Hard Learning Problems Research Articles

On Exploring the Potential of Quantum Auto-Encoder for Learning Quantum Systems.

The frequent interactions between quantum computing and machine learning revolutionize both fields. One prototypical achievement is the quantum auto-encoder (QAE), as the leading strategy to relieve the curse of dimensionality ubiquitous in the quantum world. Despite its attractive capabilities, practical applications of QAE have yet largely unexplored. To narrow this knowledge gap, here, we devise three effective QAE-based learning protocols to address three classically computational hard learning problems when learning quantum systems, which are low-rank state fidelity estimation, quantum Fisher information (QFI) estimation, and Gibbs state preparation. Attributed to the versatility of QAE, our proposals can be readily executed on near-term quantum machines. Besides, we analyze the error bounds of the trained protocols and showcase the necessary conditions to provide practical utility from the perspective of complexity theory. We conduct numerical simulations to confirm the effectiveness of the proposed three protocols. This work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.

Enhancing Reliability and Security: A Configurable Poisoning PUF Against Modeling Attacks

Physically unclonable functions (PUFs) have been widely proposed as hardware primitives for device identification and cryptographic key generation. While strong PUFs provide an exponential number of challenge–response pairs (CRPs) for device authentication, most are vulnerable to machine-learning (ML)-based modeling attacks. Regarding the inherent hard learning problem, adversarial-based PUFs pseudo-randomly switch between several predefined internal states to poison the ML algorithms. However, existing adversarial-based PUFs sacrifice reliability or security against ML attacks. Furthermore, most works only evaluated the ML resistance by empirical experiments, which provides limited evidence for ML resistance. This work explored a novel adversarial-based PUF, Configurable Poisoning PUF (CP PUF), that simultaneously maintains reliability and protects the internal state by a reliability trapdoor. We then connect the proposed CP PUF with the learning parity with noise (LPN) problem to provide a theoretical security guarantee. Experiments show that the reliability of our proposed CP PUF keeps at least 88.9% and outperforms the existing adversarial-based PUFs under different levels of noisy environments. Moreover, the proposed CP PUF achieved a 50.16% accuracy under empirical ML attacks, a near-optimal performance.

When Bad News Become Good News

Hard physical learning problems have been introduced as an alternative option to implement cryptosystems based on hard learning problems. Their high-level idea is to use inexact computing to generate erroneous computations directly, rather than to first compute correctly and add errors afterwards. Previous works focused on the applicability of this idea to the Learning Parity with Noise (LPN) problem as a first step, and formalized it as Learning Parity with Physical Noise (LPPN). In this work, we generalize it to the Learning With Errors (LWE) problem, formalized as Learning With Physical Errors (LWPE). We first show that the direct application of the design ideas used for LPPN prototypes leads to a new source of (mathematical) data dependencies in the error distributions that can reduce the security of the underlying problem. We then show that design tweaks can be used to avoid this issue, making LWPE samples natively robust against such data dependencies. We additionally put forward that these ideas open a quite wide design space that could make hard physical learning problems relevant in various applications. And we conclude by presenting a first prototype FPGA design confirming our claims.

On the Stochasticity of Ultimatum Games

Brenner and Vriend (2006) argued (experimentally and theoretically) that one should not expect proposers in ultimatum games to learn to converge to the subgame perfect Nash equilibrium offer, as finding the optimal offer is a hard learning problem for (boundedly-rational) proposers. In this paper we show that providing the proposers with given (fixed) acceptance probabilities (essentially eliminating the learning task) leads to somewhat lower offers, but still substantially above the monetary payoff-maximizing offer. By using a Risk Attitude test and a Probability Matching test, we show experimentally that the proposers’ attitude with respect to risk, as well as their ability to interpret and deal with probabilities may matter when it comes to making UG offers. Thus, we argue that the lack of convergence to the minimum offers in ultimatum games may be related to the inherent stochasticity of typical UG experiments, highlighting a possible cause of such deviations that seems a complementary explanation to existing ones.

