
.. _crei2013_Introduction:


************
Introduction
************

Background Questionaire
-----------------------

* Who has used Theano before?

 * What did you do with it?

* Who has used Python? NumPy? SciPy? matplotlib?

* Who has used iPython?

 * Who has used it as a distributed computing engine?

* Who has done C/C++ programming?

* Who has organized computation around a particular physical memory layout?

* Who has used a multidimensional array of >2 dimensions?

* Who has written a Python module in C before?

 * Who has written a program to *generate* Python modules in C?

* Who has used a templating engine?

* Who has programmed a GPU before?

 * Using OpenGL / shaders ?

 * Using CUDA (runtime? / driver?)

 * Using PyCUDA ?

 * Using OpenCL / PyOpenCL ?

 * Using cudamat / gnumpy ?

 * Other?

* Who has used Cython?


Python in one slide
-------------------

* General-purpose high-level OO interpreted language

* Emphasizes code readability

* Comprehensive standard library

* Dynamic type and memory management

* Built-in types: int, float, str, list, dict, tuple, object

* Slow execution

* Popular in web-dev and scientific communities


.. code-block:: python

    #######################
    # PYTHON SYNTAX EXAMPLE
    #######################
    a = 1                     # no type declaration required!
    b = (1, 2, 3)             # tuple of three int literals
    c = [1, 2, 3]             # list of three int literals
    d = {'a': 5, b: None}     # dictionary of two elements
                              # N.B. string literal, None

    print d['a']              # square brackets index
    # -> 5
    print d[(1, 2, 3)]        # new tuple == b, retrieves None
    # -> None
    print d[6]
    # raises KeyError Exception

    x, y, z = 10, 100, 100    # multiple assignment from tuple
    x, y, z = b               # unpacking a sequence

    b_squared = [b_i**2 for b_i in b]  # list comprehension

    def foo(b, c=3):          # function w default param c
        return a + b + c      # note scoping, indentation

    foo(5)                    # calling a function
    # -> 1 + 5 + 3 == 9       # N.B. scoping
    foo(b=6, c=2)             # calling with named args
    # -> 1 + 6 + 2 == 9

    print b[1:3]              # slicing syntax

    class Foo(object):        # Defining a class
        def __init__(self):
            self.a = 5
        def hello(self):
            return self.a

    f = Foo()                 # Creating a class instance
    print f.hello()           # Calling methods of objects
    # -> 5

    class Bar(Foo):           # Defining a subclass
        def __init__(self, a):
            self.a = a

    print Bar(99).hello()     # Creating an instance of Bar
    # -> 99

NumPy in one slide
------------------

* Python floats are full-fledged objects on the heap

 * Not suitable for high-performance computing!

* NumPy provides a N-dimensional numeric array in Python

 * Perfect for high-performance computing.
 * Slice are return view (no copy)

* NumPy provides

 * elementwise computations

 * linear algebra, Fourier transforms

 * pseudorandom numbers from many distributions

* SciPy provides lots more, including

 * more linear algebra

 * solvers and optimization algorithms

 * matlab-compatible I/O

 * I/O and signal processing for images and audio

.. code-block:: python

    ##############################
    # Properties of NumPy arrays
    # that you really need to know
    ##############################

    import numpy as np          # import can rename
    a = np.random.rand(3, 4, 5) # random generators
    a32 = a.astype('float32')   # arrays are strongly typed

    a.ndim                      # int: 3
    a.shape                     # tuple: (3, 4, 5)
    a.size                      # int: 60
    a.dtype                     # np.dtype object: 'float64'
    a32.dtype                   # np.dtype object: 'float32'

    assert a[1, 1, 1] != 10     # a[1, 1, 1] is a view
    a[1, 1, 1] = 10             # So affectation to it change the
    assert a[1, 1, 1] == 10     # original array


Arrays can be combined with numeric operators, standard mathematical
functions. NumPy has great `documentation <http://docs.scipy.org/doc/numpy/reference/>`_.

Training an MNIST-ready classification neural network in pure NumPy might look like this:

.. code-block:: python

    #########################
    # NumPy for Training a
    # Neural Network on MNIST
    #########################

    x = np.load('data_x.npy')
    y = np.load('data_y.npy')
    w = np.random.normal(
        avg=0,
        std=.1,
        size=(784, 500))
    b = np.zeros((500,))
    v = np.zeros((500, 10))
    c = np.zeros((10,))

    batchsize = 100
    for i in range(1000):
        x_i = x[i * batchsize: (i + 1) * batchsize]
        y_i = y[i * batchsize: (i + 1) * batchsize]

        hidin = np.dot(x_i, w) + b

        hidout = np.tanh(hidin)

        outin = np.dot(hidout, v) + c
        outout = (np.tanh(outin) + 1) / 2.0

        g_outout = outout - y_i
        err = 0.5 * np.sum(g_outout) ** 2

        g_outin = g_outout * outout * (1.0 - outout)

        g_hidout = np.dot(g_outin, v.T)
        g_hidin = g_hidout * (1 - hidout ** 2)

        b -= lr * np.sum(g_hidin, axis=0)
        c -= lr * np.sum(g_outin, axis=0)
        w -= lr * np.dot(x_i.T, g_hidin)
        v -= lr * np.dot(hidout.T, g_outin)


