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## Topics in Biological Physics Seminar

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**Topics in Biological Physics Seminar**Information and Computation – Session B: Turing, 1950 – Computing Machinery and Intelligence. J. Von-Neumann, 1951 – Design of Computers, Theory of Automata and Numerical Analysis. By: Adam Lampert**Can Computers Become as Intelligent as We Are?**• Fundamental part – Are we simply complicated computers? • Practical part – How do we build “intelligent” computers?**What is a computer?**• Turing Machine (Computers) • Finite Automata (Control) • Infinite tape (Store) • Executive unit**Universality of Turing Machines**All of the following are equivalent to TM: • TM • TM with many tapes • Cellular automata • Usual computers* • Logic gates • Neural networks • Physical realizations • Church-Turing thesis (informally): any realized discrete computation can be done by an equivalent Turing Machine**Are We Simply Complicated Computers Then?**• Conjecture (Turing): Computers may become indistinguishable from humans. • Why should we agree with Turing? • Universality of computational devices (Church-Turing thesis) • Consistent with our intuition about the physical world • Why shouldn't we agree with Turing? • Consciousness • Limitation of computation • Continuous computation • Self replication**Arguments Against Turing Conjecture - Consciousness**• Argument: Computes, as an automated device, does not have consciousness, and therefore are distinguishable from humans. • Answer 1: Complicated enough computers might be able to be conscious. • Answer 2: Even if computers can not be conscious, it doesn’t mean that they are empirically distinguishable from humans.**Arguments Against Turing Conjecture – Computers Are**Limited • Background: • Is there a problem that no computer can ever solve? • YES! • The halting problem. • Goedel Theorem. • Argument: Computers are fundamentally limited, so we can do better than them. • Answer: we are also fundamentally limited!**Proof of the Halting Problem**• The problem: is there an algorithm which decides whether a given TM accepts a given input or not. • Define <M> as the (string) representation of a TM M. • Assume that the algorithm exists: H(<M>,w) = True if M returns True on input w, False otherwise. • Define: S(<M>) = H(<M,<M>>) • Define: T(<M>) = ¬S(<M>) = False if M returns True on input <M>, True otherwise • T(<T>) = False if T returns True on input <T>, True otherwise. • A contradiction! • Why did we get the contradiction? • We have represented TM in the terms of its own language • Therefore, we could announce: “this statement is false”.**Arguments Against Turing Conjecture - Continuous Computation**• Background: • The Church-Turing thesis applies to discrete machines. • Continuous machines may be capable of computations beyond the Turing limit, and may solve the halting problem for Turing machines. • Among such machines are certain (theoretical models of) neural networks and chaotic systems. • Argument: Our brain is continuous capable of computations beyond the Turing limit. • Answer: Our world is noisy nearby states of the brain are indistinguishable.**Arguments Against Turing Conjecture – Self Replication**• Argument: if A construct B, then A must be more complicated than B. • Therefore, a computer can not self-replicate, but we can. • Answer: A can be just as complicated as B, and a computer can indeed self-replicate (Von-Neumann, 1951). • Furthermore, this doesn’t induce any limitation on the rest of the machine abilities.**Self-Replicating Machine – Von-Neumann Construction**• Machine A – construct machine T from its description IT. • Machine B – generate a copy of any given instruction IT. • Machine C – receive instruction IT, operate A to create T, operate B to copy IT, and supply T with IT. • Machine D is composed of the triplet A + B + C. It generates T + IT from IT. • In particular, D generates D + ID from ID. • Machine E is composed of D + ID. • E is self replicating!**Self-Replicating Machine - Langton Loops - Background**• Cellular Automata – each time step, the value of each cell is determined by the current value of its own and of its neighbors. 1D 2D**Self-Replicating Machine - Langton Loops**• Langton loops are loops-shaped object within a certain 2D CA invented by Langton in 1979. • These loops are self replicating.