Subsymbolic Representations Research Articles

Embedding Ontologies in the Description Logic ALC by Axis-Aligned Cones

This paper is concerned with knowledge graph embedding with background knowledge, taking the formal perspective of logics. In knowledge graph embedding, knowledge— expressed as a set of triples of the form (a R b) (“a is R-related to b”)—is embedded into a real-valued vector space. The embedding helps exploiting geometrical regularities of the space in order to tackle typical inductive tasks of machine learning such as link prediction. Recent embedding approaches also consider incorporating background knowledge, in which the intended meanings of the symbols a, R, b are further constrained via axioms of a theory. Of particular interest are theories expressed in a formal language with a neat semantics and a good balance between expressivity and feasibility. In that case, the knowledge graph together with the background can be considered to be an ontology. This paper develops a cone-based theory for embedding in order to advance the expressivity of the ontology: it works (at least) with ontologies expressed in the description logic ALC, which comprises restricted existential and universal quantifiers, as well as concept negation and concept disjunction. In order to align the classical Tarskian Style semantics for ALC with the sub-symbolic representation of triples, we use the notion of a geometric model of an ALC ontology and show, as one of our main results, that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a geometric model based on cones. The geometric model, if treated as a partial model, can even be chosen to be faithful, i.e., to reflect all and only the knowledge captured by the ontology. We introduce the class of axis-aligned cones and show that modulo simple geometric operations any distributive logic (such as ALC) interpreted over cones employs this class of cones. Cones are also attractive from a machine learning perspective on knowledge graph embeddings since they give rise to applying conic optimization techniques.

The Tensor Brain: A Unified Theory of Perception, Memory, and Semantic Decoding.

We present a unified computational theory of an agent's perception and memory. In our model, both perception and memory are realized by different operational modes of the oscillating interactions between a symbolic index layer and a subsymbolic representation layer. The two layers form a bilayer tensor network (BTN). The index layer encodes indices for concepts, predicates, and episodic instances. The representation layer broadcasts information and reflects the cognitive brain state; it is our model of what authors have called the "mental canvas" or the "global workspace." As a bridge between perceptual input and the index layer, the representation layer enables the grounding of indices by their subsymbolic embeddings, which are implemented as connection weights linking both layers. The propagation of activation to earlier perceptual processing layers in the brain can lead to embodiments of indices. Perception and memories first create subsymbolic representations, which are subsequently decoded semantically to produce sequences of activated indices that form symbolic triple statements. The brain is a sampling engine: only activated indices are communicated to the remaining parts of the brain. Triple statements are dynamically embedded in the representation layer and embodied in earlier processing layers: the brain speaks to itself. Although memory appears to be about the past, its main purpose is to support the agent in the present and the future. Recent episodic memory provides the agent with a sense of the here and now. Remote episodic memory retrieves relevant past experiences to provide information about possible future scenarios. This aids the agent in decision making. "Future" episodic memory, based on expected future events, guides planning and action. Semantic memory retrieves specific information, which is not delivered by current perception, and defines priors for future observations. We argue that it is important for the agent to encode individual entities, not just classes and attributes. Perception is learning: episodic memories are constantly being formed, and we demonstrate that a form of self-supervised learning can acquire new concepts and refine existing ones. We test our model on a standard benchmark data set, which we expanded to contain richer representations for attributes, classes, and individuals. Our key hypothesis is that obtaining a better understanding of perception and memory is a crucial prerequisite to comprehending human-level intelligence.

Classical Planning in Deep Latent Space

Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose Latplan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), Latplan learns a complete propositional PDDL action model of the environment. Later, when a pair of images representing the initial and the goal states (planning inputs) is given, Latplan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. We evaluate Latplan using image-based versions of 6 planning domains: 8-puzzle, 15-Puzzle, Blocksworld, Sokoban and Two variations of LightsOut.

