Anna Goldie, Azalia Mirhoseini, Mustafa Yazgan, Joe Wenjie Jiang, Ebrahim Songhori, Shen Wang, Young-Joon Lee, Eric Johnson, Omkar Pathak, Azade Nova, Jiwoo Pak, Andy Tong, Kavya Srinivasa, William Hang, Emre Tuncer, Quoc V. Le, James Laudon, Richard Ho, Roger Carpenter, Jeff Dean <<<

Abstract We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single- and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications. <<<

Quantum Natural Language Processing (QNLP) deals with the design and implementation of NLP models intended to be run on quantum hardware. In this paper, we present results on the first NLP experiments conducted on Noisy Intermediate-Scale Quantum (NISQ) computers for datasets of size greater than 100 sentences. Exploiting the formal similarity of the compositional model of meaning by Coecke, Sadrzadeh, and Clark (2010) with quantum theory, we create representations for sentences that have a natural mapping to quantum circuits. We use these representations to implement and successfully train NLP models that solve simple sentence classification tasks on quantum hardware. We conduct quantum simulations that compare the syntax-sensitive model of Coecke et al. with two baselines that use less or no syntax; specifically, we implement the quantum analogues of a “bag-of-words” model, where syntax is not taken into account at all, and of a word-sequence model, where only word order is respected. We demonstrate that all models converge smoothly both in simulations and when run on quantum hardware, and that the results are the expected ones based on the nature of the tasks and the datasets used. Another important goal of this paper is to describe in a way accessible to AI and NLP researchers the main principles, process and challenges of experiments on quantum hardware. Our aim in doing this is to take the first small steps in this unexplored research territory and pave the way for practical Quantum Natural Language Processing. <<<

Curriculum learning and imitation learning have been leveraged extensively inthe robotics domain. However, minimal research has been done on leveragingthese ideas on control tasks over highly stochastic time-series data. Here, wetheoretically and empirically explore these approaches in a representativecontrol task over complex time-series data. We implement the fundamental ideasof curriculum learning via data augmentation, while imitation learning isimplemented via policy distillation from an oracle. Our findings reveal thatcurriculum learning should be considered a novel direction in improvingcontrol-task performance over complex time-series. Our ample random-seedout-sample empirics and ablation studies are highly encouraging for curriculumlearning for time-series control. These findings are especially encouraging aswe tune all overlapping hyperparameters on the baseline -- giving an advantageto the baseline. On the other hand, we find that imitation learning should beused with caution. <<<

Abstract There are various indicators i.e. Relative Strength Index (RSI), Moving Average Convergence Divergence (MACD) , Stochastic Oscillator which have advantages in applications to determine not only market movements with buying and selling decisions in Computational Finance, but have significant drawbacks that discrepancies are easy to match against the best trading times due to fixed order-triggering boundaries and delay problems. For example, RSI ’s 70 and 30 overbuy and oversell are fixed boundaries. Orders can only be triggered when RSI’s value exceeds one of the boundaries. Its computation only considers past market situation prompting indicators like RSI to trigger orders with delay. In this paper, we proposed a method to reduce these problems with advanced AI technologies to generate indicators’ buy and sell signals executed in the best trading time. Recurrent Neural Network (RNN) has outstanding performance to learn time-series data automatic with long-time sequences but ordinary RNN units such as Long-Short-Term-Memory(LSTM) are unable to decipher the relationships between time units, so-called context. Hence, researchers have proposed an algorithm based on RNNs’ Attention Mechanism allowing RNNs to learn information such as chaotic attributes and Quantum properties contained in time sequences. Chaos Theory and Quantum Finance Theory (QFT) are also proposed to simulate these two features. One of the well-performed QFT models is Quantum Price Level (QPL) to simulate all possible vibration levels to locate price. The system used in this paper consists of two components - neural network and fuzzy logic. Neural networks are used to predict future data and to solve indicators lagging problem whereas fuzzy logic is used to solve fixed order-triggering boundaries problem. By combining these two core components, the proposed model has obtained remarkable results in backtesting previous data that it is possible for these methods to make better investment decisions when market changes constantly. <<<

Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning, owing to their reputed difficulty among the world's best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004. <<<

Here we represent human lives in a way that shares structural similarity to language, and we exploit this similarity to adapt natural language processing techniques to examine the evolution and predictability of human lives based on detailed event sequences. We do this by drawing on a comprehensive registry dataset, which is available for Denmark across several years, and that includes information about life-events related to health, education, occupation, income, address and working hours, recorded with day-to-day resolution. We create embeddings of life-events in a single vector space, showing that this embedding space is robust and highly structured. Our models allow us to predict diverse outcomes ranging from early mortality to personality nuances, outperforming state-of-the-art models by a wide margin. Using methods for interpreting deep learning models, we probe the algorithm to understand the factors that enable our predictions. Our framework allows researchers to discover potential mechanisms that impact life outcomes as well as the associated possibilities for personalized interventions. <<<

Classical reinforcement learning (CRL) has been widely applied in neuroscience and psychology; however, quantum reinforcement learning (QRL), which shows superior performance in computer simulations, has never been empirically tested on human decision-making. Moreover, all current successful quantum models for human cognition lack connections to neuroscience. Here we studied whether QRL can properly explain value-based decision-making. We compared 2 QRL and 12 CRL models by using behavioural and functional magnetic resonance imaging data from healthy and cigarette-smoking subjects performing the Iowa Gambling Task. In all groups, the QRL models performed well when compared with the best CRL models and further revealed the representation of quantum-like internal-state-related variables in the medial frontal gyrus in both healthy subjects and smokers, suggesting that value-based decision-making can be illustrated by QRL at both the behavioural and neural levels. <<<

