Understanding the receptive field of deep convolutional networks

August 25, 2022

The receptive field of a convolutional neural network is a crucial topic to remember while constructing new models or attempting to comprehend old ones. Knowing about it enables us to go further into the inner workings of the neuronal architecture we're interested in and helps us to consider potential enhancements. 

In this blog, we'll go over what the receptive field is and will touch on its various other aspects.

Precisely this blog will take you through:

  1. What is a Receptive Field?
  2. Why is the Receptive field important? 
  3. Receptive Field of Deep Convolutional Network
  4. Ways to increase receptive field
  5. Effective Receptive Field
  6. Conclusion 

What is a Receptive Field?

The receptive field, or field of vision, of a unit in a certain layer of the network, is a fundamental notion in deep CNNs. In contrast to fully connected networks, where the value of each unit is determined by the complete input to the network, a unit in convolutional networks is determined by a subset of the input. This region in the input is the unit's receptive field.

In other terms, The Receptive Field (RF) in deep learning is defined as the size of the area in the input that creates the feature. It is essentially a measure of the relationship of an output feature (of any layer) with the input area (patch). 

Why is the Receptive field important? 

Comprehension and diagnosing how deep CNNs operate requires an understanding of the idea of the receptive field. Because everything in an input picture beyond the receptive field of a unit has no effect on its value, the receptive field must be carefully controlled to ensure that it covers the whole relevant image region. 

Many tasks, particularly dense prediction tasks such as semantic picture segmentation, stereo, and optical flow estimation, require that each output pixel have a large receptive field so that no significant information is missed when generating the prediction.

Receptive Field of Deep Convolutional Network

A convolutional unit is only affected by a small section (patch) of the input. Because each unit has access to the whole input region, we never refer to the RF on fully linked layers. 

Convolutional neural networks (CNNs) have a reduced receptive field when shallow architectures are assumed.  The receptive field of CNN's expands exponentially one layer at a time. The pixels near the center of a receptive field have a substantial influence on the output of CNNs. The center pixels can transmit information to the output by many distinct channels in the forward pass, but the boundary pixels have extremely few paths to transport their values. As a result, the center pixels have a considerably bigger gradient magnitude from that output during a backward pass.

To calculate the closed-form receptive field for single-path networks below are the mathematical equations:

For two consecutive convolutional layers f2 and f1 with kernel size k, stride s, and receptive field r:

Alternatively, in a broader sense:

This equation appears to be generalizable into a very compact equation that just applies this procedure repeatedly for L layers. We may build a closed-form solution that only depends on the convolutional parameters of kernels and strides by further examining the recursive equation.

Where r0 represented the architecture's intended RF.

Ways to increase receptive field

In essence, there are several methods and tactics for increasing the RF, which may be described as follows: Increase the number of convolutional layers (make the network deeper), Increase the number of pooling layers or stride convolutions (sub-sampling), make use of dilated convolutions, and depthwise convolution.

Increase the number of convolutional layers: As each extra layer is added, the receptive field size is increased linearly by the kernel size. Furthermore, it has been empirically proven that as the theoretical receptive field increases, the effective (actual) receptive field decreases. RF stands for radio frequency, whereas ERF stands for effective radio frequency.

Subsampling: Subsampling methods such as pooling, on the other hand, double the receptive field size. These approaches are combined in modern designs such as ResNet.

Dilated Convolutions: The RF is increased exponentially by successively placing dilated convolutions. In a convolutional kernel, dilations create "holes". The "holes" effectively define a space between the kernel values. So, while the amount of weights in the kernel remains constant, the weights are no longer applied to samples that are physically close. Dilating a kernel by a factor of r introduces r striding.

Depth-wise convolutions: This tactic enhances the receptive field with a tiny computing footprint, making it a compact technique to expand the receptive field with fewer parameters. The channel-wise spatial convolution is depth wise convolution. It is important to note, however, that depth-wise convolutions do not immediately enhance the receptive field. 

However, because we utilize fewer parameters and do more compact computations, we can add additional layers. As a result, we may have a larger receptive field with nearly the same number of parameters.

Effective Receptive Field

Not all pixels in a receptive field contribute equally to the response of an output unit. Obviously, not all pixels inside the receptive field have the same effect on the output feature. Intuitively, pixels in the center of a receptive field appear to have a much bigger influence on output because they have more "paths" to contribute to the output. 

As a result, the effective receptive field (ERF) of the feature may be defined as the relative relevance of each input pixel. In other words, the effective receptive field of a central output unit is defined by ERF as the region containing any input pixel having a non-negligible impact on that unit.

The contribution of center pixels in the forward and backward pass is intuitively recognized as: "In the forward pass, core pixels may transmit information to the output through many distinct channels, whereas pixels in the receptive field's outside region have extremely few paths to disseminate their influence." Gradients from an output unit are transmitted throughout all routes in the backward pass, so the center pixels have a significantly bigger magnitude for the gradient from that output.

Conclusion

Till now we learned about the receptive field of a convolutional neural network and why knowing its size and various other aspects is important. Finally, understanding RF in convolutional neural networks is an open research issue that will give many insights into why deep convolutional networks operate so well.

