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Is Abstraction the Key to Artificial Intelligence? - Lorenza Saitta

With this comprehensive breakdown of abstraction's multiple layers and components, we can understand and answer the question if abstraction is essential to artificial intelligence.

Lorenza Saitta, Università del Piemonte Orientale

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Is Abstraction the Key to Artificial Intelligence? - Lorenza Saitta

  1. 1. Is Abstraction a Key to Artificial Intelligence? Lorenza Saitta Università del Piemonte Orientale lorenza.saitta@uniupo.it
  2. 2. Premise « Is abstraction a key to computing? » [Kramer, 2007] The same question can be posed for Artificial Intelligence « … [the process of] abstraction is the essence of intelligence and the hard part of the problems being solved » [Brooks, 1991]
  3. 3. Representation • Representation is critical in AI tasks • Search for the “best” representation • One that facilitates performing a task/solving a problem • Often difficult to know a-priori which is the best representation • Expert definition on the basis of domain knowledge, experience, analogy, … • It is important to be able to easily change representation when needed • Several types of representation changes have been proposed in AI à Abstraction is one of them
  4. 4. Abstraction = Cognitive Organizational Principle • Abstraction is a special kind of representation change, fundamental in human thinking • Difficult to be precisely defined • Abstraction aims at reducing the complexity of the perceived world « … a ubiquitous function of the cerebral cortex, one in which many if not all of its areas are involved, is that of abstraction » [Zeki, 2009] “Were it not for the ability to construct useful abstraction, intelligent agents would be completely swamped by the real world” [Russel & Norvig, 2010]
  5. 5. Abstraction’s Modus Operandi (1) • Focalization on relevant information and removal of irrelevant details • Aggregation/Grouping Sciences, notably by Barsalou and co-workers, who provide a theoretical and an experimental account of the issue [37]. An interesting connection can be done with Computer Science, namely with the epistemological status of soft- ware and the basic skills needed for writing good programs6. As a matter of fact, Kramer wonders whether “abstraction is the key to computing” [272], abstraction meaning here the capability of removing inessential details and to identify a common “essence” inside variability. This capability of going to the core of things is another fundamental aspect attributed to abstraction, namely the ability to focus on relevance. Objects, phenomena, events in the world are extremely rich in details and may be very complex. However, when solving a problem or executing a task, only some aspects of the reality are useful, and to take into consideration the whole wealth of details may be confusing. For instance, when planning an aerial trip, the physical attributes of the aircraft, such as color or exact shape and sizes, are irrelevant and can be ignored. As another example, in Figure 1.3, a satellite image of downtown Torino is reported, where the buildings and monuments can be seen. However, just to find one’s way around the city it is more convenient to reduce the information to the street network. By citing again Brooks [75], “... abstraction is the essence of intelligence and the hard part of the problem being solved”. Stampa Invia LinkIndicazioni stradali Le mie mappeStampa Invia LinkIndicazioni stradali Le mie mappe Fig. 1.3: Satellite image of the center of Torino (left): buildings and monuments are visible. The same area can be described by considering just the street network (right): this abstract map is more convenient for moving around the city. Actually, in trying to solve a complex problem it may sometime be a good strategy to proceed top-down, by starting with a coarse solution and then re- fining it. At each step of refinement new details are possibly taken into account, generating a sequence of solutions, each one more detailed than the previous one. In this case we may speak of a hierarchy of levels of abstraction, with the 6 See Chapter 2. Part–of (bicycle) Member-of (forest) Functional relation (computer, tennis set) Computer Keyboard Mouse Monitor Body Floppy wheel pedal saddle handlebar wheel
  6. 6. Abstraction’s Modus Operandi (2) • Naming Equivalence classes of objects • Discovery of new concepts (predicate invention) Chair = Object with legs, a seat and a back Hub Community
  7. 7. Abstraction’s Modus Operandi (3) • Building Hierarchies ! ules into a multilevel pyramid, as illustrated in Figure 1. At each level, we describe the horizontal relationships by a network of modules that is by itself the abstraction of the network at a lower level [3]. In contrast, the verti- cal relationships, shown as links between layers, repre- sent the inclusion relationship between modules at different levels. Using an abstraction pyramid, not only can domain experts gain a global multilevel view of a complex system from two different perspectives (hori- zontal and vertical), but they can also investigate the interconnection of the modules at a particular abstrac- tion level of interest in the hierarchy. abstraction pyramid discovered b replace the known structure of on Ontology (GO)), but instead provi that may be missing. For example mid identified from a protein-pr work could illuminate the protein levels. Some vertical or horizontal vide additional biological meaning acterized in the GO’s Directed A structure. We divide the analysis of comp tasks: module discovery and mod novelty of our two-way approach synergy of top-down and bottom rithms. This