Artificial Systems and Self-Organisation Concepts

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Questions and Answers

Which technologies are contrasted in the table regarding their artificial nature?

organic materials and synthetic compounds

carbon technology and silicon technology (correct)

biological systems and computational models

molecular biology and quantum mechanics

What is one of the main applications of the concepts discussed?

Enhancing human cognitive abilities through technology

Modeling complex biological and socio-economic systems (correct)

Developing natural languages for artificial intelligence

Creating biological organisms from scratch

Which type of interactions are associated with artificial systems as mentioned in the content?

magnetic interactions

molecular interactions

electric interactions (correct)

thermodynamic interactions

Which of the following is categorized under artificial systems in practice?

integrated circuits Signup and view all the answers

What kind of algorithms are mentioned as relevant in the philosophical context?

Evolutionary algorithms Signup and view all the answers

What principle of self-organisation refers to the lack of control from external sources?

No external control Signup and view all the answers

Which of the following is NOT one of the defining principles of self-organisation?

Emergence of new capabilities Signup and view all the answers

Which principle involves systems responding effectively to changing conditions?

Adaptability Signup and view all the answers

What does the principle of interaction in self-organisation emphasize?

Dynamic relationships among components Signup and view all the answers

Which of the following statements best represents a view on emergence?

What emerges is often subjective to the observer. Signup and view all the answers

Which principle is closely associated with systems achieving higher complexity and order?

Increase in order Signup and view all the answers

In the context of self-organisation, what is meant by asynchronism?

Different components acting at varied times without direct coordination Signup and view all the answers

How does self-organisation contribute to systems in nature?

By embedding order and complexity in all components Signup and view all the answers

What role does momentum play in the training of neural networks?

It contributes to better learning and helps avoid local minima. Signup and view all the answers

Which of the following statements about adaptive momentum estimation (ADAM) is correct?

ADAM computes averages of past gradients to facilitate learning. Signup and view all the answers

What does the variable $m_t$ represent in the ADAM algorithm?

The estimate of the 1st moment (mean) of gradients. Signup and view all the answers

In the context of backpropagation, what is an epoch?

The presentation of all training examples once. Signup and view all the answers

Which is NOT a suggested value for parameters in the ADAM algorithm?

$eta_3 = 0.8$ Signup and view all the answers

What is the role of the tangent vector in determining velocity?

It represents the instantaneous rate of change of position. Signup and view all the answers

Which characteristic is essential for non-linear systems to provide universal computation?

Non-linearity Signup and view all the answers

What is a limit cycle in the context of dynamical systems?

An oscillatory trajectory that cyclically returns to itself. Signup and view all the answers

How do Hopfield networks enable the manipulation of attractors?

By controlling the positions of the attractors to match input patterns. Signup and view all the answers

What is a defining feature of dissipative systems?

They converge to an attractor over time. Signup and view all the answers

Which best describes the energy-minimization dynamics in neural networks?

They exploit trajectories that reduce energy consumption to compute effectively. Signup and view all the answers

What is the purpose of storing a set of patterns in an associative memory?

To recall patterns that closely resemble a presented input. Signup and view all the answers

What effect does noise typically have on neural networks?

It is a characteristic feature that is often present. Signup and view all the answers

What does the universal approximation theorem assert about a multilayer perceptron (MLP)?

A single hidden layer is sufficient for a MLP to compute a near approximation. Signup and view all the answers

In the universal approximation theorem, what is the significance of the function ϕ(·)?

It should be non-constant, bounded, and monotonous-increasing. Signup and view all the answers

What does the error risk bound suggest when using an MLP?

The configuration of hidden layer neurons is related to error risk. Signup and view all the answers

Which statement is true regarding the function approximation capabilities of an MLP?

Generalization cannot be assured solely on the number of hidden layers. Signup and view all the answers

What is often a limitation of using a single hidden layer in an MLP for function approximation?

It can be inefficient in terms of training time. Signup and view all the answers

What aspects must be maintained for function approximation using neural networks according to the universal approximation theorem?

Boundedness and non-constancy of the output. Signup and view all the answers

What does the notation $F(x_1, ..., x_{m_0}) = \Sigma_{i=1}^{m_1} \Sigma_{j=1}^{m_0} α_i ϕ(w_{ij} x_j + b_i)$ represent?