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Cloud platforms offer fast access to high performance compute and deep learning algorithms, which makes it simpler to start using machine learning models and get early insights into your data. 

Cloud GPUs are better for machine learning because they have lower latency, which is important because the time it takes a neural network to learn from data affects its accuracy. Furthermore, cloud GPUs allow users to take advantage of large-scale training datasets without having to build and maintain their own infrastructure.

On Premises GPUs are better for machine learning if you need high performance or require access to cutting-edge technologies not available in the public cloud. For example, on-premises hardware can be used for deep learning applications that require high memory bandwidth and low latency.

Cloud GPUs: Cloud GPUs are remote data centers where you can rent unused GPU resources. This allows you to run your models on a massive scale, without having to install and manage a local machine learning cluster.

Lower TCO: Cloud GPUs require no upfront investment, making them ideal for companies that are looking to reduce their overall capital expenses. Furthermore, the cost of maintenance and upgrades is also low since it takes place in the cloud rather than on-premises.

Scalability & Flexibility: With cloud-based GPU resources, businesses can scale up or down as needed without any penalty. This ensures that they have the resources they need when demand spikes but also saves them money when there is little or no demand for those resources at all times.

Enhanced Capacity Planning Capabilities: Cloud GPU platforms allow businesses to better plan for future demands by providing estimates of how much processing power will be required in the next 12 months and beyond based on past data points such as workloads run and successes achieved with similar models/algorithms etc... 

Security & Compliance : Since cloud GPUs reside in a remote datacenter separate from your business' core systems, you are ensured peace of mind when it comes to security and compliance matters (eigenvector scanning / firewalls / SELinux etc...) 

Reduced Total Cost Of Ownership (TCO) over time due to pay-as-you-go pricing model which allows you only spend what you actually use vs traditional software licensing models where significant upfront investments are made.

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Impact of the Strong Dollar: Cloud Costs Increasing, Be Indian Buy Indian

Indian SMEs and startups are feeling the effects of the high dollar. These businesses use hyperscalers(MNC Cloud) who cannot modify their rates to account for the changing exchange rate. For certain companies, even a little shift in the currency rate may have a significant effect on their bottom line. Did you know, when the INR-USD exchange rate moved from 60 to 70 in December 2015, it had an impact of around 20% on Digital Innovation?

As the rupee is inching closer to 82 per dollar, the strong dollar has directly impacted the costs of cloud services for Indian businesses. The high cost of storage and computing power, along with bandwidth charges from overseas vendors, has led to a huge increase in the effective rate of these services. This is especially true for startups and SMEs that rely on cloud computing to store and process user data. With the strong dollar continuing to impact the cost of cloud services, it is essential for Indian companies to evaluate their options and adopt local alternatives wherever possible. This blog post will discuss how the strong dollar impacts cloud costs, as well as potential Indian alternatives you can explore in response to this global economic trend. 

What is a Strong Dollar?

A strong US dollar($) is a term used to describe a situation where a US’s currency has appreciated in value compared to other major currencies. This can be due to a variety of factors, including interest rate changes, a country’s current account deficit, and investor sentiment. When a currency appreciates, it means that it is worth more. A strong dollar makes imports more expensive, while making exports cheaper. Strong dollars have been a growing trend in the past couple of years. As the US Federal Reserve continues to hike interest rates, the dollar strengthens further. The rising value of the dollar means that the cost of cloud services, especially from hyperscalers based in the US, will rise as well. 

Increase in Cloud Costs Due to Strong Dollar

Cloud services are essential for modern businesses, as they provide easy access to software, storage, and computing resources. Cloud services are delivered over the internet and are typically charged on a per-use basis. This makes them incredibly convenient for businesses, as they can pay for only the resources they actually use. Cloud computing allows businesses to scale their resources up or down, depending on their current business needs. This makes it suitable for startups, where demand is uncertain, or large enterprises with global operations. Cloud computing is also inherently scalable and allows businesses to quickly react to changing business needs. Cloud computing is a very competitive industry and providers offer attractive prices to attract customers. However, these prices have been impacted by the strong dollar. The dollar has strengthened by 15-20% against the Indian rupee in the last few years. As a result, the costs of services such as storage and bandwidth have increased for Indian companies. Vendors charge their Indian customers in Indian rupees, taking into account the exchange rate. This has resulted in a significant rise in the costs of these services for Indian companies.

Why are Cloud Services Becoming More Expensive?

Cloud services are priced in US dollars. When the dollar is strong, the effective price of services will be higher in Indian rupees, as the cost is not re-adjusted. There are a couple of reasons for this price discrepancy. First, Indian customers will have to pay the same prices as American customers, despite a weaker Indian rupee. Second, vendors have to ensure that they make a profit.

Possible Indian Alternatives to Cloud Services

If you're looking for a cost-effective substitute for services provided by the U.S.-based suppliers, consider E2E Cloud, an Indian cloud service provider. When it comes to cloud services, E2E Cloud provides everything that startups and SMEs could possibly need.

