9916 −0976], Texas A&M University, College Station, TX, USA;
(4) Allen Lin [0000 −0003 −0980 −4323], Texas A&M University, College Station, TX, USA;
(5) James Caverlee [0000 −0001 −8350 −8528]. Texas A&M University, College Station, TX, USA. This paper is available on arxiv under CC BY 4.0 DEED license. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Preliminaries 2 Preliminaries 3 End-to-End Adaptive Local Learning 3 End-to-End Adaptive Local Learning 3.1 Loss-Driven Mixture-of-Experts 3.1 Loss-Driven Mixture-of-Experts 3.2 Synchronized Learning via Adaptive Weight 3.2 Synchronized Learning via Adaptive Weight 4 Debiasing Experiments and 4.1 Experimental Setup 4 Debiasing Experiments and 4.1 Experimental Setup 4.2 Debiasing Performance 4.2 Debiasing Performance 4.3 Ablation Study Ablation 4.4 Effect of the Adaptive Weight Module and 4.5 Hyper-parameter Study 4.4 Effect of the Adaptive Weight Module and 4.5 Hyper-parameter Study 5 Related Work 5 Related Work 6 Conclusion, Acknowledgements, and References 6 Conclusion, Acknowledgements, and References 4 Debiasing Experiments In this section, we present a comprehensive set of experiments to highlight the strong debiasing performance of the proposed method, validate the effectiveness of various model components, assess the impact of the proposed adaptive weight module, and examine the impact of hyperparameters. 4.1 Experimental Setup Considering the Rawlsian Max-Min fairness principle [29], the goal of debiasing is to promote the average NDCG@20 for subgroups with low mainstream scores while preserving or even improving the utility for subgroups with high mainstream scores at the same time. Hence, we also anticipate an increase in the overall NDCG@20 of the model. the goal of debiasing is to promote the average NDCG@20 for subgroups with low mainstream scores while preserving or even improving the utility for subgroups with high mainstream scores at the same time. Hence, we also anticipate an increase in the overall NDCG@20 of the model. Baselines . In the experiments, we compare the proposed TALL with MultVAE and four state-of-art debiasing methods: (1) MultVAE [26] is the widely used vanilla recommendation model without debiasing. (2) WL [39] is a global method designed to assign more weights to niche users in the training loss of MultVAE. Baselines MultVAE WL (3) LOCA [12] is a local learning model that trains multiple anchor models corresponding to identified anchor users and aggregates the outputs from anchor models based on the similarity between the target user and anchor users. (4) LFT [39] is the SOTA local learning model that first trains a global model with all data and then fine-tunes a customized local model for each user using their local data for the target user. (5) EnLFT [39] is the ensembled version of LFT, which is similar to LOCA but trains the anchor models by the approach of LFT. LOCA LFT EnLFT To fairly compare the performance of different baselines and our proposed model, for all four debiasing baselines and our proposed TALL, we adopt the MultVAE as the base model (or the expert model in TALL). LOCA, EnLFT, and TALL have the same complexity with a fixed number of MultVAE in them. And owing to the end-to-end training paradigm, TALL takes less training time than other local learning baselines. Last, LFT has the largest complexity, which has an independent MultVAE for each user. Reproducibility . All models are implemented in PyTorch and optimized by the Adam algorithm [20]. For the baseline MultVAE and the MultVAE component in other models, we set one hidden layer of size 100. And we maintain the number of local models at 100 for LOCA, EnLFT, and TALL for all datasets to ensure a fair comparison. All other hyper-parameters are grid searched by the validation sets. All code and data can be found at https:// github.com/ JP-25/ end-To-end-Adaptive-Local-Leanring-TALL-. Reproducibility Authors: (1) Jinhao Pan [0009 −0006 −1574 −6376], Texas A&M University, College Station, TX, USA; (2) Ziwei Zhu [0000 −0002 −3990 −4774], George Mason University, Fairfax, VA, USA; (3) Jianling Wang [0000 −0001 −9916 −0976], Texas A&M University, College Station, TX, USA; (4) Allen Lin [0000 −0003 −0980 −4323], Texas A&M University, College Station, TX, USA; (5) James Caverlee [0000 −0001 −8350 −8528]. Texas A&M University, College Station, TX, USA. Authors: Authors: (1) Jinhao Pan [0009 −0006 −1574 −6376], Texas A&M University, College Station, TX, USA; (2) Ziwei Zhu [0000 −0002 −3990 −4774], George Mason University, Fairfax, VA, USA; (3) Jianling Wang [0000 −0001 −9916 −0976], Texas A&M University, College Station, TX, USA; (4) Allen Lin [0000 −0003 −0980 −4323], Texas A&M University, College Station, TX, USA; (5) James Caverlee [0000 −0001 −8350 −8528]. Texas A&M University, College Station, TX, USA. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

Countering Mainstream Bias via End-to-End Adaptive Local Learning: Debiasing Experiments and Setup

Authors:
(1) Bobby He, Department of Computer Science, ETH Zurich (Correspondence to: bobby.he@inf.ethz.ch.);
(2) Thomas Hofmann, Department of Computer Science, ETH Zurich. Table of Links Abstract and Introduction Related Work Preliminaries Simplifying Transformer Blocks Further Experimental Analysis Discussion, Reproducibility Statement, Acknowledgements and References A Duality Between Downweighted Residual and Restricting Updates In Linear Layers B Block Layouts C Additional Experiments D Implementation Details 3 PRELIMINARIES A deep transformer architecture of depth L is formed by sequentially stacking L transformer blocks. The most common block is Pre-LN, depicted in Fig. 1 (left), which we treat as a baseline for comparing training speed, both in terms of per-update and runtime. It differs from the original Post-LN block only in the position of the normalisation layers relative to the skip connections, but is more popular as the Post-LN block suffers from poor training stability and signal propagation in deep layers (Xiong et al., 2020; Liu et al., 2020; Noci et al., 2022; He et al., 2023). with scalar gain weights αFF, βFF, αSA, βSA fixed to 1 by default. Here, “MHA” stands for MultiHead Attention (detailed below), and “Norm” denotes a normalisation layer (Ba et al., 2016; Zhang & Sennrich, 2019). In words, we see that the Pre-LN transformer block consists of two sequential sub-blocks (one attention and one MLP), with normalisation layers and residual connections for both sub-blocks, and crucially the normalisation layers are placed within the residual branch. The MLP is usually single hidden-layer, with hidden dimension that is some multiple of d (e.g. 4 (Vaswani et al., 2017) or 8/3 (Touvron et al., 2023)), and acts on each token in the sequence independently. The MHA sub-block allows tokens to share information between one another using self-attention. For input sequence X, the self-attention mechanism outputs: This paper is available on arxiv under CC 4.0 license. Authors: (1) Bobby He, Department of Computer Science, ETH Zurich (Correspondence to: bobby.he@inf.ethz.ch.); (2) Thomas Hofmann, Department of Computer Science, ETH Zurich. Authors: Authors: (1) Bobby He, Department of Computer Science, ETH Zurich (Correspondence to: bobby.he@inf.ethz.ch.); (2) Thomas Hofmann, Department of Computer Science, ETH Zurich. Table of Links Abstract and Introduction Abstract and Introduction Related Work Related Work Preliminaries Preliminaries Simplifying Transformer Blocks Simplifying Transformer Blocks Further Experimental Analysis Further Experimental Analysis Discussion, Reproducibility Statement, Acknowledgements and References Discussion, Reproducibility Statement, Acknowledgements and References A Duality Between Downweighted Residual and Restricting Updates In Linear Layers A Duality Between Downweighted Residual and Restricting Updates In Linear Layers B Block Layouts B Block Layouts C Additional Experiments C Additional Experiments D Implementation Details D Implementation Details 3 PRELIMINARIES A deep transformer architecture of depth L is formed by sequentially stacking L transformer blocks. The most common block is Pre-LN, depicted in Fig. 1 (left), which we treat as a baseline for comparing training speed, both in terms of per-update and runtime. It differs from the original Post-LN block only in the position of the normalisation layers relative to the skip connections, but is more popular as the Post-LN block suffers from poor training stability and signal propagation in deep layers (Xiong et al., 2020; Liu et al., 2020; Noci et al., 2022; He et al., 2023). with scalar gain weights αFF, βFF, αSA, βSA fixed to 1 by default. Here, “MHA” stands for MultiHead Attention (detailed below), and “Norm” denotes a normalisation layer (Ba et al., 2016; Zhang & Sennrich, 2019). In words, we see that the Pre-LN transformer block consists of two sequential sub-blocks (one attention and one MLP), with normalisation layers and residual connections for both sub-blocks, and crucially the normalisation layers are placed within the residual branch. The MLP is usually single hidden-layer, with hidden dimension that is some multiple of d (e.g. 4 (Vaswani et al., 2017) or 8/3 (Touvron et al., 2023)), and acts on each token in the sequence independently. The MHA sub-block allows tokens to share information between one another using self-attention. For input sequence X, the self-attention mechanism outputs: This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Improving Training Stability in Deep Transformers: Pre-LN vs. Post-LN Blocks