**Very simplified description of cell replication:**• The DNA is composer of two strands. • “DNA polimerase” et al. separated them and build up a new DNA out of each strand. • A always goes with T, C always goes with G. • Each strand contain all the information. • Two identical DNAs are composed. • Then, the cell is divided into two cells such that each one contains a DNA and about half of the other cell contents. • Computational perspective • Neither DNA nor DNA polymerase et al. contains any information about itself. • DNA polymerase can simply duplicate any given DNA. • The DNA only contain the information how to construct DNA polymerases Cell Replication**Who Do We Examine If a Machine Is Intelligent? Empirical**Test • Standard Turing test: • Imitation game:**Weaknesses of the Turing test**• May not cover all aspects of intelligence. • The interrogator should be really tough to diagnose tough computers. • Many unintelligent human behaviors must also be simulated by the machine. • The original proposed test is mostly textual, although some aspects of intelligence may not be so. • Do not examine real time responses.**Turing’s Claim (1950)**• “I believe that in about 50 years’ time it will be possible to program computers … to make them play the imitation game so well that an average interrogator will not have more than 70 percent chance of making the right identification after five minutes of questioning.”**Historical background**• 1936 – Turing machine. • 1939-40: The Bombe, machine for Enigma decryption during World War II. • 1943 J.Eckert and J. Mauchly - construction of ENIAC. Considered the first electronic computer and was used to calculate ballistic firing tables during World War II.**Historical Background - Continue**• late 30s, and 40s - Recent research in neurology had shown that the brain is an electrical network of neurons that may fire in all-or-nothing pulses. • 1943 – W. Pitts and W. McCulloch showed that networks of idealized artificial neurons may perform logical functions. • 1947 - The invasion of the transistor (replaced the vacuum tubes later). Note that a vacuum tube was estimated by Von-Neumann (1951) to be less efficient than a neuron cell by a ratio of one to million, in comparison of performance per volume and energy consumption. • 1948-1949 – G. Walter's analogous robots - capable of phototaxis: found their way to light. • 1949 – EDSAC - inspired by J. Von-Neumann, constructed by M. Wilkes and his team in England. Calculated arithmetic, differential equation, power series, etc. Bottom line: computers are used mostly to numerical purposes, but some inspiration could come from neurology**A Bit More About EDSAC (1949)**• Wight: 1 ton • Area: 45 m • Storage: 2k bytes 2**Human Intelligence vs. Machine Intelligence**• In certain problems humans have a clear advantage over today’s computers. • Visual recognition. • Language. • In certain other problems today’s computers has a clear advantage over today’s humans. • Numerical calculations. • Searching over large amount of data.**Machine Learning**• Child computer • Teacher • Adult computer**Machine Learning – Example: Generalization**• Goal: generate a computer that return y=ax+b for any given x. • Equip the child computer with “the answer is a straight line”. • This is called the inductive bias. • Teacher or environment provide it with the value of y for two values of x. • the computer generalize the answer and can calculate y for any x.**Machine Learning – Example: The Perceptron**• The perceptron is a very simple model of neural network. • Goal: give the correct answer y for any input x. • Learning program – get x as input and δ as the correct output. Changes the weights w and b according to: • The perceptron is a linear classifier: it converges if and only if the data set is linearly separable, and there are not too much mistakes. • Today there are much more sophisticated models of neural networks.**Perceptron – Example 1: And**Learning Rule: For each wrong classification: W1 = W1±α ×X1 W2 = W2 ± α ×X2 b = b α Here, α = 0.1 Initial randomized configuration: - + 0.22 Second Training Sample: X1 = 0, X2 = 1, δ = 0 0.51 0.47 Result: First Training Sample: X1 = 1, X2 = 0, δ = 0 0.42 Result: 0.41 0.37 0.32 0.51 0.37**Perceptron – Example 2: Xor**Our perceptron is not able to represent the XOR function. 0.55 0.06 0.65**Where Are We Today?**• Winner of Loebner prize in 2008 has managed to fool 3 out of 12 judges that he was human, in a short textual conversation (you can talk with “Frank” at www.artificial-solutions.com. Try also http://www.abenteuermedien.de/jabberwock, winner of 2003’s prize). • Great progress in many problems of AI. • Humans are still much better at many tasks (recognition of objects within pictures, translation of text). • Today’s computers out-compete humans at games with few choices and complete information (Checkers, Chess(?)). • Expert humans are still better at games with many choices or incomplete information (Go, Bridge).