The table below lists some of these services and compares their cost against their US equivalents. 

According to the data in the table above, Indian E2E Cloud Services are much cheaper than their American equivalents. The difference in price between some of these options is substantial. When compared to the prices charged by suppliers in the United States, E2E Cloud's bandwidth costs are surprisingly low. Although not all E2E Cloud services will be noticeably less expensive. Using Indian services, however, has an additional, crucial perk: data sovereignty.

Conclusion

The price of cloud services will rise as the US Dollar appreciates. Indian businesses will need to find ways to counteract the strong dollar's impact on their bottom lines. To do this, one must use E2E Cloud. The availability of E2E Cloud services in INR currency is a bonus on top of the already substantial cost savings. An effective protection against the negative effects of a strong dollar.

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Actions CEOs can take to get the value in Cloud Computing

It is not a new thing to say that a major transition is on the way. The transition in which businesses will rely heavily on cloud infrastructure rather than having their own physical IT structure. All of this is due to the cost savings and increased productivity that cloud technology brings to these businesses. Each technological advancement comes with a certain level of risk. Which must be handled carefully in order to ensure the long-term viability of the technology and the benefits it provides.

And CEOs are the primary motivators and decision-makers in any major shift or technological migration in the organization. In the twenty-first century, which is a data-driven century, it is up to the company's leader to decide what and how his/her organization will perform, overcome the risk and succeed in the coming days.

In this blog, we are going to address a few of the actions that CEOs can take to get value in cloud Computing.

  1. A Coordinated Effort

As the saying goes, the more you avoid the risk, the closer it gets. So, if CEOs and their management teams have yet to take an active part or give the necessary attention that their migration journey to the cloud requires, now is the best time to start top-team support for the cloud enablement required to expedite digital strategy, digitalization of the organization, 

The CEO's position is critical because no one else can mediate between the many stakeholders involved, including the CIO, CTO, CFO, chief human-resources officer (CHRO), chief information security officer (CISO), and business-unit leaders.

The move to cloud computing is a collective-action challenge, requiring a coordinated effort throughout an organization's leadership staff. In other words, it's a question of orchestration, and only CEOs can wield the baton. To accelerate the transition to the cloud, CEOs should ask their CIO and CTO what assistance they require to guide the business on the path.

     2. Enhancing business interactions 

To achieve the speed and agility that cloud platforms offer, regular engagement is required between IT managers and their counterparts in business units and functions, particularly those who control products and competence areas. CEOs must encourage company executives to choose qualified decision-makers to serve as product owners for each business capability.

  1. Be Agile

If your organization wants to benefit from the cloud, your IT department, if it isn't already, must become more agile. This entails more than simply transitioning development teams to agile product models. Agile IT also entails bringing agility to your IT infrastructure and operations by transitioning infrastructure and security teams from reactive, "ticket-driven" operations to proactive models in which scrum teams create application programme interfaces (APIs) that service businesses and developers can consume.

  1. Recruiting new employees 

CIOs and CTOs are currently in the lead due to their outstanding efforts in the aftermath of the epidemic. The CEOs must ensure that these executives maintain their momentum while they conduct the cloud transformation. 

Also, Cloud technology necessitates the hire of a highly skilled team of engineers, who are few in number but extremely expensive. As a result, it is envisaged that the CHRO's normal hiring procedures will need to be adjusted in order to attract the proper expertise. Company CEOs may facilitate this by appropriate involvement since this will be critical in deciding the success of the cloud transition.

  1. Model of Business Sustainability 

Funding is a critical component of shifting to the cloud. You will be creating various changes in your sector, from changing the way you now do business to utilizing new infrastructure. As a result, you'll have to spend on infrastructure, tools, and technologies. As CEO, you must develop a business strategy that ensures that every investment provides a satisfactory return on investment for your company. Then, evaluate your investments in order to optimise business development and value.

  1. Taking risks into consideration 

Risk is inherent in all aspects of corporate technology. Companies must be aware of the risks associated with cloud adoption in order to reduce security, resilience, and compliance problems. This includes, among other things, engaging in comprehensive talks about the appropriate procedures for matching risk appetite with technological environment decisions. Getting the business to take the correct risk tone will necessitate special attention from the CEO.

It's easy to allow concerns about security, resilience, and compliance to stall a cloud operation. Instead of allowing risks to derail progress, CEOs should insist on a realistic risk appetite that represents the company plan, while situating cloud computing risks within the context of current on-premises computing risks and demanding choices for risk mitigation in the cloud.

Conclusion

In conclusion, the benefits of cloud computing may be obtained through a high-level approach. A smooth collaboration between the CEO, CIO, and CTO may transform a digital transformation journey into a profitable avenue for the company.

CEOs must consider long-term cloud computing strategy and ensure that the organization is provided with the funding and resources for cloud adoption. The right communication is critical in cloud migration: employees should get these communications from C-suite executives in order to build confidence and guarantee adherence to governance requirements. Simply installing the cloud will not provide value for a company. Higher-level executives (particularly the CEO) must take the lead in the digital transformation path.

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