One of the most common question asked during deep learning knowledge interviews is - “Why can’t we use a quadratic cost function to train a Neural Network?”. In this article, we’ll discuss the answer to this question. There will be a lot of Math involved but nothing crazy! I will keep things simple and precise. Let’s start with contemplating the general architecture of a Neural network The General Architecture of a Neural Network We have a series of inputs forming an “input layer”, a series of neurons in the “hidden layer” and one neuron forming an “output layer” for a binary classification problem. For this question, we will assume that we are dealing with a binary classifier, so we have just one output value out of the network. Now, look at the following figure where we’ve highlighted the input layer in green, the output neuron in red, and one neuron of the hidden layer in orange. From all greens to the orange, we see that all inputs are connected to the orange neuron. In other words, the “activation” of the orange neuron happens using the “aggregation” of all the green neurons in the input layer. This process is replicated over all neurons over all layers until we reach the final red output neuron. What if we replace the orange neuron with the red neuron, i.e., we remove the hidden layer and connect the red neuron with the green neurons directly? We will get the following: For this question, we will assume the aforementioned ‘simplistic architecture’ and the result can be generalized to the complete architecture as well. Now let’s introduce some Math step-by-step. What we see above is the basic “weight update” equation for a Neural network. I have removed the extra hyperparameters such as the learning factor and the sub-sampling (min-batch), etc. w_k is the vector of weights and the weights are the ‘parameters’ of our Neural network model. w_k comprises individual weights gathered in a column vector. These weights are associated with the inputs to the model (that is the green neurons in our architecture). We have a cost function C_i where i = 1 to n are the number of data instances in our sample. The cost function C is the “error” between the actual output y and the output from the neural network (red neuron). Each data instance will produce a predicted output as against an actual output, therefore, there will be a cost or error for every data instance. The objective of the model is to minimize this cost function on an average over the entire dataset. And as we know, the minimization step involves taking a derivative with respect to the model parameters (weights). We do this using the partial derivative of the vector w_k. All this means is that the cost C will be an expression/aggregation of weights w_1 to w_q and we will differentiate to each weight w and collect that in a vector. This is called the negative “gradient vector”. It is used to update the weight vector from the k-th iteration to the (k+1)th iteration. The methodology is Stochastic Gradient descent but we will leave that out for this article. In a nutshell, the neural network learns by an update to the weights via the negative gradient vector averaged over all the samples and calculated for w_k. This helps us move to the minimization of the cost function and helps the network to learn and improve its accuracy. It is obvious that if the updates to the weights are not happening, because the negative gradient is moving towards zero, the learning has stopped. This doesn’t necessarily imply that we have reached the minimum! Because our cost function is highly complicated and we need to find a minimum in a multi-dimensional space. Therefore, there could be many local minima where the gradient is zero and the network stops learning. Anyway, we don’t have to worry about that for this problem. Let’s look at the following expression: This expression defines z_i as a weighted sum of the inputs x_ji. Note that these inputs are the green neurons in our architecture. As we have no hidden layer, we combine the inputs x_ji and the weights w_j and add a bias term to get z_i which is what is represented by the connecting arrows from the green neurons to the red neuron in our architecture. Since we have q inputs, we have x_j and w_j where j = 1 to q But, we don’t pass z_i to the red neuron. We apply an “activation function” to it. This activation function can be different for different neural networks. For the purposes of this problem, we assume the activation function is “Sigmoid” or “logistic”. I will assume here that the reader is aware of this function and move on further. Next comes our main problem statement -  How do we define the Cost function (C)? It is well known that for binary classification, the cost function is “Cross entropy” but the question here is why can’t it be “Quadratic”. Let’s define the expressions of both the cost functions: Quadratic cost function –   Cross Entropy cost function – While the quadratic cost function is straightforward (think least squares minimization between the actual output y_i and the predicted output a_i), we can offer some explanation for the cross-entropy cost function. This is akin to negative log-likelihood in our regression models. Note that there is a negative sign outside the brackets, which is used to keep the cost positive (because a_i will be between 0 and 1 - an output of sigmoid, therefore, the term inside the brackets will be always negative). Also note that when a_i gets really close to y_i, the cost gets really close to zero. This is because, when y_i = 1 and a_i ~ 1, ln(a_i) will be approximately 0. Similarly, when y_i= 0 and a_i  ~ 0, ln(1-a_i) will be approximately 0. Thus, this function keeps the cost positive and minimal when the model is predicting well. However, the same can be said about the quadratic cost function as well. But, we don’t use it. Why? Here comes the explanation We go back to the basic weight update equation we saw earlier and input the quadratic cost function to it. We get the following Now to keep things simple, we will consider only one data point, that is i=1 and n=1. And we differentiate partially for each weight w_j. We get the following: Recall that since i = 1, we have Substituting the value of z, we get That is our gradient vector which is responsible for updating the weights of the network will have a derivative of the sigmoid function when we use a quadratic cost function. Now let’s look at the behavior of the derivative of the sigmoid function: From the above plot, it is clear that the derivative, representing the slope of the sigmoid function, approaches 0 as soon as the input z becomes large! What does this mean? This means that the gradient vector will be zero when the activation input z is large. Therefore, the network will stop learning as the weights won’t get updated. Recall that this does not mean we have reached a minimum. This means we are stuck at an undesirable point and in the function space which could be far from the minimum value. This is known as “learning slow down”. However, this does NOT occur with a cross-entropy cost function. We perform the same substitution using the cross-entropy cost function and get the following: It is interesting to note that the term: occurs in the gradient for quadratic cost as well. However, there is a trick which we will use to simplify it. The gradient of the sigmoid function can be expressed as follows We substitute that into our original expression and get the following: That is our gradient vector which is responsible for updating the weights of the network does not have a derivative of the sigmoid function when we use a cross entropy cost function. Hence, there is no slowdown in learning with this cost function. We juxtapose the gradients again for a better look: This answers our original question - we don’t use the quadratic cost function because it leads to a slowdown of learning. Note that the above analysis was done only on the output layer (of one neuron), however, it is can be generalized for a general neural network as well! One of the most common question asked during deep learning knowledge interviews is - “ Why can’t we use a quadratic cost function to train a Neural Network? ”. In this article, we’ll discuss the answer to this question. There will be a lot of Math involved but nothing crazy! I will keep things simple and precise. Why can’t we use a quadratic cost function to train a Neural Network? Let’s start with