{ "source_file": "0930", "source_platform": "Medium", "author": "Dhruv Matani", "title_listed": "Tensor Quantization: The Untold Story", "keywords": "", "domain": "机器学习", "content_type": "深度技术解析", "is_paid_flag": "否", "url": "https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/", "publish_date": "2023-09-08", "corpus_stage": "", "notes": "", "id": "3419a168a3ed", "collected_at": "2026-10-02T10:41:28", "title": "Tensor Quantization: The Untold Story | 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. 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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[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\n# Tensor Quantization: The Untold Story\nA close look at the implementation details of quantization in machine learning frameworks\n[Dhruv Matani](https://towardsdatascience.com/author/dhruvbird/)\nSeptember 8, 20238 min read\n![](../images/000.png)\nCo-authored with [Naresh Singh](https://medium.com/@brocolishbroxoli).\nLearn this step by step with the interactive [Machine Learning](https://roadmap.sh/machine-learning) roadmap.\n## Table Of Contents\n * [Introduction](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#1d38)\n * [What do the terms scale and zero-point mean for quantization?](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#038c)\n * [Types of Quantization Schemes](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#b2df)\n * [Quantization Scale and Zero Point examples](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#0dd2)\n * [Quantization and Activation Normalization](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#3046)\n * [Conclusion](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#8bf9)\n * [References](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#390b)\n\n\n* * *\n## Introduction\nThroughout the rest of this article, we will try to answer the following questions with concrete examples.\n 1. What do the terms scale and zero-point mean for quantization?\n 2. What are the different types of quantization schemes?\n 3. How to compute scale and zero-point for the different quantization schemes\n 4. Why is zero-point important for quantization?\n 5. How do normalization techniques benefit quantization\n\n\n* * *\n## What do the terms scale and zero-point mean for quantization?\n**Scale:** When quantizing a floating point range, one would typically represent a floating point range [Fmin..Fmax] in the quantized range [Qmin..Qmax]. In this case, the scale is the ratio of the floating point range and the quantized range.\n![](../images/001.png)\nWe will see an example of how to compute it later.\n**Zero-point:** The zero-point for quantization is the representation of floating point 0.0 in the quantized range. Specifically, the zero-point is a quantized value, and it represents the floating point value 0.0 for all practical purposes. We shall see how it's computed with examples later, along with why such a representation is of practical interest to us.\nNext, let's take a look at the main quantization schemes used in practice and familiarize ourselves with how they are similar and how they differ.\n* * *\n## Types of Quantization Schemes\nWhen considering the types of quantization available for use during model compression, there are 2 main types to pick from\n 1. **Symmetric quantization** : In this case, the zero-point is zero - i.e. 0.0 of the floating point range is the same as 0 in the quantized range. Typically, this is more efficient to compute at runtime but may result in lower accuracy if the floating point range is unequally distributed around the floating point 0.0.\n 2. **Affine (or asymmetric) quantization** : This is the one that has a zero-point that is non-zero in value.\n\n\nBut before we jump into the details, let's try to define what zero-point means.\n* * *\n## Quantization Scale and Zero Point examples\nLet's start with a very simple example and build it up.\n### Example-1: Symmetric uint8 quantization\nLet's say we wish to map the floating point range [0.0 .. 1000.0] to the quantized range [0 .. 255]. The range [0 .. 255] is the set of values that can fit in an unsigned 8-bit integer.\n![](../images/body-06993dcf1715872b1ec0.png)\nTo perform this transformation, we want to rescale the floating point range so that the following is true:\nFloating point 0.0 = Quantized 0\nFloating point 1000.0 = Quantized 255\nThis is called symmetric quantization because the floating point 0.0 is quantized 0.\nHence, we define a scale, which is equal to\n![](../images/body-c5a7eeb1360f1dc32c2f.png)\nWhere,\n![](../images/body-9ae7a1e146eee3bffe10.png)\nIn this case, scale = 3.9215\nTo convert from a floating point value to a quantized value, we can simply divide the floating point value by the scale. For example, the floating point value 500.0 corresponds to the quantized value\n![](../images/body-cdec962de72fddbddbab.png)\nIn this simple example, the 0.0 of the floating point range maps exactly to the 0 in the quantized range. This is called symmetric quantization. Let's see what happens when this is not the case.