Semantic Information Pursuit for Multimodal Data Analysis

Lead Research Organisation: University College London
Department Name: Computer Science


In 1948, Shannon published his famous paper "A Mathematical Theory of Communication" [88], which laid the foundations of information theory and led to a revolution in communication technologies. Shannon's fundamental contribution was to provide a precise way by which information could be represented,
quantified and transmitted. Critical to Shannon's ideas was the notion that the content of a message is irrelevant to its transmission, since any signal can be represented in terms of bits.

However, Shannon's theory has some limitations. In 1953, Weaver argued that there are three levels
of communication problems: the technical problem "How accurately can the symbols of
communication be transmitted?", the semantic problem "How precisely do the transmitted symbols
convey the desired meaning?", and the effectiveness problem "How effectively does the received
meaning affect conduct in the desired way?" Hence, a key limitation of Shannon's theory is that it
is limited to the technical problem.

This was also pointed out by Bar-Hillel and Carnap in 1953, who argued that "The Mathematical Theory of Communication, often referred to also as Theory (of Transmission) of Information, as practised nowadays, is not interested in the content of the symbols whose information it measures. The measures, as defined, for instance, by Shannon, have nothing to do with what these symbols symbolise, but only with the frequency of their occurrence." While Bar-Hillel and Carnap argued that "the fundamental concepts of the theory of semantic information can be defined in a straightforward way on the basis of the theory of inductive probability", their work was based primarily on logic rules that were applicable to a very restricted class of
signals (e.g. text). In the last 60 years there has been extraordinary progress in information theory,
signal, image and video processing, statistics, machine learning and optimization, which have led
to dramatic improvements in speech recognition, machine translation, and computer vision technologies.
However, the fundamental question of how to represent, quantify and transmit semantic is what this programme of research shall address.
Description Key finding 1: Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalise this idea and to look for potential applications. We derived an adversarial algorithm for the problem of approximating an unknown quantum state. Although this could be done on universal (large) quantum computers, the adversarial formulation enables us to execute the algorithm on near-term quantum computers.

Key finding 2: Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. We trained quantum circuits to distinguish quantum states and provided an example of machine learning in the quantum setting for a task that has inherently no classical analogue.

Key finding 3: Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrated that more expressive circuits in the same family achieve better accuracy and can be used to classify highly correlated quantum states, for which there is no known efficient classical method.

Key finding 4: We showed that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time.

Key finding 5: The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling clearly limits our ability to do tomography to systems with no more than a few qubits and has been used to argue against the universal validity of quantum mechanics itself. However, from a computational learning theory perspective, it can be shown that, in a probabilistic setting, quantum states can be approximately learned using only a linear number of measurements. We experimentally demonstrate this linear scaling in optical systems with up to 6 qubits.
Exploitation Route Further research.
Sectors Digital/Communication/Information Technologies (including Software)

Description Graph Parameters and Physical Correlations: from Shannon to Connes, via Lovász and Tsirelson 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Industry/Business
Results and Impact Article in ERCIM news
Year(s) Of Engagement Activity 2018
Description ICML Tutorial 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Benjamin Guedj and I gave a tutorial on A Primer on PAC-Bayesian Learning at ICML 2019 one of the two premier conferences in machine learning and artificial intelligence. It was attended by approximately 750 people and was streamed live to a wider audience, see
Year(s) Of Engagement Activity 2019
Description NeurIPS Tutorial 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact It was an invited tutorial at the premier machine learning conference, Neural Information Processing Systems held in December 2018 in Montreal. The audience was over 500 researchers and professional practitioners from industry and business.
Year(s) Of Engagement Activity 2018