Urban-GAN: An artificial intelligence-aided computation system for plural urban design

The current urban design computation is mostly centered on the professional designer while ignoring the plural dimension of urban design. In addition, available public participation computational tools focus mainly on information and idea sharing, leaving the public excluded in design generation because of their lack of design expertise. To address such an issue, this study develops Urban-GAN, a plural urban design computation system, to provide new technical support for design empowerment, allowing the public to generate their own designs. The sub-symbolic representation and artificial intelligence techniques of deep convolutional neural networks, case-based reasoning, and generative adversarial networks are used to acquire and embody design knowledge as the density function, and generate design schemes with this knowledge. The system consists of an urban form database and five process models through which the user with little design expertise can select urban form cases, generate designs similar to those cases, and make design decisions. The Urban-GAN is applied to hypothetical design experiments, which show that the user is able to apply the system to successfully generate distinctive designs following the urban form “styles” in Manhattan, Portland, and Shanghai. This study further extends the discussion about the plural urban design computation to general reflections on the goals and values in AI technique application in planning and design.

Language Models Explain Word Reading Times Better Than Empirical Predictability.

Though there is a strong consensus that word length and frequency are the most important single-word features determining visual-orthographic access to the mental lexicon, there is less agreement as how to best capture syntactic and semantic factors. The traditional approach in cognitive reading research assumes that word predictability from sentence context is best captured by cloze completion probability (CCP) derived from human performance data. We review recent research suggesting that probabilistic language models provide deeper explanations for syntactic and semantic effects than CCP. Then we compare CCP with three probabilistic language models for predicting word viewing times in an English and a German eye tracking sample: (1) Symbolic n-gram models consolidate syntactic and semantic short-range relations by computing the probability of a word to occur, given two preceding words. (2) Topic models rely on subsymbolic representations to capture long-range semantic similarity by word co-occurrence counts in documents. (3) In recurrent neural networks (RNNs), the subsymbolic units are trained to predict the next word, given all preceding words in the sentences. To examine lexical retrieval, these models were used to predict single fixation durations and gaze durations to capture rapidly successful and standard lexical access, and total viewing time to capture late semantic integration. The linear item-level analyses showed greater correlations of all language models with all eye-movement measures than CCP. Then we examined non-linear relations between the different types of predictability and the reading times using generalized additive models. N-gram and RNN probabilities of the present word more consistently predicted reading performance compared with topic models or CCP. For the effects of last-word probability on current-word viewing times, we obtained the best results with n-gram models. Such count-based models seem to best capture short-range access that is still underway when the eyes move on to the subsequent word. The prediction-trained RNN models, in contrast, better predicted early preprocessing of the next word. In sum, our results demonstrate that the different language models account for differential cognitive processes during reading. We discuss these algorithmically concrete blueprints of lexical consolidation as theoretically deep explanations for human reading.

Cognition, Meaning and Kinship: Connectionist Models of Cultural Representation

Traditional anthropological models of kinship employ rule-based classical semantics to account for the meanings of kinship, clanship and the attribution of kin terms. This article uses cognitively-based, prototype semantics and distributed, sub-symbolic representations to explore the meanings of kinship relations among the Managalase of Papua New Guinea.

Adapting Neural Turing Machines for linguistic assessments aggregation in neural-symbolic decision support systems