\n### Example-2: Affine uint8 quantization\nLet's say we wish to map the floating point range [-20.0 .. 1000.0] to the quantized range [0 .. 255].\n![](../images/body-64ce47d0366dc8bda52f.png)\nIn this case, we have a different scaling factor since our _xmin_ is different.\n![](../images/body-1440e1c75fb5c45e94b7.png)\nLet's see what the floating point number 0.0 is represented by in the quantized range if we apply the scaling factor to 0.0\n![](../images/body-1dbe9b728c739cb3b5ac.png)\nWell, this doesn't quite seem right since, according to the diagram above, we would have expected the floating point value -20.0 to map to the quantized value 0.\nThis is where the concept of zero-point comes in. **The zero-point acts as a bias for shifting the scaled floating point value and corresponds to the value in the quantized range that represents the floating point value 0.0.** In our case, the zero point is the negative of the scaled floating point representation of -20.0, which is -(-5) = 5. The zero point is always the negative of the representation of the minimum floating point value since the minimum will always be negative or zero. We'll find out more about why this is the case in the section that explains example 4.\nWhenever we quantize a value, we will always add the zero-point to this scaled value to get the actual quantized value in the valid quantization range. In case we wish to quantize the value -20.0, we compute it as the scaled value of -20.0 plus the zero-point, which is -5 + 5 = 0. Hence, quantized(-20.0, scale=4, zp=5) = 0.\n![](../images/body-1605cc4aa64e57b532bf.png)\n![](../images/body-6dbee3da7207d4b890f4.png)\n### Example-3: Affine int8 quantization\nWhat happens if our quantized range is a signed 8-bit integer instead of an unsigned 8-bit integer? Well, the range is now [-128 .. 127].\n![](../images/body-67b02a04f8d215bc3d60.png)\nIn this case, -20.0 in the float range maps to -128 in the quantized range, and 1000.0 in the float range maps to 127 in the quantized range.\nThe way we calculate zero point is that we compute it as if the quantized range is [0 .. 255] and then offset it with -128, so the zero point in the new range is\n![](../images/body-7038e0af0d2a6fb53203.png)\n![](../images/body-2641cba376139d4cc4fe.png)\nHence, the zero-point for the new range is -123.\nSo far, we've looked at examples where the floating point range includes the value 0.0. In the next set of examples, we'll take a look at what happens when the floating point range doesn't include the value 0.0\n### The importance of 0.0\nWhy is it important for the floating point value 0.0 to be represented in the floating point range?\nWhen using a padded convolution, we expect the border pixels to be padded using the value 0.0 in the most common case. Hence, it's important for 0.0 to be represented in the floating point range. Similarly, if the value X is going to be used for padding in your network, you need to make sure that the value X is represented in the floating point range and that quantization is aware of this.\n### Example-4: The untold story - skewed floating point range\nNow, let's take a look at what happens if 0.0 isn't part of the floating point range.\n![](../images/body-117cb64c56520f175faa.png)\nIn this example, we're trying to quantize the floating point range [40.0 .. 1000.0] into the quantized range [0 .. 255].\nSince we can't represent the value 0.0 in the floating point range, we need to extend the lower limit of the range to 0.0.\n![](../images/body-f20d636a41df707f5a44.png)\nWe can see that some part of the quantized range is wasted. To determine how much, let's compute the quantized value that the floating point value 40.0 maps to.\n![](../images/body-8344db619f5c4edb6056.png)\nHence, we're wasting the range [0 .. 9] in the quantized range, which is about 3.92% of the range. This could significantly affect the model's accuracy post-quantization.\nThis skewing is necessary if we wish to make sure that the value 0.0 in the floating point range can be represented in the quantized range.\nAnother reason for including the value 0.0 in the floating point range is that efficiently comparing a quantized value to check if it's 0.0 in the floating point range is very valuable. Think of operators such as ReLU, which clip all values below 0.0 in the floating point range to 0.0.\nIt is important for us to be able to **represent the zero-point using the same data type** (signed or unsigned int8) **as the quantized values**. This enables us to perform these comparisons quickly and efficiently.\nNext, let's take a look at how activation normalization helps with model quantization. We'll specifically focus on how the standardization of the activation values allows us to use the entire quantized range effectively.\n* * *\n## Quantization and Activation Normalization\nBatch/Layer Normalization changes the activation tensor to have zero mean and unit variance per channel or per layer.\nSuppose we have an input tensor with a floating point range of [2000.0 .. 