{ "source_file": "0930", "source_platform": "Medium", "author": "Riccardo Andreoni", "title_listed": "Avoid Overfitting in Neural Networks: a Deep Dive", "keywords": "", "domain": "机器学习", "content_type": "深度技术解析", "is_paid_flag": "否", "url": "https://towardsdatascience.com/avoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507/", "publish_date": "2023-11-30", "corpus_stage": "", "notes": "", "id": "6398e561e759", "collected_at": "2026-10-02T03:12:08", "title": "Avoid Overfitting in Neural Networks: a Deep Dive | Towards Data Science", "body_markdown": "![Revisit consent button](../images/body-df29beacd7496220cc94.svg)\nWe value your privacy\nWe use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. By clicking \"Accept All\", you consent to our use of cookies.\nCustomise Reject All Accept All\nCustomise Consent Preferences ![](../images/body-2159bb67f3de8ad870eb.svg)\nWe use cookies to help you navigate efficiently and perform certain functions. You will find detailed information about all cookies under each consent category below.\nThe cookies that are categorised as \"Necessary\" are stored on your browser as they are essential for enabling the basic functionalities of the site. ... Show more\nNecessaryAlways Active\nNecessary cookies are required to enable the basic features of this site, such as providing secure log-in or adjusting your consent preferences. These cookies do not store any personally identifiable data.\n * Cookie\nBCTempID\n * Duration\n10 minutes\n * Description\nNo description available.\n\n\n * Cookie\n__cf_bm\n * Duration\n1 hour\n * Description\nThis cookie, set by Cloudflare, is used to support Cloudflare Bot Management. \n\n\n * Cookie\nAWSALBCORS\n * Duration\n7 days\n * Description\nAmazon Web Services set this cookie for load balancing.\n\n\n * Cookie\n_cfuvid\n * Duration\nsession\n * Description\nCloudflare sets this cookie to track users across sessions to optimize user experience by maintaining session consistency and providing personalized services\n\n\n * Cookie\nli_gc\n * Duration\n6 months\n * Description\nLinkedin set this cookie for storing visitor's consent regarding using cookies for non-essential purposes.\n\n\n * Cookie\n__hssrc\n * Duration\nsession\n * Description\nThis cookie is set by Hubspot whenever it changes the session cookie. The __hssrc cookie set to 1 indicates that the user has restarted the browser, and if the cookie does not exist, it is assumed to be a new session.\n\n\n * Cookie\n__hssc\n * Duration\n1 hour\n * Description\nHubSpot sets this cookie to keep track of sessions and to determine if HubSpot should increment the session number and timestamps in the __hstc cookie.\n\n\n * Cookie\nwpEmojiSettingsSupports\n * Duration\nsession\n * Description\nWordPress sets this cookie when a user interacts with emojis on a WordPress site. It helps determine if the user's browser can display emojis properly.\n\n\n * Cookie\nBCSessionID\n * Duration\n1 year 1 month 4 days\n * Description\nBlueconic sets this cookie as a unique identifier for the BlueConic profile.\n\n\n * Cookie\n_octo\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\nlogged_in\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\n__Secure-YEC\n * Duration\npast\n * Description\nYouTube sets this cookie to stores the user's video player preferences using embedded YouTube video\n\n\n * Cookie\n__eoi\n * Duration\n6 months\n * Description\nDescription is currently not available.\n\n\n * Cookie\nAWSALBTGCORS\n * Duration\n7 days\n * Description\nNo description available.\n\n\n * Cookie\nlogin-status-p\n * Duration\npast\n * Description\nDescription is currently not available.\n\n\n * Cookie\nAWSALBTG\n * Duration\n7 days\n * Description\nNo description available.\n\n\n * Cookie\ncsrf_token\n * Duration\nsession\n * Description\nNo description available.\n\n\n * Cookie\ntoken_v2\n * Duration\n1 day\n * Description\nDescription is currently not available.\n\n\n * Cookie\nD\n * Duration\n1 year\n * Description\nDescription is currently not available.\n\n\n * Cookie\nPHPSESSID\n * Duration\nsession\n * Description\nThis cookie is native to PHP applications. The cookie stores and identifies a user's unique session ID to manage user sessions on the website. The cookie is a session cookie and will be deleted when all the browser windows are closed.\n\n\n * Cookie\nVISITOR_PRIVACY_METADATA\n * Duration\n6 months\n * Description\nYouTube sets this cookie to store the user's cookie consent state for the current domain. \n\n\n * Cookie\ncookietest\n * Duration\nsession\n * Description\nThe cookietest cookie is typically used to determine whether the user's browser accepts cookies, essential for website functionality and user experience.\n\n\n * Cookie\n__Host-airtable-session\n * Duration\n1 year\n * Description\nThis cookie is used to enable us to integrate the services of Airtable.\n\n\n * Cookie\n__Host-airtable-session.sig\n * Duration\n1 year\n * Description\nThis cookie is used to enable us to integrate the services of Airtable.\n\n\n * Cookie\nm\n * Duration\n1 year 1 month 4 days\n * Description\nStripe sets this cookie for fraud prevention purposes. It identifies the device used to access the website, allowing the website to be formatted accordingly.\n\n\n * Cookie\nBIGipServer*\n * Duration\nsession\n * Description\nMarketo sets this cookie to collect information about the user's online activity and build a profile about their interests to provide advertisements relevant to the user. \n\n\n * Cookie\n__cfruid\n * Duration\nsession\n * Description\nCloudflare sets this cookie to identify trusted web traffic.\n\n\n * Cookie\n_GRECAPTCHA\n * Duration\n6 months\n * Description\nGoogle Recaptcha service sets this cookie to identify bots to protect the website against malicious spam attacks.\n\n\n * Cookie\n__Secure-YNID\n * Duration\n6 months\n * Description\nGoogle cookie used to protect user security and prevent fraud, especially during the login process.\n\n\n * Cookie\ncookieyes-consent\n * Duration\n1 year\n * Description\nCookieYes sets this cookie to remember users' consent preferences so that their preferences are respected on subsequent visits to this site. It does not collect or store any personal information about the site visitors.\n\n\nFunctional\nFunctional cookies help perform certain functionalities like sharing the content of the website on social media platforms, collecting feedback, and other third-party features.\n * Cookie\nlidc\n * Duration\n1 day\n * Description\nLinkedIn sets the lidc cookie to facilitate data center selection.\n\n\n * Cookie\nbrw\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\nbrwConsent\n * Duration\n5 minutes\n * Description\nDescription is currently not available.\n\n\n * Cookie\nWMF-Uniq\n * Duration\n1 year\n * Description\nDescription is currently not available.\n\n\n * Cookie\nloom_anon_comment\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\nloom_referral_video\n * Duration\nsession\n * Description\nDescription is currently not available.\n\n\n * Cookie\nVISITOR_INFO1_LIVE\n * Duration\n6 months\n * Description\nA cookie set by YouTube to measure bandwidth that determines whether the user gets the new or old player interface.\n\n\n * Cookie\nyt-remote-connected-devices\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to store the user's video preferences using embedded YouTube videos.\n\n\n * Cookie\nytidb::LAST_RESULT_ENTRY_KEY\n * Duration\nNever Expires\n * Description\nThe cookie ytidb::LAST_RESULT_ENTRY_KEY is used by YouTube to store the last search result entry that was clicked by the user. This information is used to improve the user experience by providing more relevant search results in the future.\n\n\n * Cookie\nyt-remote-device-id\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to store the user's video preferences using embedded YouTube videos.\n\n\n * Cookie\nyt-remote-session-name\n * Duration\nsession\n * Description\nThe yt-remote-session-name cookie is used by YouTube to store the user's video player preferences using embedded YouTube video.\n\n\n * Cookie\nyt-remote-fast-check-period\n * Duration\nsession\n * Description\nThe yt-remote-fast-check-period cookie is used by YouTube to store the user's video player preferences for embedded YouTube videos.\n\n\n * Cookie\nyt-remote-session-app\n * Duration\nsession\n * Description\nThe yt-remote-session-app cookie is used by YouTube to store user preferences and information about the interface of the embedded YouTube video player.\n\n\n * Cookie\nyt-remote-cast-available\n * Duration\nsession\n * Description\nThe yt-remote-cast-available cookie is used to store the user's preferences regarding whether casting is available on their YouTube video player.\n\n\n * Cookie\nyt-remote-cast-installed\n * Duration\nsession\n * Description\nThe yt-remote-cast-installed cookie is used to store the user's video player preferences using embedded YouTube video.\n\n\n * Cookie\ncp_session\n * Duration\n3 months\n * Description\nCodepen sets this cookie for Help systems found in the website.\n\n\n * Cookie\nloid\n * Duration\n1 year 1 month 4 days\n * Description\nThis cookie is set by the Reddit. The cookie enables the sharing of content from the website onto the social media platform.\n\n\nAnalytics\nAnalytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics such as the number of visitors, bounce rate, traffic source, etc.\n * Cookie\n__hstc\n * Duration\n6 months\n * Description\nHubspot set this main cookie for tracking visitors. It contains the domain, initial timestamp (first visit), last timestamp (last visit), current timestamp (this visit), and session number (increments for each subsequent session).\n\n\n * Cookie\nhubspotutk\n * Duration\n6 months\n * Description\nHubSpot sets this cookie to keep track of the visitors to the website. This cookie is passed to HubSpot on form submission and used when deduplicating contacts.\n\n\n * Cookie\n_ga\n * Duration\n1 year 1 month 4 days\n * Description\nGoogle Analytics sets this cookie to calculate visitor, session and campaign data and track site usage for the site's analytics report. The cookie stores information anonymously and assigns a randomly generated number to recognise unique visitors.\n\n\n * Cookie\n_ga_*\n * Duration\n1 year 1 month 4 days\n * Description\nGoogle Analytics sets this cookie to store and count page views.\n\n\n * Cookie\n__Host-psifi.analyticsTrace\n * Duration\n6 hours\n * Description\nDescription is currently not available.\n\n\n * Cookie\n__Host-psifi.analyticsTraceV2\n * Duration\n6 hours\n * Description\nDescription is currently not available.