The final approximation of function $f$ through neural computation. Signup and view all the answers

Why might it be necessary to go deeper into an MLP's architecture?

To improve the approximation capability for more complex functions. Signup and view all the answers

What should the desired outputs fall within for the hyperbolic tangent function when a = 1.7159 and ϵ = 0.7159?

dk = -1.7159 + 0.7159 Signup and view all the answers

What is one of the requirements for input normalization in a neural network?

Each input should have average close to zero. Signup and view all the answers

What is the intended role of PCA in input normalization?

To reduce the dimensionality of the input features. Signup and view all the answers

What should the initial weight values be in a neural network to avoid saturation?

Values around zero. Signup and view all the answers

What is the desired outcome of initializing random uniform synaptic weights?

To keep the average of the weights to zero. Signup and view all the answers

In weight initialization, what variance is ideally suggested for future calculations?

Should equal one for stability. Signup and view all the answers

What does a learning rate of η signify for neurons with more inputs?

It should be smaller, inversely proportional to the square root of the number of inputs. Signup and view all the answers

What is the effect of having non-correlated inputs during training?

Ensures synaptic weights learn at a similar speed. Signup and view all the answers

What is one common strategy for weight initialization related to the hyperbolic tangent function?

Setting weight variance to one. Signup and view all the answers

What does the maximum induced local field variance depend on?

Weights and inputs covariance. Signup and view all the answers

How can learning speed be affected by using information about the function?

It enhances efficiency and consistency of backpropagation. Signup and view all the answers

What is the advantage of having small initial weights during training?

Prevents saturation and maintains learning dynamics. Signup and view all the answers

What condition ideally applies to the average of inputs for effective weight training?

Average should be null. Signup and view all the answers

What is essential about the weights in relation to the number of synapses of a neuron?

Weight variance is inversely proportional to the number of synapses. Signup and view all the answers

Study Notes

Dynamical Systems

Dynamical systems involve deterministic equations that represent the time evolution of a system
Deterministic systems evolve according to a set rule with no randomness
Dynamical systems can exhibit unpredictable behavior, especially when they display chaotic traits
Real-world systems often have many interconnected parameters that evolve over time
A trajectory (or orbit) showcases the system's path in phase space, which represents all possible states of the system

Continuous vs. Discrete Dynamical Systems

Continuous dynamical systems evolve continuously over time, without discrete steps
Continuous systems are often modeled using equations like dx/dt = f(x) where the change in a variable (x) is over time (t).
Continuous systems usually have smooth, gradual change over time.
Discrete dynamical systems evolve in steps (discrete steps), with the time variable n representing discrete time intervals
Discrete systems are expressed as xn+1 = M(xn)

Chaos and Sensitive Dependence on Initial Conditions

Chaos can exist in deterministic systems, where small changes in initial conditions lead to significantly different outcomes over time, making long-term prediction impossible.
The Lyapunov exponent quantifies how sensitive initial conditions are, determining chaotic behavior. A positive exponent indicates chaotic behaviour

Bifurcations and Attractors

Bifurcation: points where the behavior of a system changes dramatically as a parameter (e.g., r in the logistic map) changes; this transition between different types of behavior can include fixed points to cyclical, repeating orbits.
Attractor: A stable state (or a cyclical pattern) and it's a region of the phase space to which orbits evolve.
Types of attractors (e.g., fixed points & limit cycles); as parameters shift, systems can transition from one to another

Stability of Fixed Points

Fixed point: a state where the system's state does not change over time (dx/dt = 0).
Stability depends on the derivative of the system at the fixed point: a value less than 1 indicates stability (attracting nearby points) ; a value greater than 1 indicates instability (repellling nearby points); and a value equals to 1 represents meta-stability

Conservative vs. Dissipative Systems

Conservative Systems: preserve total 'volume' in phase space, with no dissipation and conserving the total energy of the system.
Dissipative systems: lose "volume" in phase space, typically due to energy loss.

Chaotic Systems and Fractals

Chaotic systems exhibit sensitive dependence on initial conditions, leading to divergence with minute differences
Strange attractors (in chaotic systems): have fractal dimensions and irregular patterns; these are key properties of fractals

Symbolic Dynamics and Phase Space Partitioning

Symbolic dynamics: partitioning phase space to regions then labeling each region with a symbol
Symbolic sequences represent the system's trajectory through the phase space.
Phase Space: the phase space is the set of all possible states or values of a system in a multi-dimensional space.