What's missing?
---------------

* Non-lazy evaluation (required by Python) hurts performance

* NumPy is bound to the CPU

* NumPy lacks symbolic or automatic differentiation

Now let's have a look at the same algorithm in Theano, which runs 15 times faster if
you have GPU (I'm skipping some dtype-details which we'll come back to).

.. code-block:: python

    #########################
    # Theano for Training a
    # Neural Network on MNIST
    #########################

    import numpy as np

    import theano
    import theano.tensor as tensor

    x = np.load('data_x.npy')
    y = np.load('data_y.npy')

    # symbol declarations
    sx = tensor.matrix()
    sy = tensor.matrix()
    w = theano.shared(np.random.normal(avg=0, std=.1,
                                       size=(784, 500)))
    b = theano.shared(np.zeros(500))
    v = theano.shared(np.zeros((500, 10)))
    c = theano.shared(np.zeros(10))

    # symbolic expression-building
    hid = tensor.tanh(tensor.dot(sx, w) + b)
    out = tensor.tanh(tensor.dot(hid, v) + c)
    err = 0.5 * tensor.sum(out - sy) ** 2
    gw, gb, gv, gc = tensor.grad(err, [w, b, v, c])

    # compile a fast training function
    train = theano.function([sx, sy], err,
        updates={
            w: w - lr * gw,
            b: b - lr * gb,
            v: v - lr * gv,
            c: c - lr * gc})

    # now do the computations
    batchsize = 100
    for i in range(1000):
        x_i = x[i * batchsize: (i + 1) * batchsize]
        y_i = y[i * batchsize: (i + 1) * batchsize]
        err_i = train(x_i, y_i)


Theano in one slide
-------------------

* High-level domain-specific language tailored to numeric computation

* Compiles most common expressions to C for CPU and GPU.

* Limited expressivity means lots of opportunities for expression-level optimizations

 * No function call -> global optimization

 * Strongly typed -> compiles to machine instructions

 * Array oriented -> parallelizable across cores

 * Support for looping and branching in expressions

* Expression substitution optimizations automatically draw
  on many backend technologies for best performance.

 * FFTW, MKL, ATLAS, SciPy, Cython, CUDA

 * Slower fallbacks always available

* Automatic differentiation and R op

* Sparse matrices


Project status
--------------

* Mature: theano has been developed and used since January 2008 (5.5 yrs old)

* Driven over 87 research papers

* Good user documentation

* Active mailing list with participants from outside our lab

* Core technology for a funded Silicon-Valley startup

* Many contributors (some from outside our lab)

* Used to teach IFT6266 for many years

* Used for research at Google and Yahoo.

* Downloads (January 2011 -  June 8 2011):

 * Pypi (16 July 2013): 60k total, 159 last day, 823 last week

 * Github (`bleeding edge` repository): unknown




Why scripting for GPUs?
-----------------------

They *Complement each other*:

* GPUs are everything that scripting/high level languages are not

 * Highly parallel

 * Very architecture-sensitive

 * Built for maximum FP/memory throughput

 * So hard to program that meta-programming is easier.

* CPU: largely restricted to control

 * Optimized for sequential code and low latency (rather than high throughput)

 * Tasks (1000/sec)

 * Scripting fast enough

Best of both: scripted CPU invokes JIT-compiled kernels on GPU.


How Fast are GPUs?
------------------

* Theory

 * Intel Core i7 980 XE (107Gf/s float64) 6 cores

 * NVIDIA C2050 (515 Gf/s float64, 1Tf/s float32) 480 cores

 * NVIDIA GTX580 (1.5Tf/s float32) 512 cores

 * GPUs are faster, cheaper, more power-efficient

* Practice (our experience)

 * Depends on algorithm and implementation!

 * Reported speed improvements over CPU in lit. vary *widely* (.01x to 1000x)

 * Matrix-matrix multiply speedup: usually about 10-20x.

 * Convolution speedup: usually about 15x.

 * Elemwise speedup: slower or up to 100x (depending on operation and layout)

 * Sum: can be faster or slower depending on layout.

* Benchmarking is delicate work...

 * How to control quality of implementation?

  * How much time was spent optimizing CPU vs GPU code?

 * Theano goes up to 100x faster on GPU because it uses only one CPU core

 * Theano can be linked with multi-core capable BLAS (GEMM and GEMV)

* If you see speedup > 100x, the benchmark is probably not fair.