\n\n\n * Cookie\n_gh_sess\n * Duration\nsession\n * Description\nGitHub sets this cookie for temporary application and framework state between pages like what step the user is on in a multiple step form.\n\n\n * Cookie\nYSC\n * Duration\nsession\n * Description\nYSC cookie is set by Youtube and is used to track the views of embedded videos on Youtube pages.\n\n\n * Cookie\najs_anonymous_id\n * Duration\n1 year\n * Description\nThis cookie is set by Segment to count the number of people who visit a certain site by tracking if they have visited before.\n\n\n * Cookie\nvuid\n * Duration\n1 year 1 month 4 days\n * Description\nVimeo installs this cookie to collect tracking information by setting a unique ID to embed videos on the website. \n\n\nPerformance\nPerformance cookies are used to understand and analyse the key performance indexes of the website which helps in delivering a better user experience for the visitors.\n * Cookie\nAWSALB\n * Duration\n7 days\n * Description\nAWSALB is an application load balancer cookie set by Amazon Web Services to map the session to the target.\n\n\n * Cookie\nacq\n * Duration\npast\n * Description\nDescription is currently not available.\n\n\n * Cookie\nacq.sig\n * Duration\npast\n * Description\nDescription is currently not available.\n\n\n * Cookie\nptc\n * Duration\n2 years\n * Description\nNo description available.\n\n\nAdvertisement\nAdvertisement cookies are used to provide visitors with customised advertisements based on the pages you visited previously and to analyse the effectiveness of the ad campaigns.\n * Cookie\nmuc_ads\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to collect user behaviour and interaction data to optimize the website.\n\n\n * Cookie\nguest_id_marketing\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to identify and track the website visitor.\n\n\n * Cookie\nguest_id_ads\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to identify and track the website visitor.\n\n\n * Cookie\npersonalization_id\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to integrate and share features for social media and also store information about how the user uses the website, for tracking and targeting.\n\n\n * Cookie\nguest_id\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to identify and track the website visitor. It registers if a user is signed in to the Twitter platform and collects information about ad preferences.\n\n\n * Cookie\nbcookie\n * Duration\n1 year\n * Description\nLinkedIn sets this cookie from LinkedIn share buttons and ad tags to recognize browser IDs.\n\n\n * Cookie\n__Secure-ROLLOUT_TOKEN\n * Duration\n6 months\n * Description\nYouTube sets this cookie to manage feature rollout and experimentation. It helps Google control which new features or interface changes are shown to users as part of testing and staged rollouts, ensuring consistent experience for a given user during an experiment.\n\n\n * Cookie\nyt.innertube::nextId\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen.\n\n\n * Cookie\nyt.innertube::requests\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen.\n\n\n * Cookie\nsession_tracker\n * Duration\nsession\n * Description\nThis cookie is set by the Reddit. This cookie is used to identify trusted web traffic. It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Data Science](https://towardsdatascience.com/category/data-science/)\n# Avoid Overfitting in Neural Networks: a Deep Dive\nLearn how to implement regularization techniques to boost performances and prevent Neural Network overfitting.\n[Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\nNovember 30, 20239 min read\n### Learn how to implement regularization techniques to boost performances and prevent Neural Network overfitting\n![Image source: unsplash.com.](../images/000.jpeg)\nImage source: [unsplash.com](https://unsplash.com/photos/multicolored-illustration-gpiKdZmDQig).\nWhen training a deep neural network, it's often troublesome to achieve the same performances on **both the training and validation sets**. A considerably higher error on the validation set is a **clear flag for overfitting** : the network has become too specialized in the training data. In this article, I provide a comprehensive guide on how to bypass this issue.\nLearn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist), [Computer Science](https://roadmap.sh/computer-science) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n## Overfitting Neural Networks\nWhen dealing with any machine learning application, it's important to have a clear understanding of the **bias and variance of the model**. In traditional machine learning algorithms, we talk about the [**bias vs. variance tradeoff**](https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff#:~:text=In%20statistics%20and%20machine%20learning,bias%20in%20the%20estimated%20parameters.), which consists of the struggle of minimizing both the **variance** and the **bias** of a model.\nIn order to reduce the bias of a model (i.e. its error from erroneous assumptions), we need a **more complex model**. On the contrary, reducing the model's variance (the sensitivity of the model in capturing the variations of the training data), implies a **more simple model**. It is straightforward that the bias vs. variance tradeoff, in traditional machine learning, derives from the conflict of necessitating both a **more complex and a simpler model at the same time**.\nIn the **Deep Learning era,** we have tools to reduce just the model's variance without hurting the model's bias or, on the contrary, to reduce the bias without increasing the variance.\nBefore exploring the different techniques used to prevent the overfitting of a neural network, it's important to clarify what high variance or high bias means.\nConsider a common neural network task such as image recognition, and think over a neural network that recognizes the presence of pandas in a picture. We can confidently assess that a human can carry out this task with a near 0% error. As a consequence, this is a reasonable benchmark for the accuracy of the image recognition network. After training the neural network on the training set and evaluating its performances on both the training and validation sets, we may come up with these different results:\n 1. Train Error = 20% and Validation Error = 22%\n 2. Train Error = 1% and Validation Error = 15%\n 3. Train Error = 0.5% and Validation Error = 1%\n 4. Train Error = 20% and Validation Error = 30%\n\n\nThe first example is a typical instance of **high bias** : the error is large on **both the train and validation sets**. Conversely, the second example suffers from **high variance** , having a much lower accuracy when dealing with data **the model didn't learn from**. The third result represents **low variance and bias** , the model can be considered valid. Finally, the fourth example shows a case of **both high bias and variance** : not only the training error is large when compared with the benchmark, but the validation error is also higher.\n![Image by the author.](../images/001.png)\nImage by the author.\nFrom now on, I will present several techniques of regularization, used to reduce the model's overfitting to the training data. They are beneficial for cases 2. and 4. of the previous example.\n## L1 and L2 Regularization\nSimilar to classical regression algorithms (linear, logistic, polynomial, etc.), [**L1 and L2 regularizations**](https://towardsdatascience.com/l1-and-l2-regularization-methods-ce25e7fc831c) are also employed to prevent overfitting in high-variance neural networks. In order to keep [this article](https://neptune.ai/blog/fighting-overfitting-with-l1-or-l2-regularization) short and on-point, I won't recall how L1 and L2 regularizations work on regression algorithms, but you can check this article for additional information.\nThe idea behind the L1 and L2 regularization techniques is to **constrain the model's weights** to be smaller or to **shrink some of them** to 0.\nConsider the cost function J of a classical deep neural network:\n![](../images/body-327e08a40c844b552c40.png)\nThe cost function J is, of course, a function of the weights and biases of each layer 1, ..., L. m is the number of training examples and ℒ is the loss function.\n### L1 Regularization\nIn L1 Regularization we add the following term to the cost function J:\n![](../images/body-00578a7a129c115ccfff.png)\nwhere the matrix norm is the sum of the absolute value of the weights for each layer 1, ..., L of the network:\n![](../images/body-f2ecdbdb4081ec0fc42a.png)\nλ is the **regularization term**. It's a hyperparameter that must be **carefully tuned**. λ directly controls the impact of the regularization: as λ increases, the effects on the weights shrinking are more severe.\nThe complete cost function under L1 Regularization becomes:\n![](../images/body-b210ae76e2dbc9464546.png)\nFor λ=0, the effects of L1 Regularization are null. Instead, choosing a value of λ which is too big, will over-simplify the model, probably resulting in an underfitting network.\nL1 Regularization can be considered as a sort of neuron selection process because it would bring to zero the weights of some hidden neurons.\n### L2 Regularization\nIn L2 Regularization, the term we add to the cost function is the following:\n![](../images/body-c1deb97d8496752d196f.png)\nIn this case, the regularization term is the **squared norm of the weights** of each network's layer. This matrix norm is called [Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm) and, explicitly, it's computed as follows:\n![](../images/body-458522b7fac206332640.png)\nPlease note that the weight matrix relative to layer l has n^{[l]} rows and n^{[l-1]} columns.\nFinally, the complete cost function under L2 Regularization becomes:\n![](../images/body-473154a932ed8a6eb14f.png)\nAgain, λ is the **regularization term** and for λ=0 the effects of L2 Regularization are null.\nL2 Regularization brings towards zero the values of the weights, resulting in a more simple model.\n### How do L1 and L2 Regularization reduce overfitting?\nL1 and L2 Regularization techniques have positive effects on overfitting to the training data for two reasons:\n * The weights of some hidden units become closer (or equal) to 0. As a consequence, their effect is weakened and the resulting network is simpler because it's closer to a **smaller network**. As stated in the introduction, a simpler network is less prone to overfitting.\n * For smaller weights, also the input z of the activation function of a hidden neuron becomes smaller. For values close to 0, many activation functions behave **linearly**.