**Recap**: from guest lecture by Chris Rozell:

- Structure of a neuron
- Optimization:
- Dictionary learning (sparse Coding):
**Optimize**:- This function is not convex, so finding a global solution is intractable. Local minimum can be found using
**gradient descent**method.

- Inference (compressed Sensing):
- Dictionary is fixed. Given Y (image), which X (coefficients)?

**Optimize**:- is a convex function (with a single variable), so we can find a global solution efficiently.
**Thm**: a function f: can be minimized efficiently provided:

1. f is convex

2. f is well-rounded.

- Dictionary is fixed. Given Y (image), which X (coefficients)?

- Dictionary learning (sparse Coding):

- Surround effect and inhibition in V1 neurons
- Data can be explained by
**models**, but there are problems:- A lot of models, but not much
**theory** - Optimization: how can we justify a hypothesis that brains are innately solving complicated optimization problems?
- Could dictionaries be learned by
**evolution**?

– Optimizations via trial and error (strong survives, rest dies) over the course of very, very long time (~4 billion years = generations)

– Is generations enough to reach a globally optimized solution? There are sensors in the retina and possible patterns in V1….

- Could dictionaries be learned by

- A lot of models, but not much

**Learning**: What can we propose as a general learning process?

We can start by modeling a single neuron.

**McCullough-Pitts Model (1943):**

Using this model, we can build any Boolean logic:

**OR**:

**AND**:

**NOT**:

So, this is a model of a single neuron and by composing neurons, a computer. What about the learning process?

**Labels**: is labeled as “+” or “-” ()

**Assume**: s.t. if = 1, and if = -1. Also, and .

**Goal**: Find that can classify X’s correctly

**Algorithm (Perceptron)**:

- initialize W = 0
- Repeat: On a mistake (i.e. W*X does not “match” ):

W

**Proof**:

- .
- On each mistake (i.e., either for or for $l(x)=-1$):

- After t mistakes:

- So, after t mistakes.
- Since .

The algorithm finds a s.t. iff after at most iterations.

# Interactive Vision

**Paper**: A Critique of Pure Vision

Interactive vision is summarized as:

**Environment**: evolutionary rationale rooted in improved motor control (four Fs)**Serial Processing**: parsing image as a sequence of saccades**Prediction**: visual learning allows prediction**Interaction with other systems**: motor system and vision are closely related**Recurrence/Feedback**: rich recurrence and feedback during recognition**Memory**: memory plays a role in what we see

Also, there are **computational advantages** of interactive vision:

- Segmentation and recognition can be done more efficiently together
- Movement (of eye, head, body) makes many visual computations simpler
- Interactive perception simplifies the learning problem

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