method identifies m fashion and constructs a hierarchy network from the bottom up. In an abstraction of the network to d ferent levels in the hierarchy. divided into three procedures: (1) mity between nodes; (2) extractin the network, represented by a sp partitioning the network based o (3) generating an abstract network ing the same procedures to a new network, we can disclose an a implied in a complex network. Th provided in Figure 2 includes the f Step 1. Input a given network o Step 2. Calculate the proximit nodes and use as the link weig Step 3. Normalize the proxim z-scores; then discard the links a specified threshold to reduc the network. Step 4. Obtain the maximum- from the network and use as th Figure 1 Illustration of vertical and horizontal relationships. Each circle represents a module. Vertical relationships and horizontal relationships are denoted by dashed lines and solid lines, respectively. The thickness of a solid line increases with the importance of the connection. The original network is at the bottom (Level 4). Higher-level networks are an abstraction, to a certain degree, of the next lowest network. Analysis of Biological Networks [Cheng and Hu, 1997] Level of Details (LOD) approach [Luebke et al, 2003] s- C10, organ
  8. 8. Abstraction supports Robust Descriptions • Reduction of computational complexity • Increasing in meaningfulness Volume(x) ≤ a à Bike a < Volume(x) ≤ b à Car Volume(x) > b à Airplane Has(two_wheels & open-body & handelbar & saddle) -> Bicycle Has(four_wheels & body_with_windows) -> Car Has(retractable_wheels & body & wings) -> Airplane Task-dependent Reusable
  9. 9. Basic Properties of Abstraction
  10. 10. Intensional Notion 122 5 Boundaries of Abstraction Vehicle! Land! Vehicle! Sea! Vehicle! Air! Vehicle! Good transport! People! transport! Cart!Truck! Bus! Train! Car! Bicycle! …… ……! AB#918#RS# AH#708#SW# BN#387#LG# …………..# is-a! is-a! is-a! Instance-of! is-a! Fig. 5.2: A possible hierarchical organization of the concept vehicle = “thing used for transporting people or goods”. Transportation may occur on land, sea, or air. A vehicle Coverage Abstraction Abstraction ≠ Generalization Less informative More informative More general Less general
  11. 11. Relative Notion again we do not know what to say: maybe there are important details that the picture did not capture (for instance, the pistils), or the image is even too much detailed (maybe, only the perception of a red field, as in impressionist art, would matter). But, if we look at the picture in Fig. 5.4(b), and we compare picture !"#$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!%#$ Fig. 5.4: (a) Picture of a poppy field. If we only have this picture, it is impossible to say whether it is concrete or abstract. (b) The same picture in black and white. By comparison, this last is less informative than the colored one, because the information referring to the color has been removed; then picture (b) is more abstract than picture (a). [A color version Less abstract More informative (color information) More abstract Less informative (no color information)
  12. 12. Path in an Abstraction Space “Il vero modo et ordine per dissegnar tutte le parti ie membra del corpo humano”, [Fialetti , 1608] 5.1 Characteristic Aspects of Abstraction 127 Fig. 5.6: From Fialetti’s “Il vero modo et ordine per dissegnar tutte le parti ie membra del corpo humano”, 1608. One among a set of studies for drawing eyes. ( c• This artwork may be protected by copyright. It is printed in this book in accordance with fair use principles.) By taking the top-leftmost and bottom right-most drawings in Fig. 5.6, it is really hard, without looking at the intermediate steps, to relate them in any meaningful way. However, the relation between the two clearly appears if we consider tho whole process of stepwise transformations. Abstraction has been considered a process also in Mathematics, where the concept of number is reached, according to Husserl, through a counting process leaving aside all properties of a set of objects, except their numerosity. Lewis [299] defines explicitly abstraction as a process of removing details from the concrete5. Finally, Staub and Stern’s approach to abstraction6 mixes the idea of abstraction as a process and abstraction as a relative notion, as we do; in fact, these authors claim that concepts are obtained by reasoning, starting from the concrete world. Along the reasoning chain abstraction increases, so that the farther from the concrete world a concept is along the chain, the more abstract. As an example, real numbers are more abstract than integers. Even though this approach shares with our view the ideas of process and relativity
  13. 13. Path in an Abstraction Space “Il vero modo et ordine per dissegnar tutte le parti ie membra del corpo humano”, [Fialetti , 1608] 5.1 Characteristic Aspects of Abstraction 127 Fig. 5.6: From Fialetti’s “Il vero modo et ordine per dissegnar tutte le parti ie membra del corpo humano”, 1608. One among a set of studies for drawing eyes. ( c• This artwork may be protected by copyright. It is printed in this book in accordance with fair use principles.) By taking the top-leftmost and bottom right-most drawings in Fig. 5.6, it is really hard, without looking at the intermediate steps, to relate them in any meaningful way. However, the relation between the two clearly appears if we consider tho whole process of stepwise transformations. Abstraction has been considered a process also in Mathematics, where the concept of number is reached, according to Husserl, through a counting process leaving aside all properties of a set of objects, except their numerosity. Lewis [299] defines explicitly abstraction as a process of removing