\n\n\nThe second reason is not trivial and deserves an expansion. Consider a hyperbolic tangent (tanh) activation function, whose graph is the following:\n![Image by the author.](../images/002.png)\nImage by the author.\nFrom the function plot we can see that if the input value x is small, the function tanh(x) behaves **almost linearly**. When tanh is used as the activation function of a neural network's hidden layers, the input value is:\n![](../images/body-1958aa7189c615d532f0.png)\nwhich for small weights w is also **close to zero**.\nIf each layer of the neural network is linear, we can prove that the whole network behaves linearly. Thus, constraining some of the hidden units to mimic linear functions, leads to a simpler network and, as a consequence, helps to prevent overfitting.\nA simpler model often is [not capable to capture the noise](https://towardsdatascience.com/regularization-in-deep-learning-l1-l2-and-dropout-377e75acc036) in the training data and therefore, **overfitting is less frequent**.\n## Dropout\nThe idea of [**dropout regularization**](https://www.analyticsvidhya.com/blog/2022/08/dropout-regularization-in-deep-learning/#:~:text=In%20machine%20learning%2C%20%E2%80%9Cdropout%E2%80%9D,are%20codependent%20with%20one%20another.) is to **randomly remove some nodes** in the network. Before the training process, we set a probability (suppose p = 50%) for each node of the network. During the training phase, each node has a p **probability of being turned off**. The dropout process is random, and it is performed separately for each training example. As a consequence, each training example might be trained on a different network.\nAs for L2 Regularization, the result of dropout regularization is a simpler network, and a simpler network leads to a less complex model.\n![The effect of dropout on a simple network. Image by the author.](../images/003.png)\nThe effect of dropout on a simple network. Image by the author.\n### Dropout in practice\nIn this brief section, I show how to implement **Dropout regularization in practice**. I will go through a few simple lines of code (python). If you are only interested in the general theory of regularization, you can easily skip this section.\nSuppose we have stored the activation values of the network's layer 4 in the [NumPy](https://numpy.org/) array `a4`. First, we create the auxiliary vector `d4`:\npython\n\n```\n# Set the keeping probability\nkeep_prob = 0.7\n```\n\npython\n\n```\n# Create auxiliary vector for layer 4\nd4 = np.random.rand(a4.shape[0], a3.shape[1]) < keep_prob\n```\n\nThe vector `d4` has the same dimensions as `a4` and contains the values `True` or `False` based on the probability `keep_prob`. If we set a keeping probability of 70%, that is the probability that a given hidden unit is kept, and therefore, the probability of having `True` value on a given element of `d4`.\nWe apply the auxiliary vector `d4` to the activations `a4`:\npython\n\n```\n# Apply the auxiliary vector d4 to the activation a4\na4 = np.multiply(a4,d4)\n```\n\nFinally, we need to scale the modified vector `a4` by the `keep_prob` value:\npython\n\n```\n# Scale the modified vector a4\na4 /= keep_prob\n```\n\nThis last operation is needed to compensate for the reduction of units in the layer. Carrying out this operation during the training process allows us not to apply dropout during the test phase.\n### How does dropout reduce overfitting?\nDropout has the effect of temporarily **transforming the network into a smaller one** , and we know that smaller networks are **less complex and less prone to overfitting**.\nConsider the network illustrated above, and focus on the first unit of the second layer. Because some of its inputs may be temporarily shut down due to dropout, the unit **can't always rely on them** during the training phase. As a consequence, the hidden unit is encouraged to spread its weights across its inputs. Spreading the weights has the effect of decreasing the squared norm of the weight matrix, resulting in a **sort of L2 regularization**.\nSetting the keeping probability is a fundamental step for an effective dropout regularization. Typically, the keeping probability is set separately for each layer of the neural network. For layers with a large weight matrix, we usually set a smaller keeping probability because, at each step, we want to conserve proportionally fewer weights with respect to smaller layers.\n## Other Regularization Techniques\nIn addition to L1/L2 regularization and dropout, there exist **other regularization techniques**. Two of them are **data augmentation** and **early stopping**.\nFrom the theory, we know that training a network on more data has positive effects on reducing high variance. As getting more data is often a demanding task, data augmentation is a technique that, for some applications, allows machine learning practitioners to get more data almost for free. In computer vision, data augmentation provides a **larger training set** by flipping, zooming, and translating the original images. In the case of digit recognition, we can also impose distortion on the images.\n**Early stopping** , as the name suggests, involves **stopping the training phase** before the initially defined number of iterations. If we plot the cost function on both the training set and the validation set as a function of the iterations, we can experience that, for an overfitting model, the training error always keeps decreasing but the validation error might start to increase after a certain number of iterations. When the validation error stops decreasing, that is exactly the time to stop the training process. By stopping the training process earlier, we force the model to be simpler, thus reducing overfitting.\n## **Conclusion**\nIn conclusion, the L1 and L2 regularization techniques are indispensable tools in addressing overfitting within neural networks.\n![Image by the author.](../images/004.png)\nImage by the author.\nL1 regularization, with its ability to induce sparsity by **penalizing irrelevant features** , proves effective in **simplifying models**. On the other hand, L2 regularization, by penalizing the squared magnitude of weights, **promotes smoother models** , reducing the risk of extreme values.\nDropout, a dynamic technique involving randomly deactivating neurons during the training phase, enhances model generalization. It prevents over-reliance on specific neurons, promoting a more robust network.\nHowever, these techniques come with tradeoffs. While regularization methods effectively mitigate overfitting, they may inadvertently restrict the model's ability to capture intricate patterns in the data. The real challenge is choosing the right balance between regularization strength and model complexity.\nFor further insights, I will fill the Reference section with amazing resources. I highly suggest checking them out to refine your understanding of the subject.\n* * *\nIf you liked this story, consider following me to be notified of my upcoming projects and articles!\nHere are some of my past projects:\n> [**Advanced Dimensionality Reduction Models Made Simple**](https://towardsdatascience.com/advanced-dimensionality-reduction-models-made-simple-639fca351528)\n> [**Use Deep Learning to Generate Fantasy Names: Build a Language Model from Scratch**](https://towardsdatascience.com/use-deep-learning-to-generate-fantasy-character-names-build-a-language-model-from-scratch-792b13629efa)\n> [**Outlier Detection with Scikit-Learn and Matplotlib: a Practical Guide**](https://towardsdatascience.com/outlier-detection-with-scikit-learn-and-matplotlib-a-practical-guide-382d1411b8ec)\n## References\n * [Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville](https://www.deeplearningbook.org/)\n * [Dropout: A Simple Way to Prevent Neural Networks from Overfitting by Nitish Srivastava et al. (2014)](https://jmlr.org/papers/v15/srivastava14a.html)\n * [Regularization Techniques in Deep Learning: A Survey and Practical Guide by Navid Pustokhina, et al.](https://arxiv.org/abs/2201.03299)\n * [Understanding the Disharmony between Dropout and Batch Normalization by Variance Shift by Shibani Santurkar, et al. (2018)](https://www.researchgate.net/publication/327434121_Understanding_Regularization_in_Batch_Normalization)\n * [Neural Networks and Deep Learning: A Textbook by Charu Aggarwal](https://link.springer.com/book/10.1007/978-3-319-94463-0)\n\n\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. Create a free account today to access this article and thousands more.\nRegister for freeSign in to your account\n* * *\n![](../images/body-34347b17fbf8612c4a0c.jpeg)\nWritten By\n## [Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\n[See all from Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\n[Data Science](https://towardsdatascience.com/tag/data-science/)[Machine Learning](https://towardsdatascience.com/tag/machine-learning/)[Neural Networks](https://towardsdatascience.com/tag/neural-networks/)[Overfitting](https://towardsdatascience.com/tag/overfitting/)[Programming](https://towardsdatascience.com/tag/programming/)\nShare This Article\n * [](https://www.facebook.com/sharer/sharer.php?u=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F&title=Avoid%20Overfitting%20in%20Neural%20Networks%3A%20a%20Deep%20Dive)\n * [](https://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F&title=Avoid%20Overfitting%20in%20Neural%20Networks%3A%20a%20Deep%20Dive)\n * [](https://x.com/share?url=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F&text=Avoid%20Overfitting%20in%20Neural%20Networks%3A%20a%20Deep%20Dive)\n\n\nTowards Data Science is a community publication. Submit your insights to reach our global audience and earn through the TDS Author Payment Program.\n[Write for TDS](https://towardsdatascience.com/submissions/)\n## Related Articles\n * [![](../images/005.gif)](https://towardsdatascience.com/understand-support-vector-machines-6cc9e4a15e7e/)\n## [Understand Support Vector Machines](https://towardsdatascience.com/understand-support-vector-machines-6cc9e4a15e7e/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\npart 1 of a 5-sequence, brief articles that provide a comprehensive introduction; no prior knowledge assumed\n[Ahmar Shah, PhD (Oxford)](https://towardsdatascience.com/author/ahmarshah/)\nMarch 7, 20216 min read\n * [![](../images/body-63beb50f664a055ed739.jpg)](https://towardsdatascience.com/latest-picks-an-intuitive-look-at-the-basics-of-information-theory-2aa21286e846/)\n## [Latest picks: An Intuitive Look at the Basics of Information Theory](https://towardsdatascience.com/latest-picks-an-intuitive-look-at-the-basics-of-information-theory-2aa21286e846/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nYour daily dose of data science\n[TDS Editors](https://towardsdatascience.com/author/towardsdatascience/)\nJanuary 19, 20211 min read\n * [![](../images/007.jpg)](https://towardsdatascience.com/i-built-a-c-backend-so-my-gpu-would-stop-eating-air/)\n## [I Built a C++ Backend So My GPU Would Stop Eating Air](https://towardsdatascience.com/i-built-a-c-backend-so-my-gpu-would-stop-eating-air/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nHow to eliminate padding overhead and accelerate LLM inference at the hardware level.