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Neural Network Architecture Construction

This article is going to discuss neural network construction from a different perspective than is usual in conventional approaches. This approach, which will be referred to as Neural Architecture, is intended to explore construction of neural networks using neurons as explicit building blocks rather than anonymous elements trained en mass. Simple Python programs will be used to demonstrate the concept for simple boolean logic functions.
The approach of this article is intentionally named Neural Architecture because it is meant to parallel the way in which a traditional architect systematically constructs a fine building: by developing well-known patterns of construction elements, which may be re-used to create ever more sophisticated structures. The conventional approach to neural network development is to define a network as consisting of a few layers in a multilayer-perceptron type of topology with an input layer, output layer, and one or two hidden layers. Then a training algorithm such as backpropagation is applied to develop the interconnection weights. Sometimes a more sophisticated approach is taken such as using a cascade or recurrent topology but for all intents and purposes, the end result is a standard topology of a few highly-connected layers. This approach was a major breakthrough in the field because it led some people to start thinking outside the box of symbolic reasoning that dominated Artificial Intelligence at the time. It has also been successfully used in a variety of pattern recognition and control applications that are not effectively handled by other AI paradigms.
However, these applications would not generally be considered to represent higher levels of intelligence or cognitive processing. For example, suppose a neural network is developed that can successfully recognize human faces under a variety of conditions. This is a highly useful application and well within the realm of conventional neural networks. However, that is where the capability of the network leaves off–at recognizing the facial image. Aside from generalizing facial features, it can offer nothing more in terms of reasoning about those facial features. Further, it is asserted that the standard approach to neural network development is not suitable for realizing these higher levels of intelligence.
One of the fundamental problems is the limited manner in which we approach the neural architecture. To illustrate this problem, we will return to the building architecture analogy. In this way, our standard approach to neural architecture can be likened to designing a building using bricks. An architect who always thinks in terms of bricks will not likely progress beyond a certain level of sophistication, because as a component, a brick only offers one purpose: to support other bricks. Instead, an architecture progressively develops more sophisticated, proven structures based on the brick (or other primitive components) which can be re-used to develop higher-level components. A house is conceived, not in terms of bricks and wood, but rather in terms of walls, doors, and rooms. A sophisticated architect might even find these components mundane and instead think in more abstract terms of “spaces”, energy and flow of human traffic.
This is the notion of “patterns”, and in fact these (architectural) patterns were exactly the inspiration for the field of software patterns. The same thinking can be applied to neural networks: a neuron by itself only serves the function of exciting other neurons. And conventional neural net learning algorithms are geared toward categorization or other mapping operations. As a proponent of neural networks, one believes that arbitrarily complex intelligence processes can be realized, and we have the human brain as pretty convincing support of that belief. However, to continue progress in this direction, it is likely that we have to develop more sophisticated abilities as neural architects and develop useful, proven neural patterns similar to the way that building architects have done over time, and in the way software architects are now doing.
Enough philosophy– we will now be taking a fresh look at how patterns can be constructed starting with simple neural elements, and specifically we will start with boolean logic elements. Architecting using boolean logic does not immediately offer an advantage over using regular logic gates, but illustrates how crisp logic or symbolic elements can arise from fuzzy neural processing elements. It will also provide a conceptual foundation for future articles.
Neural networks
Neural network: information processing paradigm inspired by biological nervous systems, such as our brain
Structure: large number of highly interconnected processing elements (neurons) working together
Like people, they learn from experience.
Neural networks are configured for a specific application, such as pattern recognition or data classification, through a learning process
In a biological system, learning involves adjustments to the synaptic connections between neurons.
The first step in the architecture process is to define the primitive building block, and if you haven’t fallen asleep at this point, you have no doubt figured out that this will be a neuron. The neuron model we will use is a version of the tried-and-true model used for software neural networks, also known as the perceptron. As illustrated in , the perceptron has multiple inputs and one output. The mathematical model of the perceptron is given by:
a = squash(?(iiwi))
is input i to the perceptron
is the weight for input i
is the activation (output)
squash(x) = {
1 if x >threshold
0 otherwise
The nature of the perceptron has been discussed many times elsewhere, including in Matthews, so we won’t dwell on it here. But basically, the perceptron calculates a weighted sum of the inputs and then subjects it to a nonlinear “squashing” function–in our case, this is a simple threshold operation. The nonlinear threshold operation is part of what makes a neural net exhibit interesting behavior. Otherwise it would amount to matrix operations.