contemplating the general architecture of a Neural network Neural network The General Architecture of a Neural Network We have a series of inputs forming an “input layer”, a series of neurons in the “hidden layer” and one neuron forming an “output layer” for a binary classification problem. For this question, we will assume that we are dealing with a binary classifier, so we have just one output value out of the network. Now, look at the following figure where we’ve highlighted the input layer in green, the output neuron in red, and one neuron of the hidden layer in orange. From all greens to the orange, we see that all inputs are connected to the orange neuron. In other words, the “activation” of the orange neuron happens using the “aggregation” of all the green neurons in the input layer. This process is replicated over all neurons over all layers until we reach the final red output neuron. What if we replace the orange neuron with the red neuron, i.e., we remove the hidden layer and connect the red neuron with the green neurons directly? We will get the following: We will get the following: For this question, we will assume the aforementioned ‘simplistic architecture’ and the result can be generalized to the complete architecture as well. Now let’s introduce some Math step-by-step. Now let’s introduce some Math step-by-step. What we see above is the basic “weight update” equation for a Neural network. I have removed the extra hyperparameters such as the learning factor and the sub-sampling (min-batch), etc. w_k is the vector of weights and the weights are the ‘parameters’ of our Neural network model. w_k comprises individual weights gathered in a column vector. These weights are associated with the inputs to the model (that is the green neurons in our architecture). We have a cost function C_i where i = 1 to n are the number of data instances in our sample. The cost function C is the “error” between the actual output y and the output from the neural network (red neuron). Each data instance will produce a predicted output as against an actual output, therefore, there will be a cost or error for every data instance. The objective of the model is to minimize this cost function on an average over the entire dataset. And as we know, the minimization step involves taking a derivative with respect to the model parameters (weights). We do this using the partial derivative of the vector w_k. All this means is that the cost C will be an expression/aggregation of weights w_1 to w_q and we will differentiate to each weight w and collect that in a vector. This is called the negative “gradient vector”. It is used to update the weight vector from the k-th iteration to the (k+1)th iteration. The methodology is Stochastic Gradient descent but we will leave that out for this article. In a nutshell, the neural network learns by an update to the weights via the negative gradient vector averaged over all the samples and calculated for w_k. This helps us move to the minimization of the cost function and helps the network to learn and improve its accuracy. It is obvious that if the updates to the weights are not happening, because the negative gradient is moving towards zero, the learning has stopped. This doesn’t necessarily imply that we have reached the minimum! Because our cost function is highly complicated and we need to find a minimum in a multi-dimensional space. Therefore, there could be many local minima where the gradient is zero and the network stops learning. Anyway, we don’t have to worry about that for this problem. Let’s look at the following expression: Let’s look at the following expression: This expression defines z_i as a weighted sum of the inputs x_ji. Note that these inputs are the green neurons in our architecture. As we have no hidden layer, we combine the inputs x_ji and the weights w_j and add a bias term to get z_i which is what is represented by the connecting arrows from the green neurons to the red neuron in our architecture. Since we have q inputs, we have x_j and w_j where j = 1 to q But, we don’t pass z_i to the red neuron. We apply an “activation function” to it. This activation function can be different for different neural networks. For the purposes of this problem, we assume the activation function is “Sigmoid” or “logistic”. I will assume here that the reader is aware of this function and move on further. Next comes our main problem statement -  How do we define the Cost function (C)? It is well known that for binary classification, the cost function is “Cross entropy” but the question here is why can’t it be “Quadratic”. Let’s define the expressions of both the cost functions: Let’s define the expressions of both the cost functions: Quadratic cost function – Cross Entropy cost function – Quadratic cost function – Cross Entropy cost function – While the quadratic cost function is straightforward (think least squares minimization between the actual output y_i and the predicted output a_i), we can offer some explanation for the cross-entropy cost function. This is akin to negative log-likelihood in our regression models. Note that there is a negative sign outside the brackets, which is used to keep the cost positive (because a_i will be between 0 and 1 - an output of sigmoid, therefore, the term inside the brackets will be always negative). Also note that when a_i gets really close to y_i, the cost gets really close to zero. This is because, when y_i = 1 and a_i ~ 1, ln(a_i) will be approximately 0. Similarly, when y_i= 0 and a_i  ~ 0, ln(1-a_i) will be approximately 0. Thus, this function keeps the cost positive and minimal when the model is predicting well. However, the same can be said about the quadratic cost function as well. But, we don’t use it. Why? Here comes the explanation We go back to the basic weight update equation we saw earlier and input the quadratic cost function to it. We get the following Now to keep things simple, we will consider only one data point, that is i=1 and n=1. And we differentiate partially for each weight w_j. We get the following: Recall that since i = 1, we have Substituting the value of z, we get That is our gradient vector which is responsible for updating the weights of the network will have a derivative of the sigmoid function when we use a quadratic cost function. Now let’s look at the behavior of the derivative of the sigmoid function: Now let’s look at the behavior of the derivative of the sigmoid function: From the above plot, it is clear that the derivative, representing the slope of the sigmoid function, approaches 0 as soon as the input z becomes large! What does this mean? This means that the gradient vector will be zero when the activation input z is large. Therefore, the network will stop learning as the weights won’t get updated. Recall that this does not mean we have reached a minimum. This means we are stuck at an undesirable point and in the function space which could be far from the minimum value. This is known as “learning slow down”. However, this does NOT occur with a cross-entropy cost function. We perform the same substitution using the cross-entropy cost function and get the following: We perform the same substitution using the cross-entropy cost function and get the following: It is interesting to note that the term: occurs in the gradient for quadratic cost as well. However, there is a trick which we will use to simplify it. The gradient of the sigmoid function can be expressed as follows We substitute that into our original expression and get the following: That is our gradient vector which is responsible for updating the weights of the network does not have a derivative of the sigmoid function when we use a cross entropy cost function. Hence, there is no slowdown in learning with this cost function. not We juxtapose the gradients again for a better look: We juxtapose the gradients again for a better look: This answers our original question - we don’t use the quadratic cost function because it leads to a slowdown of learning. This answers our original question - we don’t use the quadratic cost function because it leads to a slowdown of learning. Note that the above analysis was done only on the output layer (of one neuron), however, it is can be generalized for a general neural network as well! Note that the above analysis was done only on the output layer (of one neuron), however, it is can be generalized for a general neural network as well!