\n[Anubhab Banerjee](https://towardsdatascience.com/author/anubhab.banerjee/)\nJune 3, 202627 min read\n * [![](../images/008.jpeg)](https://towardsdatascience.com/best-places-for-new-businesses-in-florianopolis-brazil-north-shore-a-foursquare-data-analysis-1a6034024011/)\n## [Best places for new businesses in Florianopolis, Brazil (North Shore): a Foursquare data analysis](https://towardsdatascience.com/best-places-for-new-businesses-in-florianopolis-brazil-north-shore-a-foursquare-data-analysis-1a6034024011/)\n[Data Science](https://towardsdatascience.com/category/data-science/)\nWhich opportunities could the data show?\n[Shaiala Marques](https://towardsdatascience.com/author/shaiala/)\nSeptember 14, 20209 min read\n * [![](../images/009.jpeg)](https://towardsdatascience.com/graph-machine-learning-icml-2023-9b5e4306a1cc/)\n## [Graph Machine Learning @ ICML 2023](https://towardsdatascience.com/graph-machine-learning-icml-2023-9b5e4306a1cc/)\n[Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/)\nRecent advancements and hot trends, August 2023 edition\n[Michael Galkin](https://towardsdatascience.com/author/mgalkin/)\nAugust 6, 202315 min read\n * [![](../images/010.jpg)](https://towardsdatascience.com/classification-with-rosenblatts-perceptron-e7f49e3af562/)\n## [Classification With Rosenblatt's Perceptron](https://towardsdatascience.com/classification-with-rosenblatts-perceptron-e7f49e3af562/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nThe \"hello-world\" of machine learning\n[Pan Cretan](https://towardsdatascience.com/author/cretanpan/)\nSeptember 8, 20237 min read\n * [![](../images/011.png)](https://towardsdatascience.com/sigmoid-and-softmax-functions-in-5-minutes-f516c80ea1f9/)\n## [Sigmoid and SoftMax Functions in 5 minutes](https://towardsdatascience.com/sigmoid-and-softmax-functions-in-5-minutes-f516c80ea1f9/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nThe math behind two of the most used activation functions in Machine Learning\n[Gabriel Furnieles](https://towardsdatascience.com/author/gabrielfurnieles/)\nSeptember 8, 20225 min read\n * [![](../images/012.png)](https://towardsdatascience.com/3-reasons-why-sparks-lazy-evaluation-is-useful-ed06e27360c4/)\n## [3 Reasons Why Spark's Lazy Evaluation is Useful](https://towardsdatascience.com/3-reasons-why-sparks-lazy-evaluation-is-useful-ed06e27360c4/)\n[Programming](https://towardsdatascience.com/category/programming/)\nSpark's Lazy Evaluation and Why You Should Care\n[Amal Hasni](https://towardsdatascience.com/author/amal-hasni/)\nSeptember 14, 20225 min read\n * [![](../images/013.jpeg)](https://towardsdatascience.com/bertelsman-arvato-financial-solution-customer-segmentation-c8528d5ac77a/)\n## [Bertelsman Arvato Financial Solution Customer Segmentation](https://towardsdatascience.com/bertelsman-arvato-financial-solution-customer-segmentation-c8528d5ac77a/)\n[Data Science](https://towardsdatascience.com/category/data-science/)\nNowadays, with big data becomes reality, people now focus on how to use the data to realize commercial values. One area which is much more...\n[Annie Wang](https://towardsdatascience.com/author/annie-wangliu/)\nJanuary 28, 20218 min read\n\n\n * [YouTube](https://www.youtube.com/c/TowardsDataScience)\n * [X](https://x.com/TDataScience)\n * [LinkedIn](https://www.linkedin.com/company/towards-data-science/)\n * [Threads](https://www.threads.net/@towardsdatascience)\n * [Bluesky](https://bsky.app/profile/towardsdatascience.com)\n\n\n[](https://towardsdatascience.com/)\nYour home for data science and AI. The world's leading publication for data science, data analytics, data engineering, machine learning, and artificial intelligence professionals.\nSubscribe to Our Newsletter[Write For TDS](https://towardsdatascience.com/submissions/)•[About](https://towardsdatascience.com/about-towards-data-science-d691af11cc2f/)•[Advertise](https://contact.towardsdatascience.com/advertise-with-towards-data-science)•[Privacy Policy](https://towardsdatascience.com/privacy-policy/)•[Terms of Use](https://towardsdatascience.com/website-terms-of-use/)\n© Insight Media Group, LLC 2026•[The New Stack](https://thenewstack.io)•[roadmap.sh](https://roadmap.sh)•[Creator Network](https://insightmediagroup.io/creator-network)\n#### Recommended Articles \nClose\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607686/image?etag=1782161464448&width=500&height=500) How Relevance Models Foreshadowed Transformers for NLP ](https://towardsdatascience.com/how-relevance-models-foreshadowed-transformers-for-nlp/ \"How Relevance Models Foreshadowed Transformers for NLP\")\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607639/image?etag=1781250125848&width=500&height=500) Javascript Fatigue: HTMX Is All You Need to Build ChatGPT — Part 1 ](https://towardsdatascience.com/javascript-fatigue-you-dont-need-js-to-build-chatgpt/ \"Javascript Fatigue: HTMX Is All You Need to Build ChatGPT — Part 1\")\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607930/image?etag=1782124566054&width=500&height=500) The Subset Sum Problem Solved in Linear Time for Dense Enough Inputs ](https://towardsdatascience.com/subset-sum-problem-solved-in-linear-time-for-dense-enough-inputs/ \"The Subset Sum Problem Solved in Linear Time for Dense Enough Inputs\")\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/3660/image?etag=1780176246070&width=500&height=500) Does Your Company Have a Data Strategy? ](https://towardsdatascience.com/does-your-company-have-a-data-strategy-e8944dbec4ae/ \"Does Your Company Have a Data Strategy?\")\n\n\n", "metadata": { "title": "Avoid Overfitting in Neural Networks: a Deep Dive | Towards Data Science", "description": "Learn how to implement regularization techniques to boost performances and prevent Neural Network overfitting.", "keywords": null, "author": "Riccardo Andreoni", "og:locale": "en_US", "og:type": "article", "og:title": "Avoid Overfitting in Neural Networks: a Deep Dive", "og:description": "Learn how to implement regularization techniques to boost performances and prevent Neural Network overfitting.", "og:url": "https://towardsdatascience.com/avoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507/", "og:site_name": "Towards Data Science", "og:image": "https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1U61rOQHR1OkVhPXMjJgwLg-scaled.jpeg", "og:image:width": "2560", "og:image:height": "1920", "og:image:type": "image/jpeg", "twitter:card": "summary_large_image", "twitter:site": "@TDataScience", "twitter:creator": "@TDataScience", "twitter:label1": "Written by", "twitter:data1": "Riccardo Andreoni", "twitter:label2": "Est. reading time", "twitter:data2": "9 min read", "article:published_time": "2023-11-30T06:06:11.000Z", "article:modified_time": "2023-11-30T06:06:11.000Z", "article:author": "https://towardsdatascience.com/author/riccardo.andreoni/" }, "paywall": { "listed_paid": false, "detected": false, "marker": "", "public_only": false, "policy": "付费/会员内容只保留页面公开可见部分，不绕过付费墙" }, "crawl": { "success": true, "status_code": 200, "error": "" }, "code_blocks": [ { "language": "txt", "file": "attachments/6398e561e759/code/block_000.txt", "chars": 46 }, { "language": "txt", "file": "attachments/6398e561e759/code/block_001.txt", "chars": 96 }, { "language": "txt", "file": "attachments/6398e561e759/code/block_002.txt", "chars": 77 }, { "language": "txt", "file": "attachments/6398e561e759/code/block_003.txt", "chars": 47 } ], "images": [ { "status": "http_404", "url": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607686/image?etag=1782161464448&width=500&height=500", "src": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607686/image?etag=1782161464448&width=500&height=500", "alt": "", "downloaded": false, "discovery": "saved_markdown", "retried_at": "2026-10-20T17:38:36Z" }, { "status": "http_404", "url": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607639/image?etag=1781250125848&width=500&height=500", "src": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607639/image?etag=1781250125848&width=500&height=500", "alt": "", "downloaded": false, "discovery": "saved_markdown", "retried_at": "2026-10-20T17:38:36Z" }, { "status": "http_404", "url": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607930/image?etag=1782124566054&width=500&height=500", "src": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607930/image?etag=1782124566054&width=500&height=500", "alt": "", "downloaded": false, "discovery": "saved_markdown", "retried_at": "2026-10-20T17:38:36Z" }, { "status": "http_404", "url": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/3660/image?etag=1780176246070&width=500&height=500", "src": "https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/3660/image?etag=1780176246070&width=500&height=500", "alt": "", "downloaded": false, "discovery": "saved_markdown", "retried_at": "2026-10-20T17:38:36Z" } ], "audio": [], "videos": [ { "url": "https://www.youtube.com/c/TowardsDataScience", "kind": "channel_reference", "status": "reference_only" } ], "links": [ { "type": "internal", "href": "https://towardsdatascience.com/" }, { "type": "internal", "href": "https://towardsdatascience.com/latest/" }, { "type": "internal", "href": "https://towardsdatascience.com/tag/editors-pick/" }, { "type": "internal", "href": "https://towardsdatascience.com/tag/the-variable/" }, { "type": "internal", "href": "https://towardsdatascience.com/shipai/" }, { "type": "internal", "href": "https://towardsdatascience.com/submissions/" }, { "type": "internal", "href": "https://towardsdatascience.com/category/data-science/" }, { "type": "internal", "href": "https://towardsdatascience.com/author/riccardo.andreoni/" }, { "type": "internal", "href": "https://towardsdatascience.com/l1-and-l2-regularization-methods-ce25e7fc831c" }, { "type": "internal", "href": "https://towardsdatascience.com/regularization-in-deep-learning-l1-l2-and-dropout-377e75acc036" }, { "type": "internal", "href": "https://towardsdatascience.com/advanced-dimensionality-reduction-models-made-simple-639fca351528" }, { "type": "internal", "href": "https://towardsdatascience.com/use-deep-learning-to-generate-fantasy-character-names-build-a-language-model-from-scratch-792b13629efa" }, { "type": "internal", "href": "https://towardsdatascience.com/outlier-detection-with-scikit-learn-and-matplotlib-a-practical-guide-382d1411b8ec" }, { "type": "internal", "href": "https://towardsdatascience.com/tag/data-science/" }, { "type": "internal", "href": "https://towardsdatascience.com/tag/machine-learning/" }, { "type": "internal", "href": "https://towardsdatascience.com/tag/neural-networks/" }, { "type": "internal", "href": "https://towardsdatascience.com/tag/overfitting/" }, { "type": "internal", "href": "https://towardsdatascience.com/tag/programming/" }, { "type": "internal", "href": "https://towardsdatascience.com/understand-support-vector-machines-6cc9e4a15e7e/" }, { "type": "internal", "href": "https://towardsdatascience.com/category/artificial-intelligence/machine-learning/" }, { "type": "external", "href": "https://write.insightmediagroup.io" }, { "type": "external", "href": "https://www.linkedin.com/company/towards-data-science/" }, { "type": "external", "href": "https://x.com/TDataScience" }, { "type": "external", "href": "https://unsplash.com/photos/multicolored-illustration-gpiKdZmDQig" }, { "type": "external", "href": "https://roadmap.sh/ai-data-scientist" }, { "type": "external", "href": "https://roadmap.sh/computer-science" }, { "type": "external", "href": "https://roadmap.sh/machine-learning" }, { "type": "external", "href": "https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff" }, { "type": "external", "href": "https://neptune.ai/blog/fighting-overfitting-with-l1-or-l2-regularization" }, { "type": "external", "href": "https://en.wikipedia.org/wiki/Matrix_norm" }, { "type": "external", "href": "https://www.analyticsvidhya.com/blog/2022/08/dropout-regularization-in-deep-learning/" }, { "type": "external", "href": "https://numpy.org/" }, { "type": "external", "href": "https://www.deeplearningbook.org/" }, { "type": "external", "href": "https://jmlr.org/papers/v15/srivastava14a.html" }, { "type": "external", "href": "https://arxiv.org/abs/2201.03299" }, { "type": "external", "href": "https://www.researchgate.net/publication/327434121_Understanding_Regularization_in_Batch_Normalization" }, { "type": "external", "href": "https://link.springer.com/book/10.1007/978-3-319-94463-0" }, { "type": "external", "href": "https://www.facebook.com/sharer/sharer.php?title=Avoid+Overfitting+in+Neural+Networks%3A+a+Deep+Dive&u=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F" }, { "type": "external", "href": "https://www.linkedin.com/shareArticle?mini=true&title=Avoid+Overfitting+in+Neural+Networks%3A+a+Deep+Dive&url=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F" }, { "type": "external", "href": "https://x.com/share?text=Avoid+Overfitting+in+Neural+Networks%3A+a+Deep+Dive&url=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F" } ], "repair_version": 2, "repaired_at": "2026-10-20T17:24:01Z", "source_url": "https://towardsdatascience.com/avoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507/", "delivery_status": "unverified", "discovery_status": "http_403", "missing_reason": "源页面未重新核验:http_403；已按保留正文补采图片", "repair_error": "", "actual_video_files": [], "expected_saved_body_images": 4, "image_discovery": "saved_markdown", "source_body_markdown": "![Revisit consent button](https://cdn-cookieyes.com/assets/images/revisit.svg)\nWe value your privacy\nWe use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. By clicking \"Accept All\", you consent to our use of cookies.\nCustomise Reject All Accept All\nCustomise Consent Preferences ![](https://cdn-cookieyes.com/assets/images/close.svg)\nWe use cookies to help you navigate efficiently and perform certain functions. You will find detailed information about all cookies under each consent category below.\nThe cookies that are categorised as \"Necessary\" are stored on your browser as they are essential for enabling the basic functionalities of the site. ... Show more\nNecessaryAlways Active\nNecessary cookies are required to enable the basic features of this site, such as providing secure log-in or adjusting your consent preferences. These cookies do not store any personally identifiable data.\n * Cookie\nBCTempID\n * Duration\n10 minutes\n * Description\nNo description available.\n\n\n * Cookie\n__cf_bm\n * Duration\n1 hour\n * Description\nThis cookie, set by Cloudflare, is used to support Cloudflare Bot Management. \n\n\n * Cookie\nAWSALBCORS\n * Duration\n7 days\n * Description\nAmazon Web Services set this cookie for load balancing.\n\n\n * Cookie\n_cfuvid\n * Duration\nsession\n * Description\nCloudflare sets this cookie to track users across sessions to optimize user experience by maintaining session consistency and providing personalized services\n\n\n * Cookie\nli_gc\n * Duration\n6 months\n * Description\nLinkedin set this cookie for storing visitor's consent regarding using cookies for non-essential purposes.\n\n\n * Cookie\n__hssrc\n * Duration\nsession\n * Description\nThis cookie is set by Hubspot whenever it changes the session cookie. The __hssrc cookie set to 1 indicates that the user has restarted the browser, and if the cookie does not exist, it is assumed to be a new session.\n\n\n * Cookie\n__hssc\n * Duration\n1 hour\n * Description\nHubSpot sets this cookie to keep track of sessions and to determine if HubSpot should increment the session number and timestamps in the __hstc cookie.\n\n\n * Cookie\nwpEmojiSettingsSupports\n * Duration\nsession\n * Description\nWordPress sets this cookie when a user interacts with emojis on a WordPress site. It helps determine if the user's browser can display emojis properly.\n\n\n * Cookie\nBCSessionID\n * Duration\n1 year 1 month 4 days\n * Description\nBlueconic sets this cookie as a unique identifier for the BlueConic profile.\n\n\n * Cookie\n_octo\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\nlogged_in\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\n__Secure-YEC\n * Duration\npast\n * Description\nYouTube sets this cookie to stores the user's video player preferences using embedded YouTube video\n\n\n * Cookie\n__eoi\n * Duration\n6 months\n * Description\nDescription is currently not available.\n\n\n * Cookie\nAWSALBTGCORS\n * Duration\n7 days\n * Description\nNo description available.\n\n\n * Cookie\nlogin-status-p\n * Duration\npast\n * Description\nDescription is currently not available.\n\n\n * Cookie\nAWSALBTG\n * Duration\n7 days\n * Description\nNo description available.\n\n\n * Cookie\ncsrf_token\n * Duration\nsession\n * Description\nNo description available.\n\n\n * Cookie\ntoken_v2\n * Duration\n1 day\n * Description\nDescription is currently not available.\n\n\n * Cookie\nD\n * Duration\n1 year\n * Description\nDescription is currently not available.\n\n\n * Cookie\nPHPSESSID\n * Duration\nsession\n * Description\nThis cookie is native to PHP applications. The cookie stores and identifies a user's unique session ID to manage user sessions on the website. The cookie is a session cookie and will be deleted when all the browser windows are closed.\n\n\n * Cookie\nVISITOR_PRIVACY_METADATA\n * Duration\n6 months\n * Description\nYouTube sets this cookie to store the user's cookie consent state for the current domain. \n\n\n * Cookie\ncookietest\n * Duration\nsession\n * Description\nThe cookietest cookie is typically used to determine whether the user's browser accepts cookies, essential for website functionality and user experience.\n\n\n * Cookie\n__Host-airtable-session\n * Duration\n1 year\n * Description\nThis cookie is used to enable us to integrate the services of Airtable.\n\n\n * Cookie\n__Host-airtable-session.sig\n * Duration\n1 year\n * Description\nThis cookie is used to enable us to integrate the services of Airtable.\n\n\n * Cookie\nm\n * Duration\n1 year 1 month 4 days\n * Description\nStripe sets this cookie for fraud prevention purposes. It identifies the device used to access the website, allowing the website to be formatted accordingly.\n\n\n * Cookie\nBIGipServer*\n * Duration\nsession\n * Description\nMarketo sets this cookie to collect information about the user's online activity and build a profile about their interests to provide advertisements relevant to the user. \n\n\n * Cookie\n__cfruid\n * Duration\nsession\n * Description\nCloudflare sets this cookie to identify trusted web traffic.\n\n\n * Cookie\n_GRECAPTCHA\n * Duration\n6 months\n * Description\nGoogle Recaptcha service sets this cookie to identify bots to protect the website against malicious spam attacks.\n\n\n * Cookie\n__Secure-YNID\n * Duration\n6 months\n * Description\nGoogle cookie used to protect user security and prevent fraud, especially during the login process.\n\n\n * Cookie\ncookieyes-consent\n * Duration\n1 year\n * Description\nCookieYes sets this cookie to remember users' consent preferences so that their preferences are respected on subsequent visits to this site. It does not collect or store any personal information about the site visitors.\n\n\nFunctional\nFunctional cookies help perform certain functionalities like sharing the content of the website on social media platforms, collecting feedback, and other third-party features.\n * Cookie\nlidc\n * Duration\n1 day\n * Description\nLinkedIn sets the lidc cookie to facilitate data center selection.\n\n\n * Cookie\nbrw\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\nbrwConsent\n * Duration\n5 minutes\n * Description\nDescription is currently not available.\n\n\n * Cookie\nWMF-Uniq\n * Duration\n1 year\n * Description\nDescription is currently not available.\n\n\n * Cookie\nloom_anon_comment\n * Duration\n1 year\n * Description\nNo description available.\n\n\n * Cookie\nloom_referral_video\n * Duration\nsession\n * Description\nDescription is currently not available.\n\n\n * Cookie\nVISITOR_INFO1_LIVE\n * Duration\n6 months\n * Description\nA cookie set by YouTube to measure bandwidth that determines whether the user gets the new or old player interface.\n\n\n * Cookie\nyt-remote-connected-devices\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to store the user's video preferences using embedded YouTube videos.\n\n\n * Cookie\nytidb::LAST_RESULT_ENTRY_KEY\n * Duration\nNever Expires\n * Description\nThe cookie ytidb::LAST_RESULT_ENTRY_KEY is used by YouTube to store the last search result entry that was clicked by the user. This information is used to improve the user experience by providing more relevant search results in the future.