Introduction: The construction of integrated neurosymbolic systems is an urgent and challenging task. Building neurosymbolic decision support systems requires new approaches to represent knowledge about a problem situation and to express symbolic reasoning at the subsymbolic level. Purpose: Development of neural network architectures and methods for effective distributed knowledge representation and subsymbolic reasoning in decision support systems in terms of algorithms for aggregation of fuzzy expert evaluations to select alternative solutions. Methods: Representation of fuzzy and uncertain estimators in a distributed form using tensor representations; construction of a trainable neural network architecture for subsymbolic aggregation of linguistic estimators. Results: The study proposes two new methods of representation of linguistic assessments in a distributed form. The first approach is based on the possibility of converting an arbitrary linguistic assessment into a numerical representation and consists in converting this numerical representation into a distributed one by converting the number itself into a bit string and further forming a matrix storing the distributed representation of the whole expression for aggregating the assessments. The second approach to translating linguistic assessments to a distributed representation is based on representing the linguistic assessment as a tree and coding this tree using the method of tensor representations, thus avoiding the step of translating the linguistic assessment into a numerical form and ensuring the transition between symbolic and subsymbolic representations of linguistic assessments without any loss of information. The structural elements of the linguistic assessment are treated as fillers with their respective positional roles. A new subsymbolic method of aggregation of linguistic assessments is proposed, which consists in creating a trainable neural network module in the form of a Neural Turing Machine. Practical relevance: The results of the study demonstrate how a symbolic algorithm for aggregation of linguistic evaluations can be implemented by connectionist (or subsymbolic) mechanisms, which is an essential requirement for building distributed neurosymbolic decision support systems.

Neural probabilistic logic programming in DeepProbLog

We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic programming language ProbLog can be adapted for the new language. We theoretically and experimentally demonstrate that DeepProbLog supports (i) both symbolic and subsymbolic representations and inference, (ii) program induction, (iii) probabilistic (logic) programming, and (iv) (deep) learning from examples. To the best of our knowledge, this work is the first to propose a framework where general-purpose neural networks and expressive probabilistic-logical modeling and reasoning are integrated in a way that exploits the full expressiveness and strengths of both worlds and can be trained end-to-end based on examples.

A connectionist account of the relational shift and context sensitivity in the development of generalisation

Similarity-based generalisation is fundamental to human cognition, and the ability to draw analogies based on relational similarities between superficially different domains is crucial for reasoning and inference. Learning to base generalisation on shared relations rather than (or in the face of) shared perceptual features has been identified as an important developmental milestone. However, recent research has highlighted the context-sensitivity of generalisation: children and adults use perceptual similarity to make inferences in some cases and relational similarity in others, a finding that suggests people track the predictive validity of different types of inferences. Here we demonstrate that this pattern of behaviour naturally emerges over the course of development in a domain-general statistical learning model that employs distributed, sub-symbolic representations. We suggest that this model offers a parsimonious account of the development of context-sensitive, similarity-based generalisation and may provide several advantages over other popular structured or symbolic approaches to modelling relational inference.

Data-driven Conceptual Spaces: Creating Semantic Representations For Linguistic Descriptions Of Numerical Data

There is an increasing need to derive semantics from real-world observations to facilitate natural information sharing between machine and human. Conceptual spaces theory is a possible approach and has been proposed as mid-level representation between symbolic and sub-symbolic representations, whereby concepts are represented in a geometrical space that is characterised by a number of quality dimensions. Currently, much of the work has demonstrated how conceptual spaces are created in a knowledge-driven manner, relying on prior knowledge to form concepts and identify quality dimensions. This paper presents a method to create semantic representations using data-driven conceptual spaces which are then used to derive linguistic descriptions of numerical data. Our contribution is a principled approach to automatically construct a conceptual space from a set of known observations wherein the quality dimensions and domains are not known a priori. This novelty of the approach is the ability to select and group semantic features to discriminate between concepts in a data-driven manner while preserving the semantic interpretation that is needed to infer linguistic descriptions for interaction with humans. Two data sets representing leaf images and time series signals are used to evaluate the method. An empirical evaluation for each case study assesses how well linguistic descriptions generated from the conceptual spaces identify unknown observations. Furthermore, comparisons are made with descriptions derived on alternative approaches for generating semantic models.