Real-World Applications

Dynamical systems provide modeling for a wide range of real-world contexts including human health, geological systems, living systems (e.g., the evolution of living organisms over time
Real world systems have complex dynamics due to many interacting variables

Summary and Reflections

Deterministic chaos theory demonstrates complex behaviors, particularly in systems with numerous interdependent variables
System transitions from stable states to periodic orbits and chaos are important and are characteristic signs of a chaotic system.
Sensitive dependence on initial conditions, and strange attractor behaviour are hallmarks of chaotic systems.

Fractality in Chaos

Fractality in chaos: Chaotic systems and attractors often exhibit self-similarity at different scales
Practical implications are vast, applying chaos theory to wider fields like biology, physics, economics, and engineering to understand complex and non-linear behaviours over time

Dynamical Systems II (Fractal Dimensions)

Dynamical Systems: the study of systems that change over time, governed by rules and equations. - Fractal Dimension: a metric used to quantify the complexity of fractals due to their irregular and self-similar structures at various scales.  - Iterated Function Systems (IFS): a collection of functions used iteratively to generate fractal patterns. - Logistic Function: a simple nonlinear function used extensively in modeling population dynamics, expressed as xn+1=f(xn)=rxn(1-xn), typically with the parameter (r) between 2 and 4

Entropy, Complexity, and Information

Entropy: a measure of randomness or disorder in a system 
Complexity: amount of information needed to describe a system's behavior
Randomness: when all possibilities are equally probable; systems with high entropy tend to be hard to predict

Fractals

Fractals: geometric objects with self-similarity; appearing identical at different scales — they can have a fractal dimension.

Methods for Calculating Fractal Dimensions

Self-Similarity Method: based on the concept that fractals are scaled versions of themselves at different scales; the fractal dimension arises from the relationship between the number of parts N and the scale E(or the scale rate)
Geometric method: method used for computing the length or area of a fractal at differing scales or sizes of a box for each scale rate to find the relationships for estimating the fractal dimension.
Box Counting Method: counting the number of boxes required to cover a fractal, which is used to calculate and estimate the fractal dimension; this method uses boxes of varying sizes
Fractal Dimensions can also be estimated using other methods including the Minkowski-Bouligand, Hausdorff, Rényi

L-Systems

An L-system is method for creating a system of rules that define how a string of symbols evolves over time.
Commonly employed for modeling processes of growth and development in various systems including the development of biological organisms and their growth patterns. - Typical components include; an alphabet of symbols representing parts of the organism; an initial state or the axiom; production rules defining the rewriting of the symbols; and ending or stopping process

Applications of Fractals and Dynamical Systems

Fractals and dynamical systems are used to model many natural occurrences and complex problems
Examples of practical applications include biological structures and systems, computer graphics, and other disciplines

Computational Artificial Life (ALife)

Investigates life by recreating underlying principles found in biological systems, using computers to create a new kind of environment for studying computational models

ALife illustrative example

Morphological and neural control under evolution
Sensory inputs
Evolutionary pressures (to move/capture)
Self-propelling beings: a major problem in the development

ALife Research Questions (RQ's)

Evolution of complexity: Is there a rational reason behind the increase in complexity?
Origins of life: Exploring pre-biotic systems
Major transitions: Exploring transitions in evolution (prokaryotes to eukaryotes, single cells to multi-cellular life)
Cultural Evolution vs. Biological Evolution: How are each intertwined?
Fundamental Intelligence requirements: What factors are fundamental for intelligence?

Course Logistics

Assessment: comprised of 3 parts, including a project (70%), Flash Test (20%), and reports from TP exercises (10%)

Historical notes on ALife

Citations include works by Christoph Adami, Cristopher Langton, Steven Levy, Claus Emmeche, Erwin Schrödinger and many more regarding the history of Artificial Life

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the intriguing world of artificial systems and the principles of self-organisation. This quiz covers key concepts such as interaction, self-organisation, and emergence, challenging your understanding of their philosophical and practical implications. Test your knowledge on algorithms and the various principles that govern these systems.