\n\n\n * Cookie\nyt-remote-device-id\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to store the user's video preferences using embedded YouTube videos.\n\n\n * Cookie\nyt-remote-session-name\n * Duration\nsession\n * Description\nThe yt-remote-session-name cookie is used by YouTube to store the user's video player preferences using embedded YouTube video.\n\n\n * Cookie\nyt-remote-fast-check-period\n * Duration\nsession\n * Description\nThe yt-remote-fast-check-period cookie is used by YouTube to store the user's video player preferences for embedded YouTube videos.\n\n\n * Cookie\nyt-remote-session-app\n * Duration\nsession\n * Description\nThe yt-remote-session-app cookie is used by YouTube to store user preferences and information about the interface of the embedded YouTube video player.\n\n\n * Cookie\nyt-remote-cast-available\n * Duration\nsession\n * Description\nThe yt-remote-cast-available cookie is used to store the user's preferences regarding whether casting is available on their YouTube video player.\n\n\n * Cookie\nyt-remote-cast-installed\n * Duration\nsession\n * Description\nThe yt-remote-cast-installed cookie is used to store the user's video player preferences using embedded YouTube video.\n\n\n * Cookie\ncp_session\n * Duration\n3 months\n * Description\nCodepen sets this cookie for Help systems found in the website.\n\n\n * Cookie\nloid\n * Duration\n1 year 1 month 4 days\n * Description\nThis cookie is set by the Reddit. The cookie enables the sharing of content from the website onto the social media platform.\n\n\nAnalytics\nAnalytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics such as the number of visitors, bounce rate, traffic source, etc.\n * Cookie\n__hstc\n * Duration\n6 months\n * Description\nHubspot set this main cookie for tracking visitors. It contains the domain, initial timestamp (first visit), last timestamp (last visit), current timestamp (this visit), and session number (increments for each subsequent session).\n\n\n * Cookie\nhubspotutk\n * Duration\n6 months\n * Description\nHubSpot sets this cookie to keep track of the visitors to the website. This cookie is passed to HubSpot on form submission and used when deduplicating contacts.\n\n\n * Cookie\n_ga\n * Duration\n1 year 1 month 4 days\n * Description\nGoogle Analytics sets this cookie to calculate visitor, session and campaign data and track site usage for the site's analytics report. The cookie stores information anonymously and assigns a randomly generated number to recognise unique visitors.\n\n\n * Cookie\n_ga_*\n * Duration\n1 year 1 month 4 days\n * Description\nGoogle Analytics sets this cookie to store and count page views.\n\n\n * Cookie\n__Host-psifi.analyticsTrace\n * Duration\n6 hours\n * Description\nDescription is currently not available.\n\n\n * Cookie\n__Host-psifi.analyticsTraceV2\n * Duration\n6 hours\n * Description\nDescription is currently not available.\n\n\n * Cookie\n_gh_sess\n * Duration\nsession\n * Description\nGitHub sets this cookie for temporary application and framework state between pages like what step the user is on in a multiple step form.\n\n\n * Cookie\nYSC\n * Duration\nsession\n * Description\nYSC cookie is set by Youtube and is used to track the views of embedded videos on Youtube pages.\n\n\n * Cookie\najs_anonymous_id\n * Duration\n1 year\n * Description\nThis cookie is set by Segment to count the number of people who visit a certain site by tracking if they have visited before.\n\n\n * Cookie\nvuid\n * Duration\n1 year 1 month 4 days\n * Description\nVimeo installs this cookie to collect tracking information by setting a unique ID to embed videos on the website. \n\n\nPerformance\nPerformance cookies are used to understand and analyse the key performance indexes of the website which helps in delivering a better user experience for the visitors.\n * Cookie\nAWSALB\n * Duration\n7 days\n * Description\nAWSALB is an application load balancer cookie set by Amazon Web Services to map the session to the target.\n\n\n * Cookie\nacq\n * Duration\npast\n * Description\nDescription is currently not available.\n\n\n * Cookie\nacq.sig\n * Duration\npast\n * Description\nDescription is currently not available.\n\n\n * Cookie\nptc\n * Duration\n2 years\n * Description\nNo description available.\n\n\nAdvertisement\nAdvertisement cookies are used to provide visitors with customised advertisements based on the pages you visited previously and to analyse the effectiveness of the ad campaigns.\n * Cookie\nmuc_ads\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to collect user behaviour and interaction data to optimize the website.\n\n\n * Cookie\nguest_id_marketing\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to identify and track the website visitor.\n\n\n * Cookie\nguest_id_ads\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to identify and track the website visitor.\n\n\n * Cookie\npersonalization_id\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to integrate and share features for social media and also store information about how the user uses the website, for tracking and targeting.\n\n\n * Cookie\nguest_id\n * Duration\n1 year 1 month 4 days\n * Description\nTwitter sets this cookie to identify and track the website visitor. It registers if a user is signed in to the Twitter platform and collects information about ad preferences.\n\n\n * Cookie\nbcookie\n * Duration\n1 year\n * Description\nLinkedIn sets this cookie from LinkedIn share buttons and ad tags to recognize browser IDs.\n\n\n * Cookie\n__Secure-ROLLOUT_TOKEN\n * Duration\n6 months\n * Description\nYouTube sets this cookie to manage feature rollout and experimentation. It helps Google control which new features or interface changes are shown to users as part of testing and staged rollouts, ensuring consistent experience for a given user during an experiment.\n\n\n * Cookie\nyt.innertube::nextId\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen.\n\n\n * Cookie\nyt.innertube::requests\n * Duration\nNever Expires\n * Description\nYouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen.\n\n\n * Cookie\nsession_tracker\n * Duration\nsession\n * Description\nThis cookie is set by the Reddit. This cookie is used to identify trusted web traffic. It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Data Science](https://towardsdatascience.com/category/data-science/)\n# Avoid Overfitting in Neural Networks: a Deep Dive\nLearn how to implement regularization techniques to boost performances and prevent Neural Network overfitting.\n[Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\nNovember 30, 20239 min read\n### Learn how to implement regularization techniques to boost performances and prevent Neural Network overfitting\n![Image source: unsplash.com.](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1U61rOQHR1OkVhPXMjJgwLg-scaled.jpeg)\nImage source: [unsplash.com](https://unsplash.com/photos/multicolored-illustration-gpiKdZmDQig).\nWhen training a deep neural network, it's often troublesome to achieve the same performances on **both the training and validation sets**. A considerably higher error on the validation set is a **clear flag for overfitting** : the network has become too specialized in the training data. In this article, I provide a comprehensive guide on how to bypass this issue.\nLearn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist), [Computer Science](https://roadmap.sh/computer-science) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n## Overfitting Neural Networks\nWhen dealing with any machine learning application, it's important to have a clear understanding of the **bias and variance of the model**. In traditional machine learning algorithms, we talk about the [**bias vs. variance tradeoff**](https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff#:~:text=In%20statistics%20and%20machine%20learning,bias%20in%20the%20estimated%20parameters.), which consists of the struggle of minimizing both the **variance** and the **bias** of a model.\nIn order to reduce the bias of a model (i.e. its error from erroneous assumptions), we need a **more complex model**. On the contrary, reducing the model's variance (the sensitivity of the model in capturing the variations of the training data), implies a **more simple model**. It is straightforward that the bias vs. variance tradeoff, in traditional machine learning, derives from the conflict of necessitating both a **more complex and a simpler model at the same time**.\nIn the **Deep Learning era,** we have tools to reduce just the model's variance without hurting the model's bias or, on the contrary, to reduce the bias without increasing the variance.\nBefore exploring the different techniques used to prevent the overfitting of a neural network, it's important to clarify what high variance or high bias means.\nConsider a common neural network task such as image recognition, and think over a neural network that recognizes the presence of pandas in a picture. We can confidently assess that a human can carry out this task with a near 0% error. As a consequence, this is a reasonable benchmark for the accuracy of the image recognition network. After training the neural network on the training set and evaluating its performances on both the training and validation sets, we may come up with these different results:\n 1. Train Error = 20% and Validation Error = 22%\n 2. Train Error = 1% and Validation Error = 15%\n 3. Train Error = 0.5% and Validation Error = 1%\n 4. Train Error = 20% and Validation Error = 30%\n\n\nThe first example is a typical instance of **high bias** : the error is large on **both the train and validation sets**. Conversely, the second example suffers from **high variance** , having a much lower accuracy when dealing with data **the model didn't learn from**. The third result represents **low variance and bias** , the model can be considered valid. Finally, the fourth example shows a case of **both high bias and variance** : not only the training error is large when compared with the benchmark, but the validation error is also higher.\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1AhFqOunFC5XjVz3aKrAwAA.png)\nImage by the author.\nFrom now on, I will present several techniques of regularization, used to reduce the model's overfitting to the training data. They are beneficial for cases 2. and 4. of the previous example.