details from the concrete5. Finally, Staub and Stern’s approach to abstraction6 mixes the idea of abstraction as a process and abstraction as a relative notion, as we do; in fact, these authors claim that concepts are obtained by reasoning, starting from the concrete world. Along the reasoning chain abstraction increases, so that the farther from the concrete world a concept is along the chain, the more abstract. As an example, real numbers are more abstract than integers. Even though this approach shares with our view the ideas of process and relativity 5.1 Characteristic Aspects of Abstraction 127 Fig. 5.6: From Fialetti’s “Il vero modo et ordine per dissegnar tutte le parti ie membra del corpo humano”, 1608. One among a set of studies for drawing eyes. ( c• This artwork may be protected by copyright. It is printed in this book in accordance with fair use principles.) Reversible path Intermediate steps can be recovered
  14. 14. Encapsulation Q1 = “How many cars are there in the line ?” Details of the cars are hidden (they are irrelevant to the question) Q2 = “How many red cars are there in the line ?” Details of the cars must be recoverable Information is not lost, in the abstraction process, but only hidden, shielded from the outside view
  15. 15. Abstraction Operators All the operations described can be defined in terms of Abstraction Operators Input = I Output = O O = ω(I,θ)Goldstone and Barsalou [1998] Giunchiglia and Walsh [1992] [Korf, 80] Goldstone and Barsalou [1998] Giunchiglia and Walsh [1992] [Korf, 80] img2 = Thresholding(img1,τ) Operators are implemented via some algorithms
  16. 16. Signals vs Symbols • Abstraction process always moves from richer, “low-level” descriptions (concepts) toward “high-level” ones. During the process, only (hopefully) information irrelevant to the current task is removed from view. • In particular, abstraction establishes a link between signals (at the lowest end of the spectrum) and symbols (at the highest end of the spectrum) • Abstraction acts as a bridge between perceptual processing and symbolic thinking. It tames the complexity of the sensory input, keeps the important information, builds up intermediate concepts to reduce reasoning complexity, and provides us with a re-organized view of the input, ready to be interpreted in the light of our world model. • We humans do not ascribe symbolic features to the sensory world, but we receive raw inputs (images, sounds, …). On the other hand, we do not interact with sets of weights, but with high level concepts and symbols • Abstraction allows the early conflict in AI between numerical and symbolic approaches to be overcome. Both signals and symbols become necessary and cooperating aspects of both natural and artificial thinking.
  17. 17. Acquiring Abstractions How are abstract operators acquired? We do not know how we humans do it Three levels of increasing difficulty 1. Given a set of predefined abstraction operators, we want to choose the best suited to a given situation • Usual approach in Machine Learning, Constraint Satisfaction problems, Planning, Search, Problem Solving, …. 2. Learning an abstraction operator itself • Some approach in Model-based Diagnosis, Constraint Satisfaction, Planning, Machine Learning, … • Deep learning 3. Meta-learning how an abstraction operator can be learned • This is for the future
  18. 18. Deep Learning Deep Learning Data acquisition Learning x f(X) Feature transformation Feature transformation Feature transformation x z1 Classifier f(X)z2 zh ….... Intermediate representations with increasing level of abstraction and meaningfulness (hopefully)
  19. 19. Learning Object Parts while Classifying Groups of pixels (motifs) that occur frequently are memorized as features and reused in various parts of an imageExamples of learned object parts from object categories Learning object parts Faces Cars Elephants Chairs Classifier Parts of objects Segments More complete parts of objects Raw input ω1 ω3 ω2
  20. 20. Local Receptive Fields • Each feature can connect only to a small region of the lower layer • (reduction in complexity) • Similar regions are merged (they share the weights) • The same features can be detected at different positions in the input image • Reduction in the number of free parameters How can intermediate features be created? Pooling • Goal: Robust to local distortion • Approach: Group similar features together to achieve invariance Aggregation operator Equivalence operator
  21. 21. An Architecture for Abstraction • Given a raw input (image, music, written text, …) consisting of elementary signals (pixels, sonds, characters, ...), there are infinite ways of forming sequences of intermediate features. Deep learning uses the output of classification to select useful features (abstraction operators, in our language). The result is task-specific. • We need a more general guiding principle: The best abstractions are those tha are useful in the greater number of different tasks Head Torso Arm Human
  22. 22. Evolution • Multitasks Approach • It is not possible to handle a large number of tasks at the same time • A temporal dimension (evolution) has to be added • A storage to keep the history of learning is necessary LTM = Repository of confirmed abstraction operators and new concepts DLk I O ωk 1, …, ωk n STM ω ωi I O DLh ωh 1, …, ωh m LTM ωj ωk Positive or negative reinforcement signal

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With this comprehensive breakdown of abstraction's multiple layers and components, we can understand and answer the question if abstraction is essential to artificial intelligence. Lorenza Saitta, Università del Piemonte Orientale

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