Learning a bidirectional mapping between human whole-body motion and natural language using deep recurrent neural networks

Linking human whole-body motion and natural language is of great interest for the generation of semantic representations of observed human behaviors as well as for the generation of robot behaviors based on natural language input. While there has been a large body of research in this area, most approaches that exist today require a symbolic representation of motions (e.g. in the form of motion primitives), which have to be defined a-priori or require complex segmentation algorithms. In contrast, recent advances in the field of neural networks and especially deep learning have demonstrated that sub-symbolic representations that can be learned end-to-end usually outperform more traditional approaches, for applications such as machine translation. In this paper we propose a generative model that learns a bidirectional mapping between human whole-body motion and natural language using deep recurrent neural networks (RNNs) and sequence-to-sequence learning. Our approach does not require any segmentation or manual feature engineering and learns a distributed representation, which is shared for all motions and descriptions. We evaluate our approach on 2 846 human whole-body motions and 6 187 natural language descriptions thereof from the KIT Motion-Language Dataset. Our results clearly demonstrate the effectiveness of the proposed model: We show that our model generates a wide variety of realistic motions only from descriptions thereof in form of a single sentence. Conversely, our model is also capable of generating correct and detailed natural language descriptions from human motions.

Classical Planning in Deep Latent Space: Bridging the Subsymbolic-Symbolic Boundary

Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose LatPlan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), and a pair of images representing the initial and the goal states (planning inputs), LatPlan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. The contribution of this paper is twofold: (1) State Autoencoder, which finds a propositional state representation of the environment using a Variational Autoencoder. It generates a discrete latent vector from the images, based on which a PDDL model can be constructed and then solved by an off-the-shelf planner. (2) Action Autoencoder / Discriminator, a neural architecture which jointly finds the action symbols and the implicit action models (preconditions/effects), and provides a successor function for the implicit graph search. We evaluate LatPlan using image-based versions of 3 planning domains: 8-puzzle, Towers of Hanoi and LightsOut.

Ingredients of intelligence: From classic debates to an engineering roadmap.

We were encouraged by the broad enthusiasm for building machines that learn and think in more human-like ways. Many commentators saw our set of key ingredients as helpful, but there was disagreement regarding the origin and structure of those ingredients. Our response covers three main dimensions of this disagreement: nature versus nurture, coherent theories versus theory fragments, and symbolic versus sub-symbolic representations. These dimensions align with classic debates in artificial intelligence and cognitive science, although, rather than embracing these debates, we emphasize ways of moving beyond them. Several commentators saw our set of key ingredients as incomplete and offered a wide range of additions. We agree that these additional ingredients are important in the long run and discuss prospects for incorporating them. Finally, we consider some of the ethical questions raised regarding the research program as a whole.

Towards a Domain Specific Language for Sensor-Based Actions

Actual robot systems are typically used within an industrial environment, where they perform tasks in the areas of manufacturing, assembly, or inspection. Many of these tasks require the definition and execution of sensor-based motions. Such motions are typically defined using a subsymbolic representation like manipulation primitive nets [1] or iTaSC [2]. These representations are only suitable for experts in the domain of robotics because they require the definition of low-level parameters like setpoints, control strategies, or task frames. Since the application domains of robot systems shall be extended to SMEs or private households, existing representations lack in an intuitive interface for users without expert knowledge in the area of robotics. In this work, we describe an intuitive interface for the definition of sensor-based actions. Our approach is based on manipulation primitive nets and consists of a transformation between the subsymbolic manipulation primitive nets and a symbolic user interface, described by a domain specific language.

Autonomous generation of symbolic representations through subsymbolic activities

This paper explores an approach for autonomous generation of symbolic representations from an agent's subsymbolic activities within the agent-environment interaction. The paper describes a psychologically plausible general framework and its various methods for autonomously creating symbolic representations. The symbol generation is accomplished within, and is intrinsic to, a generic and comprehensive cognitive architecture for capturing a wide variety of psychological processes (namely, CLARION). This work points to ways of obtaining more psychologically/cognitively realistic symbolic and subsymbolic representations within the framework of a cognitive architecture, and accentuates the relevance of such an approach to cognitive science and psychology.