\n## L1 and L2 Regularization\nSimilar to classical regression algorithms (linear, logistic, polynomial, etc.), [**L1 and L2 regularizations**](https://towardsdatascience.com/l1-and-l2-regularization-methods-ce25e7fc831c) are also employed to prevent overfitting in high-variance neural networks. In order to keep [this article](https://neptune.ai/blog/fighting-overfitting-with-l1-or-l2-regularization) short and on-point, I won't recall how L1 and L2 regularizations work on regression algorithms, but you can check this article for additional information.\nThe idea behind the L1 and L2 regularization techniques is to **constrain the model's weights** to be smaller or to **shrink some of them** to 0.\nConsider the cost function J of a classical deep neural network:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1-N86OtfsYownsXoe8yl-ww.png)\nThe cost function J is, of course, a function of the weights and biases of each layer 1, ..., L. m is the number of training examples and ℒ is the loss function.\n### L1 Regularization\nIn L1 Regularization we add the following term to the cost function J:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1ugLBtbX1DKIFWy1YZ22qmg.png)\nwhere the matrix norm is the sum of the absolute value of the weights for each layer 1, ..., L of the network:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1_4QKzvI_rs17YiYwcnQBlQ.png)\nλ is the **regularization term**. It's a hyperparameter that must be **carefully tuned**. λ directly controls the impact of the regularization: as λ increases, the effects on the weights shrinking are more severe.\nThe complete cost function under L1 Regularization becomes:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1UNHir4t0uAw-FuLQWsd6GA.png)\nFor λ=0, the effects of L1 Regularization are null. Instead, choosing a value of λ which is too big, will over-simplify the model, probably resulting in an underfitting network.\nL1 Regularization can be considered as a sort of neuron selection process because it would bring to zero the weights of some hidden neurons.\n### L2 Regularization\nIn L2 Regularization, the term we add to the cost function is the following:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1i9WoOD-by_9iwRQEDHxl9g.png)\nIn this case, the regularization term is the **squared norm of the weights** of each network's layer. This matrix norm is called [Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm) and, explicitly, it's computed as follows:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1pAA2Cter2B3-qfkFDXshug.png)\nPlease note that the weight matrix relative to layer l has n^{[l]} rows and n^{[l-1]} columns.\nFinally, the complete cost function under L2 Regularization becomes:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1oxp-gleLyXbOFbpNmqf5zQ.png)\nAgain, λ is the **regularization term** and for λ=0 the effects of L2 Regularization are null.\nL2 Regularization brings towards zero the values of the weights, resulting in a more simple model.\n### How do L1 and L2 Regularization reduce overfitting?\nL1 and L2 Regularization techniques have positive effects on overfitting to the training data for two reasons:\n * The weights of some hidden units become closer (or equal) to 0. As a consequence, their effect is weakened and the resulting network is simpler because it's closer to a **smaller network**. As stated in the introduction, a simpler network is less prone to overfitting.\n * For smaller weights, also the input z of the activation function of a hidden neuron becomes smaller. For values close to 0, many activation functions behave **linearly**.\n\n\nThe second reason is not trivial and deserves an expansion. Consider a hyperbolic tangent (tanh) activation function, whose graph is the following:\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/187wjw3ZUODAe3MjZgKsyBw.png)\nImage by the author.\nFrom the function plot we can see that if the input value x is small, the function tanh(x) behaves **almost linearly**. When tanh is used as the activation function of a neural network's hidden layers, the input value is:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/16swg9QB3Vzou2MrhtF8qtw.png)\nwhich for small weights w is also **close to zero**.\nIf each layer of the neural network is linear, we can prove that the whole network behaves linearly. Thus, constraining some of the hidden units to mimic linear functions, leads to a simpler network and, as a consequence, helps to prevent overfitting.\nA simpler model often is [not capable to capture the noise](https://towardsdatascience.com/regularization-in-deep-learning-l1-l2-and-dropout-377e75acc036) in the training data and therefore, **overfitting is less frequent**.\n## Dropout\nThe idea of [**dropout regularization**](https://www.analyticsvidhya.com/blog/2022/08/dropout-regularization-in-deep-learning/#:~:text=In%20machine%20learning%2C%20%E2%80%9Cdropout%E2%80%9D,are%20codependent%20with%20one%20another.) is to **randomly remove some nodes** in the network. Before the training process, we set a probability (suppose p = 50%) for each node of the network. During the training phase, each node has a p **probability of being turned off**. The dropout process is random, and it is performed separately for each training example. As a consequence, each training example might be trained on a different network.\nAs for L2 Regularization, the result of dropout regularization is a simpler network, and a simpler network leads to a less complex model.\n![The effect of dropout on a simple network. Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/1qvbJTLsbhD7t4_SZ7ToJeA.png)\nThe effect of dropout on a simple network. Image by the author.\n### Dropout in practice\nIn this brief section, I show how to implement **Dropout regularization in practice**. I will go through a few simple lines of code (python). If you are only interested in the general theory of regularization, you can easily skip this section.\nSuppose we have stored the activation values of the network's layer 4 in the [NumPy](https://numpy.org/) array `a4`. First, we create the auxiliary vector `d4`:\npython\n\n```\n# Set the keeping probability\nkeep_prob = 0.7\n```\n\npython\n\n```\n# Create auxiliary vector for layer 4\nd4 = np.random.rand(a4.shape[0], a3.shape[1]) < keep_prob\n```\n\nThe vector `d4` has the same dimensions as `a4` and contains the values `True` or `False` based on the probability `keep_prob`. If we set a keeping probability of 70%, that is the probability that a given hidden unit is kept, and therefore, the probability of having `True` value on a given element of `d4`.\nWe apply the auxiliary vector `d4` to the activations `a4`:\npython\n\n```\n# Apply the auxiliary vector d4 to the activation a4\na4 = np.multiply(a4,d4)\n```\n\nFinally, we need to scale the modified vector `a4` by the `keep_prob` value:\npython\n\n```\n# Scale the modified vector a4\na4 /= keep_prob\n```\n\nThis last operation is needed to compensate for the reduction of units in the layer. Carrying out this operation during the training process allows us not to apply dropout during the test phase.\n### How does dropout reduce overfitting?\nDropout has the effect of temporarily **transforming the network into a smaller one** , and we know that smaller networks are **less complex and less prone to overfitting**.\nConsider the network illustrated above, and focus on the first unit of the second layer. Because some of its inputs may be temporarily shut down due to dropout, the unit **can't always rely on them** during the training phase. As a consequence, the hidden unit is encouraged to spread its weights across its inputs. Spreading the weights has the effect of decreasing the squared norm of the weight matrix, resulting in a **sort of L2 regularization**.\nSetting the keeping probability is a fundamental step for an effective dropout regularization. Typically, the keeping probability is set separately for each layer of the neural network. For layers with a large weight matrix, we usually set a smaller keeping probability because, at each step, we want to conserve proportionally fewer weights with respect to smaller layers.\n## Other Regularization Techniques\nIn addition to L1/L2 regularization and dropout, there exist **other regularization techniques**. Two of them are **data augmentation** and **early stopping**.\nFrom the theory, we know that training a network on more data has positive effects on reducing high variance. As getting more data is often a demanding task, data augmentation is a technique that, for some applications, allows machine learning practitioners to get more data almost for free. In computer vision, data augmentation provides a **larger training set** by flipping, zooming, and translating the original images. In the case of digit recognition, we can also impose distortion on the images.\n**Early stopping** , as the name suggests, involves **stopping the training phase** before the initially defined number of iterations. If we plot the cost function on both the training set and the validation set as a function of the iterations, we can experience that, for an overfitting model, the training error always keeps decreasing but the validation error might start to increase after a certain number of iterations. When the validation error stops decreasing, that is exactly the time to stop the training process. By stopping the training process earlier, we force the model to be simpler, thus reducing overfitting.\n## **Conclusion**\nIn conclusion, the L1 and L2 regularization techniques are indispensable tools in addressing overfitting within neural networks.\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/11/11Wcq_S7IdO6uxMaHGVJaNg.png)\nImage by the author.\nL1 regularization, with its ability to induce sparsity by **penalizing irrelevant features** , proves effective in **simplifying models**. On the other hand, L2 regularization, by penalizing the squared magnitude of weights, **promotes smoother models** , reducing the risk of extreme values.\nDropout, a dynamic technique involving randomly deactivating neurons during the training phase, enhances model generalization. It prevents over-reliance on specific neurons, promoting a more robust network.\nHowever, these techniques come with tradeoffs. While regularization methods effectively mitigate overfitting, they may inadvertently restrict the model's ability to capture intricate patterns in the data. The real challenge is choosing the right balance between regularization strength and model complexity.\nFor further insights, I will fill the Reference section with amazing resources. I highly suggest checking them out to refine your understanding of the subject.\n* * *\nIf you liked this story, consider following me to be notified of my upcoming projects and articles!