Traditional diagnostic formulations of psychotic disorders have low correspondence with underlying disease neurobiology. This has led to a growing interest in using brain-based biomarkers to capture biologically-informed psychosis constructs. Building upon our prior work on the B-SNIP Psychosis Biotypes, we aimed to examine whether structural MRI (an independent biomarker not used in the Biotype development) can effectively classify the Biotypes. Whole brain voxel-wise grey matter density (GMD) maps from T1-weighted images were used to train and test (using repeated randomized train/test splits) binary L2-penalized logistic regression models to discriminate psychosis cases (n = 557) from healthy controls (CON, n = 251). A total of six models were evaluated across two psychosis categorization schemes: (i) three Biotypes (B1, B2, B3) and (ii) three DSM diagnoses (schizophrenia (SZ), schizoaffective (SAD) and bipolar (BD) disorders). Above-chance classification accuracies were observed in all Biotype (B1 = 0.70, B2 = 0.65, and B3 = 0.56) and diagnosis (SZ = 0.64, SAD = 0.64, and BD = 0.59) models. However, the only model that showed evidence of specificity was B1, i.e., the model was able to discriminate B1 vs. CON and did not misclassify other psychosis cases (B2 or B3) as B1 at rates above nominal chance. The GMD-based classifier evidence for B1 showed a negative association with an estimate of premorbid general intellectual ability, regardless of group membership, i.e. psychosis or CON. Our findings indicate that, complimentary to clinical diagnoses, the B-SNIP Psychosis Biotypes may offer a promising approach to capture specific aspects of psychosis neurobiology. <<<

In the mid 1980s, while working on establishing completion theorems for equivariant Algebraic K-Theory similar to the well-known Atiyah-Segal completion theorem for equivariant topological K-theory, the late Robert Thomason found the strong finiteness conditions that are required in such theorems to be too restrictive. Then he made a conjecture on the existence of a completion theorem in the sense of Atiyah and Segal for equivariant algebraic G-theory, for actions of linear algebraic groups on schemes that holds without any of the strong finiteness conditions that are required in such theorems proven by him, and also appearing in the original Atiyah-Segal theorem. The main goal of the present paper is to provide a proof of this conjecture in as broad a context as possible, making use of the technique of derived completion, and to consider several of the applications. Our solution is broad enough to allow actions by all linear algebraic groups, irrespective of whether they are connected or not, and acting on any quasi-projective scheme of finite type over a field, irrespective of whether they are regular or projective. This allows us therefore to consider the equivariant algebraic G-Theory of large classes of varieties like all toric varieties (for the action of a torus) and all spherical varieties (for the action of a reductive group). Restricting to actions by split tori, we are also able to consider actions on algebraic spaces. Moreover, the restriction that the base scheme be a field is also not required often, but is put in mainly to simplify some of our exposition. These enable us to obtain a wide range of applications, some of which are briefly sketched and which we plan to explore in detail in the future. In fact, we discuss an extension of our results to equivariant homotopy K-theory along with various Riemann-Roch theorems in a sequel. A comparison of our results with previously known results, none of which made use of derived completions, shows that without the use of derived completions one can only obtain results which are indeed very restrictive. <<<

We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub and Smale for computations over $\mathbb{R}$ (which in turn followed those of the classical, discrete, complexity theory as laid down by Cook, Karp, and Levin, among others). In particular, we focus on complexity classes of decision problems and, paramount among them, on appropriate versions of the classes $\mathsf{P}$, $\mathsf{NP}$, and $\mathsf{EXP}$ of polynomial, nondeterministic polynomial, and exponential time, respectively. We prove some basic relationships between these complexity classes, and provide natural NP-complete problems. <<<

Julien Perolat, Bart De Vylder, Daniel Hennes, Eugene Tarassov, Florian Strub, Vincent de Boer, Paul Muller, Jerome T Connor, Neil Burch, Thomas Anthony, Stephen McAleer, Romuald Elie, Sarah H Cen, Zhe Wang, Audrunas Gruslys, Aleksandra Malysheva, Mina Khan, Sherjil Ozair, Finbarr Timbers, Toby Pohlen, Tom Eccles, Mark Rowland, Marc Lanctot, Jean-Baptiste Lespiau, Bilal Piot, Shayegan Omidshafiei, Edward Lockhart, Laurent Sifre, Nathalie Beauguerlange, Remi Munos, David Silver, Satinder Singh, Demis Hassabis, Karl Tuyls <<<

We introduce DeepNash, an autonomous agent that plays the imperfect information game Stratego at a human expert level. Stratego is one of the few iconic board games that artificial intelligence (AI) has not yet mastered. It is a game characterized by a twin challenge: It requires long-term strategic thinking as in chess, but it also requires dealing with imperfect information as in poker. The technique underpinning DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego through self-play from scratch. DeepNash beat existing state-of-the-art AI methods in Stratego and achieved a year-to-date (2022) and all-time top-three ranking on the Gravon games platform, competing with human expert players. <<<

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with N≥3) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors. <<<