Learning Parity with Physical Noise: Imperfections, Reductions and FPGA Prototype

Hard learning problems are important building blocks for the design of various cryptographic functionalities such as authentication protocols and post-quantum public key encryption. The standard implementations of such schemes add some controlled errors to simple (e.g., inner product) computations involving a public challenge and a secret key. Hard physical learning problems formalize the potential gains that could be obtained by leveraging inexact computing to directly generate erroneous samples. While they have good potential for improving the performances and physical security of more conventional samplers when implemented in specialized integrated circuits, it remains unknown whether physical defaults that inevitably occur in their instantiation can lead to security losses, nor whether their implementation can be viable on standard platforms such as FPGAs. We contribute to these questions in the context of the Learning Parity with Physical Noise (LPPN) problem by: (1) exhibiting new (output) data dependencies of the error probabilities that LPPN samples may suffer from; (2) formally showing that LPPN instances with such dependencies are as hard as the standard LPN problem; (3) analyzing an FPGA prototype of LPPN processor that satisfies basic security and performance requirements.

Learning with Physical Noise or Errors

Hard learning problems have recently attracted significant attention within the cryptographic community, both as a versatile assumption on which to build various protocols, and as a potentially sound basis for lightweight (possibly side-channel and fault resistant) implementations. Yet, in this second case, a recurrent drawback of primitives based on the Learning Parity with Noise and Learning With Errors problems is their additional randomness requirements to generate noise or errors. In parallel, the move towards nanoscale devices renders modern implementations increasingly prone to various types of errors. As a result, inexact computing has emerged as a new paradigm to efficiently deal with the challenges raised by such erroneous computations, and mitigate the cost and power consumption overheads they cause. In this paper, we show that these cryptographic and electronic challenges can actually be turned into new opportunities, and provide an elegant solution one to the other. That is, we show that inexact implementations of inner product computations lead to a natural way to define new Learning with Physical Noise or Error assumptions, paving the way to more efficient and physically secure implementations, with potential interest for securing emerging Internet of Things applications.

An easy-to-hard learning strategy for within-image co-saliency detection

Within-image co-saliency detection is to detect/highlight the common saliency (similar-appearance salient objects) in a single image. Ideally, it can be solved by detecting each individual salient object first and then comparing them, which is possible for some images with simple representations. However, in practice, this way is not accurate and robust for some images with complex representations. In this paper, we propose an easy-to-hard learning strategy to solve this problem. By directly localizing and comparing salient objects in simple images, superpixel confidences as co-salient objects are inferred by an easy learning method, which provide promising but also noisy supervisions for complex images. Therefore, within-image co-saliency detection in complex images can be modeled as a hard learning problem with noisy labels. A multi-scale Multiple Instance Learning (MIL) model together with a new sampling method is proposed to solve this hard learning problem with noisy labels. Experimental results show that the proposed method achieves the best performance on a public benchmark dataset and two synthetic datasets.

Introducing a Novel Hybrid Artificial Intelligence Algorithm to Optimize Network of Industrial Applications in Modern Manufacturing

Recent advances in modern manufacturing industries have created a great need to track and identify objects and parts by obtaining real-time information. One of the main technologies which has been utilized for this need is the Radio Frequency Identification (RFID) system. As a result of adopting this technology to the manufacturing industry environment, RFID Network Planning (RNP) has become a challenge. Mainly RNP deals with calculating the number and position of antennas which should be deployed in the RFID network to achieve full coverage of the tags that need to be read. The ultimate goal of this paper is to present and evaluate a way of modelling and optimizing nonlinear RNP problems utilizing artificial intelligence (AI) techniques. This effort has led the author to propose a novel AI algorithm, which has been named “hybrid AI optimization technique,” to perform optimization of RNP as a hard learning problem. The proposed algorithm is composed of two different optimization algorithms: Redundant Antenna Elimination (RAE) and Ring Probabilistic Logic Neural Networks (RPLNN). The proposed hybrid paradigm has been explored using a flexible manufacturing system (FMS), and results have been compared with Genetic Algorithm (GA) that demonstrates the feasibility of the proposed architecture successfully.

Efficient Authentication from Hard Learning Problems

We construct efficient authentication protocols and message authentication codes (MACs) whose security can be reduced to the learning parity with noise (LPN) problem. Despite a large body of work—starting with the $${\mathsf {HB}}$$ protocol of Hopper and Blum in 2001—until now it was not even known how to construct an efficient authentication protocol from LPN which is secure against man-in-the-middle attacks. A MAC implies such a (two-round) protocol.