4000.0]. This is what the quantized range would look like.\n![](../images/body-ba1d6393eed1e612776f.png)\nWe observe that half of the quantized range [-127 .. -1] is unused. This is problematic since we're quantizing the entire floating point range using just 7 of the available 8 bits. This will undoubtedly result in a higher quantization error and reduced model accuracy. To address this let's apply layer normalization to the activation tensor.\nAfter applying layer normalization to an activation tensor, the activation tensor will have a floating point range of [-2.0 .. 2.0]. This can be represented in the signed int8 range [-128 .. 127]. To ensure symmetry of the distribution, we restrict the quantized range to be [-127 .. 127].\n![](../images/body-6b9f343a23296eff32e9.png)\nHence, normalization avoids holes or unused parts in the quantized range.\n* * *\n## Conclusion\nWe saw what affine (asymmetric) and symmetric quantization are and how they differ. We also learned about what scale and zero-point mean and how to compute them for both these types of quantization schemes.\nNext, we saw the need to include float 0.0 in the floating point range and why and how this is done in practice. This results in a downside, namely wasted space in the quantized range.\nLastly, we saw how normalization helps quantization by bringing the activations in a fixed range and avoiding wasted space in the quantized range. In fact, the 0 mean based normalization can help convert affine quantization to symmetric quantization, and that can speed things up during inference.\nAll images in this post are created by the author(s).\n* * *\n## References\n 1. [Efficient Deep Learning Book, Chapter-2: Introduction to Compression Techniques](https://github.com/EfficientDL/book/raw/main/book/%5BEDL%5D%20Chapter%202%20-%20Compression%20Techniques.pdf)\n 2. [Hugging Face: Quantization](https://huggingface.co/docs/optimum/concept_guides/quantization)\n 3. [TensorRT: Quantization](https://docs.nvidia.com/deeplearning/tensorrt/tensorflow-quantization-toolkit/docs/docs/intro_to_quantization.html)\n 4. [Neural Network Distiller: Quantization](https://intellabs.github.io/distiller/algo_quantization.html)\n 5. [Lei Mao: Quantization](https://leimao.github.io/article/Neural-Networks-Quantization/)\n 6. [Quantizing floats](https://zeux.io/2010/12/14/quantizing-floats/)\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. 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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[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\n# Tensor Quantization: The Untold Story\nA close look at the implementation details of quantization in machine learning frameworks\n[Dhruv Matani](https://towardsdatascience.com/author/dhruvbird/)\nSeptember 8, 20238 min read\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0nKEzyyqQukfSm6Ft.png)\nCo-authored with [Naresh Singh](https://medium.com/@brocolishbroxoli).\nLearn this step by step with the interactive [Machine Learning](https://roadmap.sh/machine-learning) roadmap.\n## Table Of Contents\n * [Introduction](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#1d38)\n * [What do the terms scale and zero-point mean for quantization?](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#038c)\n * [Types of Quantization Schemes](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#b2df)\n * [Quantization Scale and Zero Point examples](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#0dd2)\n * [Quantization and Activation Normalization](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#3046)\n * [Conclusion](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#8bf9)\n * [References](https://towardsdatascience.com/tensor-quantization-the-untold-story-d798c30e7646/#390b)\n\n\n* * *\n## Introduction\nThroughout the rest of this article, we will try to answer the following questions with concrete examples.\n 1. What do the terms scale and zero-point mean for quantization?\n 2. What are the different types of quantization schemes?\n 3. How to compute scale and zero-point for the different quantization schemes\n 4. Why is zero-point important for quantization?\n 5. How do normalization techniques benefit quantization\n\n\n* * *\n## What do the terms scale and zero-point mean for quantization?\n**Scale:** When quantizing a floating point range, one would typically represent a floating point range [Fmin..Fmax] in the quantized range [Qmin..Qmax]. In this case, the scale is the ratio of the floating point range and the quantized range.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0ucxfYyT2ZUCiPz5g.png)\nWe will see an example of how to compute it later.\n**Zero-point:** The zero-point for quantization is the representation of floating point 0.0 in the quantized range. Specifically, the zero-point is a quantized value, and it represents the floating point value 0.0 for all practical purposes. We shall see how it's computed with examples later, along with why such a representation is of practical interest to us.