Why Quadratic Cost Functions Are Ineffective in Neural Network Training

কেন চতুর্মুখী খরচ ফাংশন নিউরাল নেটওয়ার্ক প্রশিক্ষণ অকার্যকর হয়

Warum quadratische Kostenfunktionen beim Training neuronaler Netze unwirksam sind

Por qué las funciones de costo cuadrático son ineficaces en el entrenamiento de redes neuronales

Pourquoi les fonctions de coût quadratiques sont inefficaces dans la formation sur les réseaux neuronaux

न्यूरल नेटवर्क प्रशिक्षण में द्विघात लागत फ़ंक्शन अप्रभावी क्यों हैं

ニューラルネットワークのトレーニングで二次コスト関数が効果がない理由

신경망 훈련에서 2차 비용 함수가 비효율적인 이유

Por que as funções de custo quadráticas são ineficazes no treinamento de redes neurais

Почему квадратичные функции стоимости неэффективны при обучении нейронных сетей

İkinci Dereceden Maliyet Fonksiyonları Sinir Ağı Eğitiminde Neden Etkisizdir?

Tại sao hàm chi phí bậc hai không hiệu quả trong đào tạo mạng lưới thần kinh

为什么二次成本函数在神经网络训练中无效

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com];
(2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za];
(3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za];
(4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction
Methodology
Neural Network Methodology
Numerical results, implementation and discussion
Conclusion, Acknowledgments, and Funding
Availability of data, code and materials, Contributions and Declarations
References 3. Neural Network Methodology The neural network (NN) algorithm is used for solving problems relating to dimensionality reduction [42, 49], visualization of data [31], clustering [11, 52] and classification issues [37, 40]. It is also used in regression [2, 21, 45] in solving regression problems since they do not require prior knowledge about the distribution of the data. The NN algorithm often has the tendency to predict with higher accuracy than other techniques due to the NN’s capability to fit any continuous functions [18]. Mathematically, the NN can be referred to as a directed graph having neurons as vertices and links as edges. Different forms of NN depend on the connectivity of their neurons, and the simplest one is the Multi-layer perceptron, also known as the feedforward NN. Basically, a NN can have only one input and one output layer in its simplest form, and this can be written as: where m is the number of input variables, Φ is the activation function, wi,k is the weight of the input layer i with respect to the output k, b is the bias, and the input vector x is connected to the output k (denoting the kth neuron in the output layer) through a biased weighted sum. In the presence of hidden layers positioned between the input layers and the output layers, the output can be written as: where m1 is the number of input variables, m2 is the number of nodes in the hidden layer, Φ : R → R refers to non-linear activation functions for each of the layers in the brackets, and Φout is the possibly new output function. Recently, the NN has become an indispensable tool for learning the solutions of differential equations, and this section will utilize the potential of the NN in solving PDE-related problems [1, 10, 20, 50]. Also, the NN has been implemented in solving equations without analytical solutions. For instance, Nwankwo et al. [38] considered the solution of the American options PDE by incorporating the Landau transformation and solving the corresponding transformed function via a neural network approach. In many scientific and industrial contexts, there is a need to solve parametric PDEs using NN techniques and Khoo et al. [24] developed such a technique which solves PDE with inhomogeneous coefficient fields. For high-dimensional parametric PDE, [14] analyzed the deep parametric PDE method to solve high-dimensional parametric PDEs with much emphasis on financial applications. In the following, we describe the Bitcoin options with the corresponding Black-Scholes pricing PDE: The above equation which is a non-homogeneous PDE can be re-written as Standard theorems guarantee a classical smooth solution exists for the pricing PDE (3.13) given the assumed dynamics. The continuity and linear growth conditions on the coefficient functions ensure they satisfy Lipschitz continuity. Contingent claims theory shows that Lipschitz continuity is sufficient for existence and uniqueness under the stochastic process specifications. In particular, the smooth past price dependence in the diffusion coefficient allows the application results for delayed Black-Scholes equations. Therefore, the Cauchy problem is well-posed under the model assumptions, and a smooth pricing solution is guaranteed to exist based on the theorems. This provides the theoretical foundation for using a neural network to approximate the price function numerically. Thus, employing the ANN to solve the PDE, we introduce an approximating function ζ(t, S : θ) with parameter set θ. The loss or cost function associated with this training is measured by how well the approximation function satisfies the differential operator, boundary conditions and the terminal condition of the option pricing PDE. These are given respectively as Suppose L(ζ) = 0, then ζ(t, S : θ) is a solution of the PDE in equation (3.13). The major aim is to obtain a set of parameters θ such that the function ζ(t, S : θ) minimizes the observed error of L(ζ). The procedure for seeking a good parameter set by minimizing this loss function using the stochastic gradient descent (SGD) optimizer is called “training”. Thus, using a Machine Learning approach, and in this case, the artificial NN, it will be feasible to minimize the function L(ζ) by applying the SGD approach on the sequence of asset and time points which are drawn at random. A part of the input samples, fully dependent on the mini-batch size, is drawn within each iteration to estimate the gradient of the given objective function. The gradient is then estimated over these mini-batches due to the limitations of the computer memory [30]. The training of NN is classified into first identifying the network’s hyperparameters, that is, the architectural structure and the loss function of the network. Next, use the SGD to optimize or estimate the loss minimizer, and then the derivatives of the loss function are computed using the backpropagation techniques. Essentially, the process of searching and identifying the best θ parameter by minimizing the loss function using the gradient descent-based optimizers is referred to as “training”. The whole procedure is well illustrated in the algorithm below [46], and can be implemented in solving the PDE in equation (3.13): The learning rate α is employed to scale the intensity of the parameter updates during the gradient descent. Choosing the learning rate, as the descent parameter α, in the network training is crucial since this factor plays a significant role in aiding the algorithm’s convergence to the true solution in the gradient descent. It equally affects the pace at which the algorithm learns and whether or not the cost function is minimized. When α implies divergence, and thus, the optimal point can be missed. Also, a fixed value of α can most likely make the local optima overshoot after some iterations, leading to divergence. Defining the learning rate as a dynamic decreasing function is preferable since it allows the algorithm to identify the needed point rapidly. Another limitation in employing the gradient descent method is obtaining the value of the initial parameters of the loss function. If the value is significantly close to the local optimum, then the slope of the loss function reduces, thereby leading to the optimal convergence. Otherwise, there will be no convergence as the solution explodes abnormally. 3.1. Solution of bitcoin option pricing PDE While the pricing PDE has a proven smooth solution under the model dynamics, obtaining the analytical form is intractable. Numerical methods must be used to approximate the solution. Neural networks provide a flexible parametric approach based on their universal approximation theoretical results. Given sufficient network capacity, neural networks can represent a wide class of functions, including solutions to PDEs like the pricing equation. However, challenges remain in finding the optimal network parameters to recover the true solution robustly. While existence is guaranteed, the non-convex optimization of neural networks does not assure convergence to global optimality. Care must be taken in specifying the network architecture, loss function, regularization, and training methodology to promote the learning of the pricing function. Subject to these caveats, neural networks present a promising computational technique for approximating smooth pricing solutions, circumventing discretization of the domain. We note the limitations of using neural networks as function approximators. However, their generalization capabilities provide a methodology for data-driven extraction of the pricing mapping across the entire domain. This avoids the constraints of methods like grid-based techniques that rely on local consistency. Future work should explore neural network training enhancements and theoretical guarantees to ensure robust solutions. This paper is available on arxiv under CC 4.0 license. Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References Abstract and Introduction Abstract and Introduction Methodology Methodology Neural Network Methodology Neural Network Methodology Numerical results, implementation and discussion Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations Availability of data, code and materials, Contributions and Declarations References References 3. Neural Network Methodology The neural network (NN) algorithm is used for solving problems relating to dimensionality reduction [42, 49], visualization of data [31], clustering [11, 52] and classification issues [37, 40]. It is also used in regression [2, 21, 45] in solving regression problems since they do not require prior knowledge about the distribution of the data. The NN algorithm often has the tendency to predict with higher accuracy than other techniques due to the NN’s capability to fit any continuous functions [18]. Mathematically, the NN can be referred to as a directed graph having neurons as vertices and links as edges. Different forms of NN depend on the connectivity of their neurons, and the simplest one is the Multi-layer perceptron, also known as the feedforward NN. Basically, a NN can have only one input and one output layer in its simplest form, and this can be written as: where m is the number of input variables, Φ is the activation function, wi,k is the weight of the input layer i with respect to the output k, b is the bias, and the input vector x is connected to the output k (denoting the kth neuron in the output layer) through a biased weighted sum. In the presence of hidden layers positioned between the input layers and the output layers, the output can be written as: where m1 is the number of input variables, m2 is the number of nodes in the hidden layer, Φ : R → R refers to non-linear activation functions for each of the layers in the brackets, and Φout is the possibly new output function. Recently, the NN has become an indispensable tool for learning the solutions of differential equations, and this section will utilize the potential of the NN in solving PDE-related problems [1, 10, 20, 50]. Also, the NN has been implemented in solving equations without analytical solutions. For instance, Nwankwo et al. [38] considered the solution of the American options PDE by incorporating the Landau transformation and solving the corresponding transformed function via a neural network approach. In many scientific and industrial contexts, there is a need to solve parametric PDEs using NN techniques and Khoo et al. [24] developed such a technique which solves PDE with inhomogeneous coefficient fields. For high-dimensional parametric PDE, [14] analyzed the deep parametric PDE method to solve high-dimensional parametric PDEs with much emphasis on financial applications. In the following, we describe the Bitcoin options with the corresponding Black-Scholes pricing PDE: The above equation which is a non-homogeneous PDE can be re-written as Standard theorems guarantee a classical smooth solution exists for the pricing PDE (3.13) given the assumed dynamics. The continuity and linear growth conditions on the coefficient functions ensure they satisfy Lipschitz continuity. Contingent claims theory shows that Lipschitz continuity is sufficient for existence and uniqueness under the stochastic process specifications. In particular, the smooth past price dependence in the diffusion coefficient allows the application results for delayed Black-Scholes equations. Therefore, the Cauchy problem is well-posed under the model assumptions, and a smooth pricing solution is guaranteed to exist based on the theorems. This provides the theoretical foundation for using a neural network to approximate the price function numerically. Thus, employing the ANN to solve the PDE, we introduce an approximating function ζ(t, S : θ) with parameter set θ. The loss or cost function associated with this training is measured by how well the approximation function satisfies the differential operator, boundary conditions and the terminal condition of the option pricing PDE. These are given respectively as Suppose L(ζ) = 0, then ζ(t, S : θ) is a solution of the PDE in equation (3.13). The major aim is to obtain a set of parameters θ such that the function ζ(t, S : θ) minimizes the observed error of L(ζ). The procedure for seeking a good parameter set by minimizing this loss function using the stochastic gradient descent (SGD) optimizer is called “training”. Thus, using a Machine Learning approach, and in this case, the artificial NN, it will be feasible to minimize the function L(ζ) by applying the SGD approach on the sequence of asset and time points which are drawn at random. A part of the input samples, fully dependent on the mini-batch size, is drawn within each iteration to estimate the gradient of the given objective function. The gradient is then estimated over these mini-batches due to the limitations of the computer memory [30]. The training of NN is classified into first identifying the network’s hyperparameters, that is, the architectural structure and the loss function of the network. Next, use the SGD to optimize or estimate the loss minimizer, and then the derivatives of the loss function are computed using the backpropagation techniques. Essentially, the process of searching and identifying the best θ parameter by minimizing the loss function using the gradient descent-based optimizers is referred to as “training”. The whole procedure is well illustrated in the algorithm below [46], and can be implemented in solving the PDE in equation (3.13): The learning rate α is employed to scale the intensity of the parameter updates during the gradient descent. Choosing the learning rate, as the descent parameter α, in the network training is crucial since this factor plays a significant role in aiding the algorithm’s convergence to the true solution in the gradient descent. It equally affects the pace at which the algorithm learns and whether or not the cost function is minimized. When α implies divergence, and thus, the optimal point can be missed. Also, a fixed value of α can most likely make the local optima overshoot after some iterations, leading to divergence. Defining the learning rate as a dynamic decreasing function is preferable since it allows the algorithm to identify the needed point rapidly. Another limitation in employing the gradient descent method is obtaining the value of the initial parameters of the loss function. If the value is significantly close to the local optimum, then the slope of the loss function reduces, thereby leading to the optimal convergence. Otherwise, there will be no convergence as the solution explodes abnormally. 3.1. Solution of bitcoin option pricing PDE 3.1. Solution of bitcoin option pricing PDE While the pricing PDE has a proven smooth solution under the model dynamics, obtaining the analytical form is intractable. Numerical methods must be used to approximate the solution. Neural networks provide a flexible parametric approach based on their universal approximation theoretical results. Given sufficient network capacity, neural networks can represent a wide class of functions, including solutions to PDEs like the pricing equation. However, challenges remain in finding the optimal network parameters to recover the true solution robustly. While existence is guaranteed, the non-convex optimization of neural networks does not assure convergence to global optimality. Care must be taken in specifying the network architecture, loss function, regularization, and training methodology to promote the learning of the pricing function. Subject to these caveats, neural networks present a promising computational technique for approximating smooth pricing solutions, circumventing discretization of the domain. We note the limitations of using neural networks as function approximators. However, their generalization capabilities provide a methodology for data-driven extraction of the pricing mapping across the entire domain. This avoids the constraints of methods like grid-based techniques that rely on local consistency. Future work should explore neural network training enhancements and theoretical guarantees to ensure robust solutions.