Nature of the game
Now that we have the model for a basic neuron defined, we can now proceed to define basic logic gates by simply working out two things:
the weight values
the threshold
For our discussion we will assume that weights can be positive (excitory) or negative (inhibitory) and be in the range between -1 and 1. The threshold will also be assumed to be in the range -1 to 1.
If we cast this in terms of signals, then it equates to the requirement that both inputs have to be sufficiently high to produce an output. So, we will set our threshold to a high value of 0.8. Next we will set the weights for the two inputs at 0.5 each. If one input is one (=1) then the neuron activation (output) will be given by
= squash( 1 * 0.5 0 * 0.5)
= squash( 0.5 )
= 0 since 0.5 <0.8 {the threshold}
Therefore if either or both inputs is 0, the output is zero. If both are 1, then the weighted sum will be greater than the threshold. Listing 1 show the Python program that demonstrates the neural AND gate, and will be used as a template for other logic functions. The author prefers Python for prototyping, because it results in compact code that looks very close to pseudocode.
Program to test Inverter
We have shown how a simple set of logic gates may be implemented using neurons. In theory, this is all we would need to implement a universal digital computer of arbitrary complexity, because that is all a microprocessor does. In fact, it can be shown that all the logic functions can be implemented with one type of gate: either all NAND gates or NOR gates. However, if that was our goal, there would be no advantage to this approach over using standard logic gates. The point is that a neural approach can be used for designing intelligent structures–that is explicitly architecting (there’s that word again) structures–as well as evolving them using conventional neural network training paradigms. With neural architecture, we can start with simple logic operations and build them up into more interesting logical structures. As an example, consider our first example, the simple AND gate. This could be used to digitally perform an operation on bits, but it can also be used to perform a logical AND operation on two rules, for example: IF rule X AND rule Y THEN fire (output is active). Furthermore, by using neurons, the inputs are not at all limited to binary signals, they could be analog signals (rule X is sort of true) or even the output of an entire neural network.
The neural architecture approach can be seen to have the following key advantages or possibilities:
Can develop structures built on a universal neuron building block.
The same basic building block can be considered as a neuron (standard perceptron) or a logic gate.
The approach allows crisp structures to interface with fuzzy ones, combining the nondeterministic and evolutionary properties of neural networks along with the advantages of explicit, structured design.
Can develop recognizable higher level building blocks, a important requirement for realizing continuously more complex architectures.

Historical Influences on Architecture of Süleymaniye Mosque

How has diverse cultures and architecture throughout history influenced the architecture of the Süleymaniye Mosque?
The main issue that will be covered by the author in this thesis is the question of how different cultures and architectural styles have influenced the Süleymaniye Mosque’s design and structure. The reason for this investigation is to identify features, which have been acquired from other cultures, and also the way in which Architect Sinan developed an architectural style that was also influenced through the use of other landmark buildings around him such as the Hagia Sophia. Having said this, it is important to identify his engineering expertise, which will be discussed further in the second chapter of the thesis. It will be useful to also have a look at the influence that Architect Sinan acquired during his lifetime through other architectures and whether he has reflected these onto the making of the Süleymaniye Mosque.
The initial section of the thesis will be centered on familiarizing the reader with the history of Mosques respectively and how they have transformed over time up until the Ottoman Empire, as well as during the age of Sinan; where his style and works will be discussed. This will give the reader an understanding of how the stylistic and structural characteristics of traditional forms have developed over time and evolved into Ottoman Mosques and consequently the Suleymaniye. Which brings us onto the second chapter of the thesis.