\nNext, let's take a look at the main quantization schemes used in practice and familiarize ourselves with how they are similar and how they differ.\n* * *\n## Types of Quantization Schemes\nWhen considering the types of quantization available for use during model compression, there are 2 main types to pick from\n 1. **Symmetric quantization** : In this case, the zero-point is zero - i.e. 0.0 of the floating point range is the same as 0 in the quantized range. Typically, this is more efficient to compute at runtime but may result in lower accuracy if the floating point range is unequally distributed around the floating point 0.0.\n 2. **Affine (or asymmetric) quantization** : This is the one that has a zero-point that is non-zero in value.\n\n\nBut before we jump into the details, let's try to define what zero-point means.\n* * *\n## Quantization Scale and Zero Point examples\nLet's start with a very simple example and build it up.\n### Example-1: Symmetric uint8 quantization\nLet's say we wish to map the floating point range [0.0 .. 1000.0] to the quantized range [0 .. 255]. The range [0 .. 255] is the set of values that can fit in an unsigned 8-bit integer.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/01exMKZMh14ZrRc5p.png)\nTo perform this transformation, we want to rescale the floating point range so that the following is true:\nFloating point 0.0 = Quantized 0\nFloating point 1000.0 = Quantized 255\nThis is called symmetric quantization because the floating point 0.0 is quantized 0.\nHence, we define a scale, which is equal to\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0NH-CXHbYEug52O9P.png)\nWhere,\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0YWVRZrkS_TiADvlS.png)\nIn this case, scale = 3.9215\nTo convert from a floating point value to a quantized value, we can simply divide the floating point value by the scale. For example, the floating point value 500.0 corresponds to the quantized value\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0e4Ocq96D0_dJnC7B.png)\nIn this simple example, the 0.0 of the floating point range maps exactly to the 0 in the quantized range. This is called symmetric quantization. Let's see what happens when this is not the case.\n### Example-2: Affine uint8 quantization\nLet's say we wish to map the floating point range [-20.0 .. 1000.0] to the quantized range [0 .. 255].\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0lep5OKOJmHf33LU5.png)\nIn this case, we have a different scaling factor since our _xmin_ is different.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0T7hV0dAfFOBSu0yy.png)\nLet's see what the floating point number 0.0 is represented by in the quantized range if we apply the scaling factor to 0.0\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0aAEL5MIEDTeoiYlI.png)\nWell, this doesn't quite seem right since, according to the diagram above, we would have expected the floating point value -20.0 to map to the quantized value 0.\nThis is where the concept of zero-point comes in. **The zero-point acts as a bias for shifting the scaled floating point value and corresponds to the value in the quantized range that represents the floating point value 0.0.** In our case, the zero point is the negative of the scaled floating point representation of -20.0, which is -(-5) = 5. The zero point is always the negative of the representation of the minimum floating point value since the minimum will always be negative or zero. We'll find out more about why this is the case in the section that explains example 4.\nWhenever we quantize a value, we will always add the zero-point to this scaled value to get the actual quantized value in the valid quantization range. In case we wish to quantize the value -20.0, we compute it as the scaled value of -20.0 plus the zero-point, which is -5 + 5 = 0. Hence, quantized(-20.0, scale=4, zp=5) = 0.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0RKKmFBuKbWYoMhru.png)\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0YErZ5YAeMMa4lnYF.png)\n### Example-3: Affine int8 quantization\nWhat happens if our quantized range is a signed 8-bit integer instead of an unsigned 8-bit integer? Well, the range is now [-128 .. 127].\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0zRyGYYs0XqM6yTjC.png)\nIn this case, -20.0 in the float range maps to -128 in the quantized range, and 1000.0 in the float range maps to 127 in the quantized range.\nThe way we calculate zero point is that we compute it as if the quantized range is [0 .. 255] and then offset it with -128, so the zero point in the new range is\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/065jbaHMKmk-Y6kXQ.png)\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0BM2tNJsxxQ5sYumf.png)\nHence, the zero-point for the new range is -123.\nSo far, we've looked at examples where the floating point range includes the value 0.0. In the next set of examples, we'll take a look at what happens when the floating point range doesn't include the value 0.0\n### The importance of 0.0\nWhy is it important for the floating point value 0.0 to be represented in the floating point range?