Category Archives: Education

Assistant Teaching- Alec B.

I have finally reached my goal of being able to sit in classes of both middle school and lower school. At the moment, it is challenging trying to balance out class time with eighth grade and lower school, but I am managing to find times to get good experience. The remainder of my month will be tough as well because I need to choose whether to focus more on eighth grade, or fifth grade.

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Assistant Teaching- Alec B.

I am getting closer to the end of my studies here, but yet it feels like I am only just beginning. If I was asked last year in the early spring if I saw myself dedicating a whole year to studying education as a class, I would have thought that couldn’t be me. I had the same ambition to be a teacher, but never thought I could start the journey this early. Here I am however, in April, and have worked in sixth, seventh, eighth, and now fifth grade.

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Assistant Teaching- Alec B.

As I sit in this eighth grade class and watch the teacher, I can’t help but picture myself in their place. The small little interactions and the seemingly simple advice to students make me think of my future. The more I see this particular class, the more it makes me reflect on my middle school years as well and how they were enhanced by the teachers.

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Assistant Teaching- Alec B.

Within these last two months of the school year, I can see the anxiety in both students and teachers. With this said however, the class remains grounded quite well and focusing on their work just as much as ever. Now that the eighth grade class is reading Persepolis, I can start forming my chapter discussions for them. Continue reading

Assistant Teaching- Alec B.

For my project, the accomplishments have been minor so far. I have been sitting in on eighth grade classrooms and observing the nature of the class and interactions between teacher and student. I have stepped in a few times to give input to students on how their work is.

In the future, I will be finding time to go into lower school, primarily fourth and fifth grade to do what I have been doing which is observing and helping out with certain assignments and activities. Also, with eighth grade, I will be attempting to lead discussions in the book they’re reading.

I don’t see any adjustments there need to be to achieve my goal, because my goal is to gain the experience of being in the classroom and what the roll of being a teacher is like.

Moving Below the Surface (3): TensorFlow — William

Tensorflow is one of the most widely used programming frameworks for algorithms with a large number of mathematical operations and computations. Specifically, Tensorflow is designed for the algorithms of Machine Learning. Tensorflow was first developed by Google and its source code soon became available on Github, the largest open-source code sharing website. Google uses this library in almost its all Machine Learning applications. From Google photos to Google Voice, we have all been using Tensorflow directly or indirectly, while a fast-growing group of independent developers incorporates Tensorflow into their own software. Tensorflow is able to run on large clusters of computing hardware and its excellence in perceptual tasks gives it an edge to Tensorflow in competitions against other Machine Learning libraries.

In this blog, we will explore the conceptual structure of Tensorflow. Although Tensorflow is mostly used along with the programming language Python, only fundamental knowledge of computer science is needed for you to proceed further in this blog. As its name suggests, Tensorflow comprises two core components: the Tensors and the computational graph (or “the flow”). Let me briefly introduce each of them.

Mathematically speaking, a Tensor is an N-Dimensional vector representing a set of data in the N-Dimensional space. In other words, a Tensor includes a group of points in a coordinate with N axes. It is difficult to visualize points in high dimensions, but the following examples in two or three dimensions give a good idea of how Tensors look like.

As the dimension increases, the volume of data represented grows exponentially. For example, a Tensor with form (3,3) is a matrix with 3 rows and 3 columns, while a Tensor with form (6,7,8) is a set of 6 matrices with 7 rows and 8 columns. In these cases, the form (3,3) and the form (6,7,8) are called the shape or the Dimension of the Tensor. In Tensorflow, the Tensors could be either a constant with fixed values, or a variable allowing alternations during computations.

After we understand what Tensor means, it’s time to go with the Flow. The Flow refers to a computational graph or a graph in short. Such graphs are always acyclic, have a distinct input and output, and never feed back into itself. Each node in the graph represents a single mathematical operation. It could be an addition, a multiplication, etc. Data and numbers flow from one node to the next in the form of Tensors, and the result is a new Tensor. The following is a simple computational graph.

Screen Shot 2018-01-05 at 22.05.07.png

The expression of this graph is not complicated: e = (a+b)*(b+1). Let’s start from the bottom of the graph. The nodes at the lowest level of the graph are called leaves. The leaves of the graph do not accept inputs and only provides a Tensor as output. Actually, a Tensor would not be in a non-leaf node for this reason. The three leaves are variables a and b, and a constant 1.