\nHere are some of my past projects:\n> [**Advanced Dimensionality Reduction Models Made Simple**](https://towardsdatascience.com/advanced-dimensionality-reduction-models-made-simple-639fca351528)\n> [**Use Deep Learning to Generate Fantasy Names: Build a Language Model from Scratch**](https://towardsdatascience.com/use-deep-learning-to-generate-fantasy-character-names-build-a-language-model-from-scratch-792b13629efa)\n> [**Outlier Detection with Scikit-Learn and Matplotlib: a Practical Guide**](https://towardsdatascience.com/outlier-detection-with-scikit-learn-and-matplotlib-a-practical-guide-382d1411b8ec)\n## References\n * [Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville](https://www.deeplearningbook.org/)\n * [Dropout: A Simple Way to Prevent Neural Networks from Overfitting by Nitish Srivastava et al. (2014)](https://jmlr.org/papers/v15/srivastava14a.html)\n * [Regularization Techniques in Deep Learning: A Survey and Practical Guide by Navid Pustokhina, et al.](https://arxiv.org/abs/2201.03299)\n * [Understanding the Disharmony between Dropout and Batch Normalization by Variance Shift by Shibani Santurkar, et al. (2018)](https://www.researchgate.net/publication/327434121_Understanding_Regularization_in_Batch_Normalization)\n * [Neural Networks and Deep Learning: A Textbook by Charu Aggarwal](https://link.springer.com/book/10.1007/978-3-319-94463-0)\n\n\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. Create a free account today to access this article and thousands more.\nRegister for freeSign in to your account\n* * *\n![](https://assets.insightmediagroup.io/media/1787657095428_xaezyc.jpeg)\nWritten By\n## [Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\n[See all from Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\n[Data Science](https://towardsdatascience.com/tag/data-science/)[Machine Learning](https://towardsdatascience.com/tag/machine-learning/)[Neural Networks](https://towardsdatascience.com/tag/neural-networks/)[Overfitting](https://towardsdatascience.com/tag/overfitting/)[Programming](https://towardsdatascience.com/tag/programming/)\nShare This Article\n * [](https://www.facebook.com/sharer/sharer.php?u=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F&title=Avoid%20Overfitting%20in%20Neural%20Networks%3A%20a%20Deep%20Dive)\n * [](https://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F&title=Avoid%20Overfitting%20in%20Neural%20Networks%3A%20a%20Deep%20Dive)\n * [](https://x.com/share?url=https%3A%2F%2Ftowardsdatascience.com%2Favoid-overfitting-in-neural-networks-a-deep-dive-b4615a2d9507%2F&text=Avoid%20Overfitting%20in%20Neural%20Networks%3A%20a%20Deep%20Dive)\n\n\nTowards Data Science is a community publication. Submit your insights to reach our global audience and earn through the TDS Author Payment Program.\n[Write for TDS](https://towardsdatascience.com/submissions/)\n## Related Articles\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2021/03/1VF_oqrRmgVdtAizny5T3-A.gif)](https://towardsdatascience.com/understand-support-vector-machines-6cc9e4a15e7e/)\n## [Understand Support Vector Machines](https://towardsdatascience.com/understand-support-vector-machines-6cc9e4a15e7e/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\npart 1 of a 5-sequence, brief articles that provide a comprehensive introduction; no prior knowledge assumed\n[Ahmar Shah, PhD (Oxford)](https://towardsdatascience.com/author/ahmarshah/)\nMarch 7, 20216 min read\n * [![](https://towardsdatascience.com/images/fallback-image.jpg)](https://towardsdatascience.com/latest-picks-an-intuitive-look-at-the-basics-of-information-theory-2aa21286e846/)\n## [Latest picks: An Intuitive Look at the Basics of Information Theory](https://towardsdatascience.com/latest-picks-an-intuitive-look-at-the-basics-of-information-theory-2aa21286e846/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nYour daily dose of data science\n[TDS Editors](https://towardsdatascience.com/author/towardsdatascience/)\nJanuary 19, 20211 min read\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2026/06/vram-aware-packing.jpg)](https://towardsdatascience.com/i-built-a-c-backend-so-my-gpu-would-stop-eating-air/)\n## [I Built a C++ Backend So My GPU Would Stop Eating Air](https://towardsdatascience.com/i-built-a-c-backend-so-my-gpu-would-stop-eating-air/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nHow to eliminate padding overhead and accelerate LLM inference at the hardware level.\n[Anubhab Banerjee](https://towardsdatascience.com/author/anubhab.banerjee/)\nJune 3, 202627 min read\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/09/1DsuvTgwSYSi4WOqPElqk9g.jpeg)](https://towardsdatascience.com/best-places-for-new-businesses-in-florianopolis-brazil-north-shore-a-foursquare-data-analysis-1a6034024011/)\n## [Best places for new businesses in Florianopolis, Brazil (North Shore): a Foursquare data analysis](https://towardsdatascience.com/best-places-for-new-businesses-in-florianopolis-brazil-north-shore-a-foursquare-data-analysis-1a6034024011/)\n[Data Science](https://towardsdatascience.com/category/data-science/)\nWhich opportunities could the data show?\n[Shaiala Marques](https://towardsdatascience.com/author/shaiala/)\nSeptember 14, 20209 min read\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/08/138Um1nDjooXaqvaxVeHpow.jpeg)](https://towardsdatascience.com/graph-machine-learning-icml-2023-9b5e4306a1cc/)\n## [Graph Machine Learning @ ICML 2023](https://towardsdatascience.com/graph-machine-learning-icml-2023-9b5e4306a1cc/)\n[Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/)\nRecent advancements and hot trends, August 2023 edition\n[Michael Galkin](https://towardsdatascience.com/author/mgalkin/)\nAugust 6, 202315 min read\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0TP5jW-8mri5dHs03-scaled.jpg)](https://towardsdatascience.com/classification-with-rosenblatts-perceptron-e7f49e3af562/)\n## [Classification With Rosenblatt's Perceptron](https://towardsdatascience.com/classification-with-rosenblatts-perceptron-e7f49e3af562/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nThe \"hello-world\" of machine learning\n[Pan Cretan](https://towardsdatascience.com/author/cretanpan/)\nSeptember 8, 20237 min read\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/09/1SgscrlOX-P8eljSZukn9dQ.png)](https://towardsdatascience.com/sigmoid-and-softmax-functions-in-5-minutes-f516c80ea1f9/)\n## [Sigmoid and SoftMax Functions in 5 minutes](https://towardsdatascience.com/sigmoid-and-softmax-functions-in-5-minutes-f516c80ea1f9/)\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\nThe math behind two of the most used activation functions in Machine Learning\n[Gabriel Furnieles](https://towardsdatascience.com/author/gabrielfurnieles/)\nSeptember 8, 20225 min read\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/09/1w-X5igGod0iIlDrf_-4KNw.png)](https://towardsdatascience.com/3-reasons-why-sparks-lazy-evaluation-is-useful-ed06e27360c4/)\n## [3 Reasons Why Spark's Lazy Evaluation is Useful](https://towardsdatascience.com/3-reasons-why-sparks-lazy-evaluation-is-useful-ed06e27360c4/)\n[Programming](https://towardsdatascience.com/category/programming/)\nSpark's Lazy Evaluation and Why You Should Care\n[Amal Hasni](https://towardsdatascience.com/author/amal-hasni/)\nSeptember 14, 20225 min read\n * [![](https://assets.insightmediagroup.io/media/wp-content/uploads/2021/01/1xky8pWOg-4hTUDlTfxqrNQ-scaled.jpeg)](https://towardsdatascience.com/bertelsman-arvato-financial-solution-customer-segmentation-c8528d5ac77a/)\n## [Bertelsman Arvato Financial Solution Customer Segmentation](https://towardsdatascience.com/bertelsman-arvato-financial-solution-customer-segmentation-c8528d5ac77a/)\n[Data Science](https://towardsdatascience.com/category/data-science/)\nNowadays, with big data becomes reality, people now focus on how to use the data to realize commercial values. One area which is much more...\n[Annie Wang](https://towardsdatascience.com/author/annie-wangliu/)\nJanuary 28, 20218 min read\n\n\n * [YouTube](https://www.youtube.com/c/TowardsDataScience)\n * [X](https://x.com/TDataScience)\n * [LinkedIn](https://www.linkedin.com/company/towards-data-science/)\n * [Threads](https://www.threads.net/@towardsdatascience)\n * [Bluesky](https://bsky.app/profile/towardsdatascience.com)\n\n\n[](https://towardsdatascience.com/)\nYour home for data science and AI. The world's leading publication for data science, data analytics, data engineering, machine learning, and artificial intelligence professionals.\nSubscribe to Our Newsletter[Write For TDS](https://towardsdatascience.com/submissions/)•[About](https://towardsdatascience.com/about-towards-data-science-d691af11cc2f/)•[Advertise](https://contact.towardsdatascience.com/advertise-with-towards-data-science)•[Privacy Policy](https://towardsdatascience.com/privacy-policy/)•[Terms of Use](https://towardsdatascience.com/website-terms-of-use/)\n© Insight Media Group, LLC 2026•[The New Stack](https://thenewstack.io)•[roadmap.sh](https://roadmap.sh)•[Creator Network](https://insightmediagroup.io/creator-network)\n#### Recommended Articles \nClose\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607686/image?etag=1782161464448&width=500&height=500) How Relevance Models Foreshadowed Transformers for NLP ](https://towardsdatascience.com/how-relevance-models-foreshadowed-transformers-for-nlp/ \"How Relevance Models Foreshadowed Transformers for NLP\")\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607639/image?etag=1781250125848&width=500&height=500) Javascript Fatigue: HTMX Is All You Need to Build ChatGPT — Part 1 ](https://towardsdatascience.com/javascript-fatigue-you-dont-need-js-to-build-chatgpt/ \"Javascript Fatigue: HTMX Is All You Need to Build ChatGPT — Part 1\")\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/607930/image?etag=1782124566054&width=500&height=500) The Subset Sum Problem Solved in Linear Time for Dense Enough Inputs ](https://towardsdatascience.com/subset-sum-problem-solved-in-linear-time-for-dense-enough-inputs/ \"The Subset Sum Problem Solved in Linear Time for Dense Enough Inputs\")\n * [ ![](https://h030.towardsdatascience.com/rest/v2/contentStores/d7d3a4ab-7caf-4383-bbd2-fbf7fb4f1787/items/3660/image?etag=1780176246070&width=500&height=500) Does Your Company Have a Data Strategy? ](https://towardsdatascience.com/does-your-company-have-a-data-strategy-e8944dbec4ae/ \"Does Your Company Have a Data Strategy?\")\n\n\n", "body_base_path": "attachments/6398e561e759/pages/", "body_markdown_path": "attachments/6398e561e759/pages/archived-body.md", "local_html": "attachments/6398e561e759/pages/archived-body.html", "body_source": "prior_capture" }