Cognitive Developmental Grasp Robots: From Infant Development to Computational Modeling

We addressed the idea that a hybrid of symbolic and sub-symbolic representations is the best method to represent cognition for developmental robots. Basing the learning mechanisms of a cognitive developmental robot on principles of human-like learning, we developed an intelligent grasping robot architecture based on the hierarchical learning. The hybrid of different representations and memory in IGR also gave a new direction for developing robots with high intelligence.

Theory learning as stochastic search in the language of thought

We present an algorithmic model for the development of children's intuitive theories within a hierarchical Bayesian framework, where theories are described as sets of logical laws generated by a probabilistic context-free grammar. We contrast our approach with connectionist and other emergentist approaches to modeling cognitive development. While their subsymbolic representations provide a smooth error surface that supports efficient gradient-based learning, our symbolic representations are better suited to capturing children's intuitive theories but give rise to a harder learning problem, which can only be solved by exploratory search. Our algorithm attempts to discover the theory that best explains a set of observed data by performing stochastic search at two levels of abstraction: an outer loop in the space of theories and an inner loop in the space of explanations or models generated by each theory given a particular dataset. We show that this stochastic search is capable of learning appropriate theories in several everyday domains and discuss its dynamics in the context of empirical studies of children's learning.

Proto logic and neural subsymbolic reasoning

The subsymbolic representation of the world often corresponds to a pattern that mirrors the world as described by the biological sense organs. Sparse binary vectors can describe subsymbolic representations, which can be efficiently stored in associative memories. According to the production system theory, a geometrically based problem-solving model can be defined as a production system operating on subsymbols. Our goal is to form a sequence of associations, which lead to a desired state represented by subsymbols, from an initial state represented by subsymbols. A simple and universal heuristic function can be defined, which takes into account the relationship between the vector and the corresponding similarity of the represented object or state in the real world. The manipulation of the subsymbols is described by a simple proto logic, which verifies if a subset of subsymbols is present in a set of subsymbols.

Improving Perception to Make Distant Connections Closer

One of the challenges for perceptually grounded accounts of high-level cognition is to explain how people make connections and draw inferences between situations that superficially have little in common. Evidence suggests that people draw these connections even without having explicit, verbalizable knowledge of their bases. Instead, the connections are based on sub-symbolic representations that are grounded in perception, action, and space. One reason why people are able to spontaneously see relations between situations that initially appear to be unrelated is that their eventual perceptions are not restricted to initial appearances. Training and strategic deployment allow our perceptual processes to deliver outputs that would have otherwise required abstract or formal reasoning. Even without people having any privileged access to the internal operations of perceptual modules, these modules can be systematically altered so as to better serve our high-level reasoning needs. Moreover, perceptually based processes can be altered in a number of ways to closely approximate formally sanctioned computations. To be concrete about mechanisms of perceptual change, we present 21 illustrations of ways in which we alter, adjust, and augment our perceptual systems with the intention of having them better satisfy our needs.

Unifying Conceptual Spaces: Concept Formation in Musical Creative Systems

We examine Gardenfors' theory of conceptual spaces, a geometrical form of knowledge representation (Conceptual spaces: The geometry of thought, MIT Press, Cambridge, 2000), in the context of the general Creative Systems Framework introduced by Wiggins (J Knowl Based Syst 19(7):449---458, 2006a; New Generation Comput 24(3):209---222, 2006b). Gardenfors' theory offers a way of bridging the traditional divide between symbolic and sub-symbolic representations, as well as the gap between representational formalism and meaning as perceived by human minds. We discuss how both these qualities may be advantageous from the point of view of artificial creative systems. We take music as our example domain, and discuss how a range of musical qualities may be instantiated as conceptual spaces, and present a detailed conceptual space formalisation of musical metre.