As mentioned, the second section will largely cover the Süleymaniye Mosque’s history, function and structure. It is important to note that the Süleymaniye Mosque has been through restoration many times due to earthquakes (which are a common occurrence in Istanbul) and wars, and how this has changed certain aspects of the building. The author will also look into whether or not the mosque has adapted to the changing times and social needs which the passing of time has brought with itself. Further, as seen from the table of contents, the functionality of the mosque will also be explored. As part of a larger complex, also known as the ‘Suleymaniye complex’, the Suleymaniye is a small but important part of this complex which also bears with it different functionalities. These will be described, as it will also give more of an insight into the possible changing nature of the Süleymaniye Mosque through the acquisition of different functionalities within the complex itself. The structure is a major feature within the mosque, as it was influenced over time by many cultures and architectures such as the Hagia Sophia again, and Palladio, as well as influencing other architecture such as Michel angelo’s dome found above the roof of St Peter’s, Rome.
The third chapter will initially look into the influence of other cultures such as the Islamic influence, the influence of the Byzantine Empire as well as the Barque-Style. However, as Turkey is wholly an Islamic country, and has been an Islamic country for many years pre-dating the Ottoman era, it is clear that the main influence will be the Islamic culture. However, it is important to also look into other cultural influences especially since people from other cultures also populate Turkey. Istanbul itself has been a city which seen the presence of people from different countries and or cultures brought by war etc. The issue of diverse cultural influences will arise within this study when we talk about the structure of the Süleymaniye Mosque and its characteristics as different parts have been influenced or attained from a variety of different cultures. The Mosque has merged Islamic and Byzantine architectural elements.
Within the final chapter of the thesis, the author will consider the influential effect of other architecture on the Süleymaniye Mosque. Again, culture will be prevalent in this chapter too in order to understand how architecture is of an influence. For example, Architect Sinan has combined tall, slender towers with large domed buildings reinforced by half domes in the style of the Byzantine churchHagia Sophia. Many other styles from other cultures are evident within the Mosque, for example when the Süleymaniye Mosque was destroyed by afire in 1660and was restored on the command of sultan Mehmed IV by architect Fossatı. However the restoration changed the mosque into a more baroque style architecture.
Taking elements from foreign cultures and religions and combining them into something original can be recognized in the Süleymaniye Mosque. The originality of the great Ottoman mosques did not develop by removing all the foreign influences; instead it is a mixture that developed by the procedure of integration of foreign culture by the Turks of Byzantine culture. This is the symbol of the Ottoman Empire, a multiracial, multilingual, and multicultural empire. This will cast an understanding on the history of the Mosques and Ottoman Architecture that will hence lead to a conclusion of the influences on the Süleymaniye Mosque. The sources mentioned in the bibliography will be of great use in acquiring the relevant information. These can be accessed through the web. The thesis will also require looking beyond these articles and books, as a site visit is required.
The Süleymaniye Mosque
The Süleymaniye mosque was built in Istanbul between 1550 and 1557. It is the largest of the Ottoman building enterprises and is regarded as one of Architect Sinan’s (Mimar Sinan) most famous masterpieces, as well as one of the most important examples of Ottoman architecture. Sinan was born in the last decade of the sixteenth century. Being enrolled as a teenager into the Janissary Corps that is a school for apprentices, he advanced his, carpentry, aarchitectural and engineering skill. Sinan served in various military roles during the reign of Suleyman the Magnificent, where he gradually developed approval for his engineering skills and achievements. During the Moldavian campaign was when Sinan was chosen to be the chief architect by the Prime Minister, Lutfi Pasha. Sinan was the chief architect for almost fifty years and was responsible for the design, construction and restoration of over 400 buildings, of which the Suleymaniye being one of the most important. During his time as chief architect, he contributed to the
formation of an architecture that
is now recognized as ‘Ottoman Architecture’. His most innovative blends and
interpretations of forms were reserved
for the mosques he built for Sultans. [1] Due to the experiences he gained through the practical aspects of his architectural life as well as his travels, he developed a reputation of an innovative designer of mosques and domed structures, which he then applied to the Süleymaniye Mosque. Out of all of Sinan’s works, the Süleymaniye Mosque aimed to exceed any other imperial mosque in beauty and size, which in most people’s opinions was a success.