Neural Network for Valuing Bitcoin: Neural Network Methodology

In our fast-paced world, machine learning and artificial intelligence are infiltrating every corner of our daily lives. But what is AI really all about? What is behind this magic? How can such a complex phenomenon be explained so simply? Join us on an amazing journey where we will immerse you in the world of artificial intelligence with clear and accessible examples! A neuron is the basic element of any neural network. To understand how a neuron works, let's take a closer look at it. are the values that the neuron takes in. This data can be anything, such as image pixels or feature values. Input data is the number by which the input data is multiplied. The weights determine how strongly the neuron responds to the input data. The weighting factor is the result of multiplying the input data by the weighting factor. Output value Each layer of an artificial neural network contains neurons, but they perform different functions. In the input layer, neurons simply transmit input data without additional processing. In the hidden layer, neurons actively process information by applying weighting coefficients and activation functions. And in the output layer, the neuron generates a final result based on the processed information from the previous layer. How Does a Neuron Make Predictions? To make a prediction, the neuron simply multiplies the input data by its weighting factor: prediction=input×weight
prediction=input×weight Sample code: def neural_network(input, weight):
    prediction = input * weight
    return prediction In the code above, I've given you a peek behind the scenes of a simple neural network. This is a basic model with a single input. Here is our tuning tool. Multiplying it by the input, we get the prediction. But it's actually much more interesting than that! weight In the future, we will extend this model with more inputs and complexity. And yes, you will learn more about this mysterious `weight' a little later. Ready to dive deeper? The World Is Multifaceted: When One Characteristic Isn't Enough Imagine determining whether you're looking at a cat or a dog based on more than just their weight. After all, each animal has its own unique coat color, height and many other characteristics. What if your neural network could analyze all this mosaic of information at once and make accurate predictions? Each input neuron is like a detective examining different clues, and together they come to the right conclusion! Let's use the example of defining an animal. Imagine we have an animal shelter, and we often have to determine whether an arriving pet is a cat or a dog based on various characteristics. We will use the following data for each animal: - the length of the animal's paw. paw_length - the frequency of sounds produced (meowing or barking). sound_freq - the number of people (volunteers) who want to care for this animal. fan_count Based on the experience of previous shelter professionals, we have initial coefficients to help us make predictions: weights = [0.4, -0.2, 0.1] These coefficients were obtained by analyzing previous data: for paw length: Paw length was found to have little effect on animal identification. 0.1 for frequency of sounds: The frequency of sounds produced appeared to be a more important characteristic. 0.2 for number of volunteers: This parameter has no effect on determining who a pet is, but it may be useful for other tasks, such as predicting how long an animal will stay at the shelter. 0 We can now use these weights to determine who is in front of us: paw_lengths = [1.5, 7.5, 9.0, 7.0]
sound_freqs = [1.3, 0.85, 0.5, 0.9]
fan_counts = [1.1, 1.2, 1.4, 1.3]
 
input_data = [paw_lengths[0], sound_freqs[0], fan_counts[0]] Based on the provided data, our neural network will try to make a prediction. If we need to improve the accuracy of the prediction, we can adjust the weights based on additional data and feedback. This graph shows the distribution of the characteristics of each animal. You can easily compare how much each characteristic makes up for each animal. Let's write our code! def w_sum(a, b):
    assert (len(a) == len(b))
    output = 0
    for i in range(len(a)):
        output += (a[i] * b[i])
    return output This is our data blending cookbook! Think of it as a chef carefully combining ingredients to create the perfect dish. We take two lists, multiply their values element by element, and then add them up. This process is like creating art from simple colors! w_sum: def neural_network(input, weights):
    prediction = w_sum(input, weights)
    return prediction This is our cheat sheet for the data world! All you need to do is give it the information and weights and it will "decipher" the answer for you. Is it a cat or a dog? Like a true detective, this feature will solve this mystery. neural_network: input_data = [paw_length[0], sound_freq[0], enthusiasm[0]]
prediction = neural_network(input_data, weights)

if prediction > 0.5:
    print("It's probably a dog!")
else:
    print("It's probably a cat!") We chose a threshold value of 0.5 (or any other number) because this value optimally separated cats and dogs based on our test data. If the prediction is above this threshold, we consider that we have a dog in front of us, otherwise, we consider it a cat. Final Python Code import numpy as np


# Function for calculating the weighted sum of inputs
def w_sum(a, b):
    assert len(a) == len(b)
    output = 0
    for i in range(len(a)):
        output += (a[i] * b[i])
    return output


# Activation function (here we use the identity function for simplicity)
def activation(x):
    return x


# Neural network function
def neural_network(input, weights):
    pred = w_sum(input, weights)
    return activation(pred)


# Input data (foot length, sound frequency, number of fans)
input_data = [1.5, 0.85, 1.2]

# Starting weights
weights = [0.1, 0.2, 0]

# Making a prediction
prediction = neural_network(input_data, weights)
print("Initial prediction:", prediction)

# Target (let 0 be a cat, 1 be a dog)
target = 1

# Learning curve
learning_rate = 0.01

# The learning process
for iteration in range(100):
    prediction = neural_network(input_data, weights)
    error = (prediction - target) ** 2
    print("Error:", error, "Prediction:", prediction)

    # Adjusting the weights
    for i in range(len(weights)):
        direction_and_amount = (prediction - target) * input_data[i]
        weights[i] -= direction_and_amount * learning_rate

# Final prediction after training
prediction = neural_network(input_data, weights)
print("Final prediction after training:", prediction) In this code, we start with an initial prediction based on the input data and initial weights. We then proceed to a learning process where we gradually adjust the weights based on the error between the current prediction and the target value. The goal of training is to minimize the error. Once the training is complete, the final prediction is output. This example demonstrates the basic principles of a neural network, including the training process and the adjustment of weights. It is intended for training purposes and to illustrate the concepts presented in the article. Conclusion: The Art of the Possible The journey into the world of artificial intelligence and machine learning is not just about learning about technology; it is about exploring how we can push the boundaries of what is possible. We started with the basics - neurons and how they work, going through the creation of simple neural networks that can tell the difference between a cat and a dog using just a few characteristics. And while our examples were simplistic, they serve as a powerful demonstration of what artificial intelligence can do. Standing on the cusp of a new era, we see that AI and machine learning are no longer just tools for processing data or automating tasks. They are a new way of interacting with the world and understanding the complexities of nature and even our own minds. They are tools that help us solve problems we couldn't even dream of before. Each of us can be part of this amazing journey. Regardless of your background in programming or math, it's easier than ever to start learning AI today. Plenty of resources, courses, and communities are ready to support your interest and help you grow. Our simple examples and basic models are just a starting point from which you can begin your journey into the world of artificial intelligence. Remember, every great discovery begins with a first step. Your research and experimentation can lead to the development of new technologies that help solve global problems, improve lives, and open new horizons for all of humanity. Artificial intelligence isn't just the technology of the future; it's shaping our future right now. And each of us can be part of this amazing process. Together, we can create a world where machines and humans work side by side, pushing the boundaries of our understanding and abilities. So, get inspired, experiment, and don't be afraid to explore the unknown. After all, it is in the unknown that lies the future we create together. Let's go, to new discoveries!

Decoding AI: Dive Deep Into Neural Networks and Create Your Own from Scratch!