One level up is two operation nodes. Each one of them represents an addition. Both take two inputs from the nodes below. These middle and higher levels depend on their predecessors, for they could not be computed without the outputs from a, b, or 1. Note that both addition operations are parallel to each other at the same level: Tensorflow does not need to wait on all of them to complete before moving on to the next node.

The final node is a multiplication node. It take c and d as input, forming the expression e = (c)*(d), while c = a+b and d = b+1. Therefore, combining the two expressions, we have the final result of e = (a+b)*(b+1).

That is all for our introduction to basic Tensorflow concepts. We will discuss further advanced features of Tensorflow in later posts. Stay tuned and see you next time!

Works Cited

“TensorFlow open source machine intelligence library makes its way to Windows.” On MSFT, 29 Nov. 2016, http://www.onmsft.com/news/tensorflow-open-source-machine-intelligence-library-makes-its-way-to-windows.
HN, Narasimha Prasanna. “A beginner introduction to TensorFlow (Part-1) – Towards Data Science.” Towards Data Science, Towards Data Science, 28 Oct. 2017, towardsdatascience.com/a-beginner-introduction-to-tensorflow-part-1-6d139e038278.

Moving Below the Surface (3): Simulated Annealing — William

In this blog, we are going to talk about another optimization algorithm, the simulated annealing. As we mentioned last time, the goal of machine learning algorithms is to minimize the difference between the predicted values of the trained model and the actual values from either surveying or measuring or to find the minimum of the error function. Compared to gradient descent method introduced in the previous blog, simulated annealing algorithm offers a more efficient way to find the global maximum instead of a local one in a certain dataset. Though this method is not complex in nature, it requires some understanding of a field of physics that is not widely known and is a bit abstract.

As its name suggests, simulated annealing algorithm is derived from the annealing process in metallurgy. This process is a controlled heating and then cooling of metal to achieve desired properties, specifically increase the strength of the metal. First, the material is heated up to its melting point and is cast and formed. Heat, at the atomic level, is represented as the kinetic energy of particles. During this stage, all particles have a tremendous amount of kinetic energy and move rather quickly, since the hotter the material is, the greater kinetic energy the particles possess. As the particles roam through space, it is almost impossible to form chemical bonds and therefore the metal loses its physical form and turns into the liquid.

Then the metal starts to be cooled. As the temperature decreases, the kinetic energy also falls. More particles slow down, and permanent bonds start to form between the atoms. Therefore, small freezing “seeds” came into existence and particles around them form crystals upon the seeds. As seeds slowly grow into larger and larger lattices, particles have enough time to fit into the state of minimum energy, giving the whole piece of metal a more steady structure and minimizing inner tension inside the metal. The cooling process is carefully adjusted so that every atom could end up with the least possible energy. If the process is run too quickly, the result would not be desired.

In simulated annealing, the same method applies. Instead of working with real metal, we treat the problem like an atomic thermodynamic system, “crystallizing” the coefficients of our error function into their lowest “energy” state. A typical simulated annealing includes a number of consecutive jumps across the plot of our error function. The amplitude of each jump is determined by the current temperature of the system. The following is an example of a simulated annealing:

The horizontal axis is the possibility of different coefficients in our error function and the vertical axis is the fitness of our model. In other words, the bigger the value in the graph, the better the coefficients fits the data, and the lower the error.

We start at point 1, which is completely chosen at will. We made a random jump towards point 2. Note that with a high system temperature, such large-scaled jumps are allowed, though it is really likely to end up with a worse landing point than the starting. Now we continue the jump to point 3, which is actually worse than point 2. No worries, “it’s gonna get worse before it gets better”, as the old saying goes. When we accumulate more jumps, the temperature of the system decreases, limiting the amplitude of the jumps. After numerous jumps, we could finally reach point 9, which is the global maximum and is where we end the algorithm as the temperature reaches 0.

Simulated Annealing offers a unique interpretation of a physical model and brings it into the optimization process. The randomness included in the algorithm actually gives it a shorter solving time compared to other optimization processes, marking it with distinctive qualities.

We will continue to explore Tensorflow, the programming package that allows us to build our own artificial intelligence model, in my next post. See you very soon!

Works Cited

“Simulated Annealing, a brief introduction.” I Eat Bugs For Breakfast, 14 Mar. 2012, ieatbugsforbreakfast.wordpress.com/2011/10/14/simulated-annealing-a-brief-introduction/.