PAutomaC: a probabilistic automata and hidden Markov models learning competition

Approximating distributions over strings is a hard learning problem. Typical techniques involve using finite state machines as models and attempting to learn these; these machines can either be hand built and then have their weights estimated, or built by grammatical inference techniques: the structure and the weights are then learned simultaneously. The Probabilistic Automata learning Competition (PAutomaC), run in 2012, was the first grammatical inference challenge that allowed the comparison between these methods and algorithms. Its main goal was to provide an overview of the state-of-the-art techniques for this hard learning problem. Both artificial data and real data were presented and contestants were to try to estimate the probabilities of strings. The purpose of this paper is to describe some of the technical and intrinsic challenges such a competition has to face, to give a broad state of the art concerning both the problems dealing with learning grammars and finite state machines and the relevant literature. This paper also provides the results of the competition and a brief description and analysis of the different approaches the main participants used.

Learning the areas of expertise of classifiers in an ensemble

Abstract There are various machine learning algorithms for extracting patterns from data; but recently, decision combination has become popular to improve accuracy over single learner systems. The fundamental idea behind combining the decisions of an ensemble of classifiers is that different classifiers most probably misclassify different patterns and by suitably combining the decisions of complementary classifiers, accuracy can be improved. In this paper, we investigate two kinds of classifier systems which are capable of estimating how much to weight each base classifier dynamically; during the calculation of the overall output for a given test data instance: (1) In ‘referee-based system’, a referee is associated with each classifier which learns the area of expertise of its associated classifier and weights it accordingly. (2) However, ‘gating system’ learns to partition the input space among all classifiers. Each referee in referee-based system learns a two-class problem (i.e., whether to use or not to use a classifier) whereas a gating system learns an L-class problem assigning the input to one of L base classifiers. Our analysis on 20 datasets from different domains and a classifier pool including 21 base learning algorithms reveals that the gating system tends to concentrate on a few of the base classifiers whereas a use of referees leads to a more balanced use of the base classifiers. Moreover, in the case of referees, it is better to use a small subset of base classifiers, instead of a single one. The study shows that, by using well-trained selection unit (referee or gating), we can get as high accuracy as using all the base classifiers (to combine their decisions) with drastic decrease in the number of base classifiers used, and also improve accuracy. The improvement is significant especially in cases when none of the base classifiers has high accuracy and it indicates that selecting classifiers appears promising as a means of solving hard learning problems.

A unified framework for multilayer high order CNN

We propose a unified notation for representing any CNN topology. The framework presented here is an attempt to provide a common base for the future development of more general CNN structures, such as multilayer and/or high-order CNNs, which have already been of great interest in many disciplines including biology, chemistry, ecology, physics, etc. The paper is divided in two parts: first (Sections 1–3) it is shown how to cast any CNN structure into a so called ‘compact form’, from which we can derive a vector of ordinary differential equations (ODE) which can be used for mathematical analysis and for computer simulation of the CNN; in the second part (Section 4) some examples show how multilayer structures are required to solve hard learning problems such as the parity problem. © 1998 John Wiley & Sons, Ltd.

A unified framework for multilayer high order CNN

We propose a unified notation for representing any CNN topology. The framework presented here is an attempt to provide a common base for the future development of more general CNN structures, such as multilayer and/or high-order CNNs, which have already been of great interest in many disciplines including biology, chemistry, ecology, physics, etc. The paper is divided in two parts: first (Sections 1–3) it is shown how to cast any CNN structure into a so called ‘compact form’, from which we can derive a vector of ordinary differential equations (ODE) which can be used for mathematical analysis and for computer simulation of the CNN; in the second part (Section 4) some examples show how multilayer structures are required to solve hard learning problems such as the parity problem. © 1998 John Wiley & Sons, Ltd.

Hardware implementation of a pulse-stream neural network

The authors describe the design and test of an artificial neural network, using a pulse-stream approach, that is implemented using BiCMOS technology. Networks are constructed from arrays of customised neuron chips and synapse chips. The neuron chip uses novel circuitry to implement an accurate sigmoid transfer characteristic. The synapse chip uses a new pulse-stream implementation of the differential amplifier and requires only five transistors to produce a linear multiplier. Measured results from the chips show that the neuron has an accurate sigmoid transfer characteristic and gradient suitable for the error backpropagation learning algorithm. The synapse has excellent 1% linearity and properties suitable for multiplication. The chips have been used to implement a three-layer artificial neural network which has been tested using hard learning problems.