This paper is under CC 4.0 license. available on arxiv Authors: (1) Amir Noorizadegan, Department of Civil Engineering, National Taiwan University; (2) D.L. Young, Core Tech System Co. Ltd, Moldex3D, Department of Civil Engineering, National Taiwan University & dlyoung@ntu.edu.tw; (3) Y.C. Hon, Department of Mathematics, City University of Hong Kong; (4) C.S. Chen, Department of Civil Engineering, National Taiwan University & dchen@ntu.edu.tw. Table of Links Abstract & Introduction Neural Networks PINN for Solving Inverse Burgers’ Equation Residual Network Numerical Results Results, Acknowledgments & References 4 Residual Network In this study, we propose a power-enhanced variant of the ResNet that skips every other layer, denoted as the “Power-Enhanced SkipResNet.” The modification involves altering the recursive definition in (9) as follows: For the purpose of comparison among Plain NN, ResNet, and SQR-SkipResNet (Figs. 2(a)-(c), respectively), we evaluate the output of the third hidden layer concerning the input y0 = X . The results for the plain neural network are as follows: Figure 2(d) visually represents the “expression tree” for the case with p = 2, providing an insightful illustration of the data flow from input to output. The graph demonstrates the existence of multiple paths that the data can traverse. Each of these paths represents a distinct configuration, determining which residual modules are entered and which ones are skipped. Our extensive numerical experiments support our approach, indicating that a power of 2 is effective for networks with fewer than 30 hidden layers. However, for deeper networks, a larger power can contribute to network stability. Nonetheless, deploying such deep networks does not substantially enhance accuracy and notably increases CPU time. In tasks like interpolation and solving PDEs, a power of 2 generally suffices, and going beyond may not justify the added complexity in terms of accuracy and efficiency

Physics-Informed with Power-Enhanced Residual Network: Residual Network

Your grandfather wears those comfy slipper-y shoes all day, every day, and they’re starting to get holes in the toe and a detached sole. For his birthday, you’d love to surprise him with a new pair of those. You jump on your favorite retail website and land in the search box, only to realize that your aging human brain doesn’t remember the name of those. Not slippers, not loafers…some Indian name. If after scratching your head, your best guess is still “soft shoes my grandpa wears”, all is not lost. Because if the search engine is on the ball, it will simply dig a little deeper, harnessing the power of data science to decipher what you’re actually looking: your underlying . search intent Slippers, shoes, or something else? In the digital world nowadays, search intent is a very hot topic. To succeed in providing an excellent user experience, website managers must know more than just which keywords people are entering. Now, the best practice is for search engines to have the ability to what users want, even if these humans can’t come close to articulating it. fully comprehend That’s where “brainy” neural network logistics come in. Neural network–based search technology facilitates “understanding” of search intent and related themes to find exactly what people need. A neural network takes into account the to improve search . So when you search for something like “soft shoes my grandpa wears”, a savvy search engine will instantly read between the lines and show you all the moccasins your granddad could ever need. context of words and connected ideas relevance What is a neural network? Neural networks were conceived as mathematical models by of the University of Chicago (1944). This concept exists in two realms: Warren McCullough and Walter Pitts Animal brains, including humans’, have biological neural networks and feedback loops that can process input data from the senses — sights, sounds, and scents — plus learn from the surroundings. Nature: Computer scientists have figured out how to replicate the model of neurons in natural neural networks. Artificial neural networks (ANNs) are the basis for artificial intelligence (AI) and machine learning, sitting at the center of many contemporary AI tools. These versions, complete with artificial neurons, allow computers to more effectively process an input dataset. As for the “intelligent” machines involved, the quality of their output is limited to the material they receive, but they do “think” like an animal does. Technology: Three Processing Layers With naturally occurring networks, information is processed through nodes (computational units) that sit in various layers. An artificial neural net is also a series of nodes, organized in layers and connected through inputs and outputs. Neural networks work their magic through three layers: this first layer is where data is received before being passed along to the next-layer nodes. Input layer: where weighted connections and non-linear activation functions generate the output  (this level could include multiple layers). Hidden layer: where the finished data is expressed. Output layer: The number of layers in a neural network is a clue to its classification. A basic neural network has two or three layers. One that has at least two layers — which adds some complexity — is technically a neural network. A very large neural network is a deep-learning tool; IBM’s definition is that more than three layers (including the input and output) constitutes a deep-learning algorithm. deep How ANNs Work Artificial neural networks contain a number of weighted responses that trigger different reactions within the hidden layer. These responses dictate what gets produced as the outcome. To do their jobs, a little training data is in order. Neural networks (or neural nets, for short) are “trained” by adjusting weighting and testing on different types of outcomes. A neural network must have the right rules and weighted responses to do the particular job for which it’s intended. For example, the ChatGPT neural network contains nodes in the hidden layer that allow it to effectively process language. Different Types of Neural Networks There are multiple kinds of artificial neural networks. Some are generative and can “learn” as they work. Some simply focus on automating and improving tasks such as facial recognition or data analysis. Some are fantastic for aiding image processing and automation; others are excellent for enhancing . Different applications of neural networks can also be tailored for the type of use case. search and discovery Here are six types of neural network with their key data points: Feed Forward Feed-forward neural networks are linear: they process information in one direction until an output is ready. This is the simplest form of neural network architecture. When used alone, as opposed to as part of a modular network, they don’t contain the feedback loops required to build artificial intelligence. This architecture is often used in classification software like spam filter, where each step in the analysis brings us closer to the final result without intermediate results needing to be reused later downstream. Recurrent In terms of complexity, recurrent neural networks (RNNs) pick up where feed-forward networks leave off, reprocessing their own outputs to generate more-accurate future outputs. This creates a feedback loop, — a recurring process — in the hidden layer. Because an RNN can create more-valuable insights by reusing its output — pushing data back through the network to contextualize and “understand” the information — it’s ideal for utilizing with AI-powered tools like ChatGPT. Convolutional (CNNs) are often used for pattern recognition, image recognition, and image classification applications. This subset of machine learning categorizes data as it’s processed through multiple convolutional layers, breaking it down and recategorizing based on importance. The resulting information can then be used to differentiate similar images from one another, spotting critical pixel differences, for instance, that the human eye might not see. One consideration: if a CNN isn’t set up optimally, it can consider some information “unimportant”. Convolutional neural networks That’s where a convolutional neural network comes in handy. de Deconvolutional Deconvolutional neural networks (DNNs) work in the opposite way to CNNs. They start with “raw” data and work backward toward usable image output. DNNs can be used to identify information discarded by or missed when using CNNs, and they can be used in conjunction with CNNs to self-test outcomes. Modular Modular neural networks are made up of multiple neural networks that work separately toward a common goal by using ensemble learning, a method that connects different models to pool results and test outcomes before presenting findings. An organization can use this variation of network technology to ensure accurate outcomes. For example, a finance company might utilize it to generate more-accurate stock-market predictions as the different networks produce different outcomes; the findings can then be used to accurately peg averages and outliers. Transformers Did you know that the in ChatGPT and GPT-4 stands for transformer? The transformer, the element that makes generative AI so powerful, is a relatively new form of that utilizes modular neural networks. Transformers use something called a self-attention layer, along with feed-forward neural networks and RNNs, to focus on complex tasks such as language processing. T machine learning Take your search to neural levels As in many industries, AI is steadily changing the fabric of real-world search. Neural networks are being pressed into service to improve software’s comprehension of what consumers want. These tools can help among people, content, and data, as well as connections between user interests and search queries (both current and past). ecommerce identify relationships At Algolia, we harness machine learning and (NLP) to get at the heart of search intent; then the best query results can be and provided to your users. natural language processing ranked Want to smarten your search engine with the ? Maybe improve your (image recognition or computer vision skills), or perhaps optimize your ? advantages of neural search visual search voice search To assist your decision-making, let’s look at your needs and weigh the options. with us today. Get in touch Also published . here

What are the Types of Neural Networks and How Do They Work?