\nWhen using a padded convolution, we expect the border pixels to be padded using the value 0.0 in the most common case. Hence, it's important for 0.0 to be represented in the floating point range. Similarly, if the value X is going to be used for padding in your network, you need to make sure that the value X is represented in the floating point range and that quantization is aware of this.\n### Example-4: The untold story - skewed floating point range\nNow, let's take a look at what happens if 0.0 isn't part of the floating point range.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0Fiz_qTJYIiLfLwEA.png)\nIn this example, we're trying to quantize the floating point range [40.0 .. 1000.0] into the quantized range [0 .. 255].\nSince we can't represent the value 0.0 in the floating point range, we need to extend the lower limit of the range to 0.0.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0oDWX6xFkKWnGmEKu.png)\nWe can see that some part of the quantized range is wasted. To determine how much, let's compute the quantized value that the floating point value 40.0 maps to.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0_bdVimG64b0tJe-h.png)\nHence, we're wasting the range [0 .. 9] in the quantized range, which is about 3.92% of the range. This could significantly affect the model's accuracy post-quantization.\nThis skewing is necessary if we wish to make sure that the value 0.0 in the floating point range can be represented in the quantized range.\nAnother reason for including the value 0.0 in the floating point range is that efficiently comparing a quantized value to check if it's 0.0 in the floating point range is very valuable. Think of operators such as ReLU, which clip all values below 0.0 in the floating point range to 0.0.\nIt is important for us to be able to **represent the zero-point using the same data type** (signed or unsigned int8) **as the quantized values**. This enables us to perform these comparisons quickly and efficiently.\nNext, let's take a look at how activation normalization helps with model quantization. We'll specifically focus on how the standardization of the activation values allows us to use the entire quantized range effectively.\n* * *\n## Quantization and Activation Normalization\nBatch/Layer Normalization changes the activation tensor to have zero mean and unit variance per channel or per layer.\nSuppose we have an input tensor with a floating point range of [2000.0 .. 4000.0]. This is what the quantized range would look like.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0NEuv8GroWSu-jB26.png)\nWe observe that half of the quantized range [-127 .. -1] is unused. This is problematic since we're quantizing the entire floating point range using just 7 of the available 8 bits. This will undoubtedly result in a higher quantization error and reduced model accuracy. To address this let's apply layer normalization to the activation tensor.\nAfter applying layer normalization to an activation tensor, the activation tensor will have a floating point range of [-2.0 .. 2.0]. This can be represented in the signed int8 range [-128 .. 127]. To ensure symmetry of the distribution, we restrict the quantized range to be [-127 .. 127].\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2023/09/0EdLdtkgYPwwQ7IGK.png)\nHence, normalization avoids holes or unused parts in the quantized range.\n* * *\n## Conclusion\nWe saw what affine (asymmetric) and symmetric quantization are and how they differ. We also learned about what scale and zero-point mean and how to compute them for both these types of quantization schemes.\nNext, we saw the need to include float 0.0 in the floating point range and why and how this is done in practice. This results in a downside, namely wasted space in the quantized range.\nLastly, we saw how normalization helps quantization by bringing the activations in a fixed range and avoiding wasted space in the quantized range. In fact, the 0 mean based normalization can help convert affine quantization to symmetric quantization, and that can speed things up during inference.\nAll images in this post are created by the author(s).\n* * *\n## References\n 1. [Efficient Deep Learning Book, Chapter-2: Introduction to Compression Techniques](https://github.com/EfficientDL/book/raw/main/book/%5BEDL%5D%20Chapter%202%20-%20Compression%20Techniques.pdf)\n 2. [Hugging Face: Quantization](https://huggingface.co/docs/optimum/concept_guides/quantization)\n 3. [TensorRT: Quantization](https://docs.nvidia.com/deeplearning/tensorrt/tensorflow-quantization-toolkit/docs/docs/intro_to_quantization.html)\n 4. [Neural Network Distiller: Quantization](https://intellabs.github.io/distiller/algo_quantization.html)\n 5. [Lei Mao: Quantization](https://leimao.github.io/article/Neural-Networks-Quantization/)\n 6. [Quantizing floats](https://zeux.io/2010/12/14/quantizing-floats/)\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. 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