In the late 1540’s, the Sultan Suleyman the Magnificent ordered Sinan to build a mosque within a kulliye (complex of buildings adjacent to a mosque). Just like most imperial mosques, the Süleymaniye Mosque is more than just a place of worship. The complex consisted of various social, religious and educational functions such as schools, a hospital, a caravanserai, Turkish baths, and more.[2] The mosque is located on the Old Palace, on a hill overlooking the Golden Horn. The mosque is symbolic in the city of Istanbul, as it sits on the highest hill, thus implies the power and strength of the Turkish Ottoman Empire. The complex was planned as a great centre of learning comprising of madrasas (a School for Islamic instruction) for studies in theology and holy law and medicine. Wide walkways surround the complex, where the outer sides consist of two rows of madrasas on the longer sides and social service buildings along the third side. Over time their has been additions of further buildings into the complex such as the hadith college, which have resulted in a lack of symmetry within the complex by attempting to adapt the buildings into older street networks. The mosque is located at the centre of the complex positioned towards the qiblah (direction of the Mecca, south-east). Around the mosque is a spacious courtyard measuring 44 by 58 meters, which has a fountain in the middle and a minaret in each corner, with a colonnaded peristyle with columns of marble, granite and porphyry.[3] The courtyard surrounded by an arched colonnade is a standard feature of Ottoman imperial mosques. Some of the marble and granite columns used for the Suleymaniye were collected from an old Byzantine Hippodrome, and from other locations in the city. In addition many materials where also collected from Roman and Byzantine buildings in Greece, Egypt, and other parts of the Ottoman Empire. This shows the diversity of cultures involved in the aesthetical and structural features within the mosques design.
The courtyard is enclosed on three sides by stonewalls, through the windows of which the sanctuary and funerary garden may be viewed. The fourth side has no wall built, allowing a panoramic view of the city and Golden horn. The minarets of the Suleymaniye have a total of 10 balconies; this was due to Suleyman the Magnificent being the 10th Ottoman sultan. Two taller minarets both frame the forecourt and mark the entrance to the interior space of worship where the sidewalls of the forecourt meet the mosque.[4]
The mosque has many structural characteristics that resemble the Hagia Sophia. Sinan knew the Hagia Sophia well as he contributed to its preservation. For almost 500 yearsByzantine architecturesuch as the church of Hagia Sophia functioned as models for many of the Ottoman mosques including the Süleymaniye. [5] Although both were constructed in very different times, one representing the Christian-Byzantine Empire and the other representing the capability of the architect Sinan and the Islamic-Ottoman Empire, they have similarities as the Hagia Sophia influenced the Suleymaniye. Similar to the Hagia Sophia four giant piers hold up the main domes over a square plan. However the reinforcement system is much more complex ‘two half-domes stand on the axis of qiblah and hugearched walls filled with windows stand on the cross-axis’. The multiple domes and the arches supporting them also help to strengthen and distribute the weight of the massive central dome.[6] As well as the columns being an essential part of the complex dome and support system of the mosque, it also had significant symbolic value religiously, symbolically and also architecturally. Although this supports the idea of influence of Hagia Sophia on the mosque, it also shows that the Süleymaniye Mosque remains a unique piece of architecture due to its complexity, from the clashing aspects Sinan applied to the mosque. Taking elements from foreign cultures and religions and combining them into something original can be recognized in the Süleymaniye Mosque just by examining at the structural qualities and materials. The originality of the great Ottoman mosques did not appear by removing all the foreign influences, nor can it merely be reduced to the Byzantine style. It is a mixture that developed by the procedure of integration of foreign culture by the Turks of Byzantine culture. This is what Ottoman Empire is, a multiracial, multilingual, and multicultural empire, which is what will be explored further throughout this study.
1. Cansever, Turget. “The Architecture of Mimar Sinan.” Architectural Design. V. 74. n. 6. Nov/Dec 2004. pg 64-70.
2. Celebi, Sai Mustafa. Book of Buildings: Memoirs of Sinan the Architect. Kocbank: Istanbul, 2002. pg. 68.
3. Freely, John and Augusto Romano Burelli. Sinan: Architect of Suleyman the Magnificent and the Ottoman Golden Age. Thames