Python is a high-level programming language that is widely used for Machine Learning (ML) applications. It is known for its readability, versatility and ease of use, making it an ideal choice for developers, data scientists, and machine learning engineers alike. The Python ecosystem has a large number of libraries and tools that support machine learning, such as NumPy, Pandas, Matplotlib, TensorFlow, and scikit-learn. These libraries provide powerful algorithms and tools that enable developers to perform complex data analysis, build predictive models and perform data visualization. Python is also popular in machine learning projects due to its robust and active development community, which is constantly updating and improving the libraries and tools available. Why Is Python Preferred for Machine Learning and AI? Python has long been the preferred language for building . There are several reasons why AI and ML developers choose Python: machine learning models : Python is known for its simple and readable syntax, making it easier for developers to write and understand code. Ease of use : Python has a large and active community of developers and data scientists who continuously contribute to the development of libraries and tools for machine learning. Large community : Python has a vast library of powerful tools and algorithms for machine learning. Robust libraries : Python can be used for a variety of purposes, including web development, data Versatility analysis, and scientific computing, making it a popular choice for AI and ML applications. : Python integrates well with other programming languages and tools, making it easy to integrate with existing systems and technologies. Interoperability 10 Best Python Machine Learning Tutorials These Python ML tutorials can help you get off the ground if you are new to Python, machine learning, or both. This tutorial provides a step-by-step guide to creating your first machine learning project using Python. The tutorial is designed to be accessible to beginners and provides a comprehensive guide to machine learning using Python. Step-By-Step: Your First Machine Learning Project in Python The tutorial starts with downloading and installing the Python SciPy library and loading a dataset. Next, you will perform statistical summaries and data visualizations to understand the dataset structure. Then, you will create 6 different machine learning models, evaluate their performance and choose the best one. Finally, you will use k-fold cross-validation to build confidence in the accuracy of the chosen model and make predictions on new data. Read the tutorial This tutorial is a step-by-step guide to implementing the fundamental machine learning technique in Python. The tutorial covers the prerequisites, including basic knowledge of statistics and probability, familiarity with Python and its libraries, and understanding of gradient descent. Tutorial on Linear Regression in Python The tutorial includes the steps to load the data, split it into training and test sets, fit the linear regression model to the training data, make predictions using the test data, evaluate the performance of the model, and plot the data and the regression line. By the end of this tutorial, you will have learned how to implement linear regression in Python and how to evaluate the performance of the model. Read the tutorial This tutorial teaches how to build a neural network from scratch using Python for AI applications. It covers the basics of artificial intelligence, machine learning, and deep learning, and explains how a neural network functions internally. The tutorial includes step-by-step instructions on defining input and output layers, creating a hidden layer, and using the sigmoid activation function. It also covers how to make predictions with the neural network and evaluate its accuracy. Tutorial: Build a Neural Network and Make Predictions Read the tutorial This tutorial provides an introduction to Machine Learning and Python, covering various algorithms and techniques including k-nearest neighbor classifier, neural networks, Naive Bayes classifier, linear regression, decision trees, and clustering algorithms. It also covers various libraries and tools such as NumPy, scikit-learn, and TensorFlow. Introduction to Machine Learning with Python The tutorial will help beginners understand the basics of machine learning and provide a solid foundation in implementing these algorithms in Python. It covers both supervised and unsupervised learning, model evaluation, cross-validation, and hyperparameter tuning. Read the tutorial This tutorial provides a comprehensive introduction to NumPy, a Python library for data science. It covers the core concepts and techniques involved in using NumPy, including creating arrays, manipulating arrays to perform useful calculations, and indexing and slicing arrays. NumPy Tutorial: Introduction to Data Science in Python The tutorial also covers more advanced topics such as broadcasting arrays, basic array operations, and advanced array operations such as matrix multiplication and statistical functions. By the end of the tutorial, the reader will have a solid understanding of NumPy and will be equipped with the skills needed to use it for data science. Read the tutorial This tutorial provides an introduction to the basics of Python machine learning using the scikit-learn library. It covers data exploration, preprocessing, model construction, prediction, validation, and performance evaluation. The tutorial teaches how to use the KMeans algorithm to build an unsupervised model and the Support Vector Machines (SVM) algorithm to build a classification model. Scikit-Learn Tutorial: Python Machine Learning By the end of the tutorial, the reader will have a solid understanding of how to use scikit-learn to build and evaluate machine learning models in Python. Whether a beginner or an experienced practitioner, the tutorial provides the knowledge and skills to get started with scikit-learn and Python machine learning. Read the tutorial This tutorial provides an introduction to sentiment analysis using the NLTK library in Python. The tutorial covers the important features of NLTK for processing text data and the different approaches used for sentiment analysis. The tutorial covers topics such as splitting and filtering text data, analyzing word frequency, finding concordance and collocations, and performing sentiment analysis using built-in and custom classifiers. Sentiment Analysis Tutorial: Introduction to the Python NLTK Library By the end of the tutorial, the user will have a good understanding of the basic features of NLTK and the different approaches used for sentiment analysis, allowing them to perform their own sentiment analysis and make data-driven decisions based on the insights gathered. Read the tutorial This tutorial provides an overview of how to use a tool called DVC for data version control in machine learning and data science projects. It explains how to install and initialize the tool, track datasets and models, commit changes, and share work with team members. It also highlights the importance of data version control in accurately reproducing experiments and avoiding data loss. Tutorial: Data Version Control with Python and DVC By using DVC, developers can effectively manage and version control their data and models, creating reproducible experiments and improving collaboration among team members. Read the tutorial This tutorial introduces . It covers the process of how computers understand features in images and how to analyze these features to detect human faces. It uses the OpenCV library and demonstrates how to use a minimal Python solution to detect faces in images. Face Detection Tutorial with Python face detection with Python The tutorial also covers the advantages and disadvantages of using traditional face detection techniques, and provides tips on improving accuracy through data augmentation techniques. It is designed for beginner to intermediate-level programmers who are familiar with Python programming and have some knowledge of computer vision and image processing. By the end of the tutorial, participants will have the ability to detect faces in images using a simple Python script. Read the tutorial This tutorial provides an introduction to speech recognition and how to incorporate it into a Python application. It covers the basics of how speech recognition works and the various packages available on PyPI. It focuses on the SpeechRecognition package, explaining how to install it and use it to recognize speech from audio files or microphone input. An example code is provided to demonstrate how to use the package. Speech Recognition Tutorial with Python The tutorial concludes by highlighting the benefits of incorporating speech recognition into a Python application, such as improved accessibility and interactivity. Read the tutorial Conclusion The field of machine learning is constantly evolving and the demand for skilled professionals in this area is growing. Python is a popular language for ML projects, with a vast ecosystem of libraries and tools. The tutorials discussed in this article are some of the best resources available to help individuals get started with Python machine learning. These tutorials cover a range of topics, from the basics of machine learning algorithms to advanced techniques such as deep learning and neural networks. If you are getting started with data science in Python, these tutorials are a great starting point for building your machine learning skills and knowledge.

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