Quantum Algorithm for Finding the Negative Curvature Direction

Non-convex optimization is an essential problem in the field of machine learning. Optimization methods for non-convex problems can be roughly di- vided into first-order methods and second-order methods, depending on the or- der of the derivative to the objective function they used. Generally, to find the local minima, the second-order methods are applied to find the effective direction to escape the saddle point. Specifically, finding the Negative Curvature is considered as the subroutine to analyze the characteristic of the saddle point. However, the calculation of the Negative Curvature is expensive, which prevents the practical usage of second-order algorithms. In this thesis, we present an efficient quantum algorithm aiming to find the negative curvature direction for escaping the saddle point, which is a critical subroutine for many second-order non-convex optimization algorithms. We prove that our algorithm could produce the target state corresponding to the negative curvature direction with query complexity O ̃(polylog(d) ε^(-1)), where d is the dimension of the optimization function. The quantum negative curvature finding algorithm is exponentially faster than any known classical method, which takes time at least O(dε^(-1/2)). Moreover, we propose an efficient quantum algorithm to achieve the classical read-out of the target state. Our classical read-out algorithm runs exponentially faster on the degree of d than existing counterparts

Salience Coding in the Basal Forebrain and the Heterogeneous Underpinnings Underlying Novelty Computations

Humans and animals are consistently learning from the environment by interacting with it and getting feedback from their actions. In the environment, some objects are more important than others, because they are associated with reward, uncertainty, surprise, or novelty etc. These objects are salient to the animal. Salient objects attract attention and orientation, increase arousal, facilitate learning and memory, and affect reinforcement learning and credit assignment. However, the neural basis to support these effects is still not fully understood.We first studied how the basal forebrain, one of the principal sources of modulation of the neocortex, encodes salience events. We found two types of neurons that process salient events in distinct manners: one with phasic burst activity to cues predicting salient events and one with ramping activity anticipating such events. Bursting neurons respond to reward itself and cues that predict the magnitude, probability, and timing of reward. However, they do not have a selective response to reward omission. Thus, bursting neurons signal surprise associated with external events, which is different from the reward prediction error signaled by the midbrain dopamine neurons. Furthermore, they discriminate fully expected novel visual objects from familiar objects and respond to object-sequence violations. In contrast, ramping neurons predict the timing of many salient, novel, and surprising events. Their ramping activity is highly sensitive to the subjects\u27 confidence in event timing and on average encodes the subjects\u27 surprise after unexpected events occur. These data suggest that the primate BF contains mechanisms to anticipate the timing of a diverse set of salient external events (via tonic ramping activity) and to rapidly deploy cognitive resources when these events occur (via phasic bursting activity). Then we sailed out to study one special salience signal – Novelty. The basal forebrain responds to novelty, but the neuronal mechanisms of novelty detection remain unclear. Prominent theories propose that novelty is either derived from the computation of recency or is a form of sensory surprise. Here, we used high-channel electrophysiology in primates to show that, in many prefrontal, temporal, and subcortical brain areas, object novelty sensitivity is related to both computations of recency (the sensitivity to how long ago a stimulus was experienced) and sensory surprise (violation of predictions about incoming sensory information). Also, we studied neuronal novelty-to-familiarity transformations during learning across many days and found a diversity of timescales in neurons\u27 learning rates and between-session forgetting rates within and across brain regions that is well suited to support flexible behavior and learning in response to novelty. These findings show that novelty sensitivity arises on multiple timescales across single neurons due to diverse related computations of sensory surprise and recency, and shed light on the logic and computational underpinnings of novelty detection in the primate brain

Training Theory of Variational Quantum Machine Learning

Recent advancements in machine learning have revolutionised research across various fields. Despite their success, conventional learning techniques are hindered by their significant computational resources and energy requirements. Prompted by recent experimental breakthroughs in quantum computing, variational quantum machine learning (QML) – machine learning integrated with variational quantum circuits (VQCs) – has emerged as a promising alternative. Nonetheless, the theoretical framework underpinning the advantages of variational QML is still rudimentary. Specifically, the training of VQCs faces several challenges, such as the barren plateau problem, where the gradient diminishes exponentially with an increasing qubits. A related issue arises in variational QML training, where the convergence rate is exponentially small. In this thesis, we present theoretically guaranteed solutions to these challenges. First, we construct innovative circuit architectures to address the vanishing gradient problem in deep VQCs. We propose quantum controlled-layer and quantum ResNet structures, demonstrating that the expected gradient norm's lower bound is unaffected by the increase in qubits and circuit depth. Next, we introduce an initialization strategy to mitigate the vanishing gradient issue in general deep quantum circuits. We prove that Gaussian-initialized parameters ensure the gradient norm's decay rate remains inversely polynomial despite the increase in qubit numbers and circuit depth. Finally, we propose a novel and effective theory for analysing the training of quantum neural networks with moderate depths. We prove that, under certain randomness conditions in the circuits and datasets, training converges linearly with a rate inversely proportional to the dataset size. Our approach surpasses previous results, achieving exponentially larger convergence rates with modest depth, or conversely, requiring exponentially less depth for equivalent rates

Reproductive Health Financing, Service Availability and Needs in Rural China

In the last decade, major changes have occurred in the financing of health services in rural China. Simultaneously, major changes have occurred in the organisation and delivery of maternal and child health and family planning services. The effect of these two sets of changes on reproductive health service utilisation and outcomes has neither been fully described nor evaluated

Quantum Imitation Learning

Despite remarkable successes in solving various complex decision-making tasks, training an imitation learning (IL) algorithm with deep neural networks (DNNs) suffers from the high computation burden. In this work, we propose quantum imitation learning (QIL) with a hope to utilize quantum advantage to speed up IL. Concretely, we develop two QIL algorithms, quantum behavioural cloning (Q-BC) and quantum generative adversarial imitation learning (Q-GAIL). Q-BC is trained with a negative log-likelihood loss in an off-line manner that suits extensive expert data cases, whereas Q-GAIL works in an inverse reinforcement learning scheme, which is on-line and on-policy that is suitable for limited expert data cases. For both QIL algorithms, we adopt variational quantum circuits (VQCs) in place of DNNs for representing policies, which are modified with data re-uploading and scaling parameters to enhance the expressivity. We first encode classical data into quantum states as inputs, then perform VQCs, and finally measure quantum outputs to obtain control signals of agents. Experiment results demonstrate that both Q-BC and Q-GAIL can achieve comparable performance compared to classical counterparts, with the potential of quantum speed-up. To our knowledge, we are the first to propose the concept of QIL and conduct pilot studies, which paves the way for the quantum era.Comment: Manuscript submitted to a journal for review on January 5, 202

Efficient State Read-out for Quantum Machine Learning Algorithms

Many quantum machine learning (QML) algorithms that claim speed-up over their classical counterparts only generate quantum states as solutions instead of their final classical description. The additional step to decode quantum states into classical vectors normally will destroy the quantum advantage in most scenarios because all existing tomographic methods require runtime that is polynomial with respect to the state dimension. In this Letter, we present an efficient readout protocol that yields the classical vector form of the generated state, so it will achieve the end-to-end advantage for those quantum algorithms. Our protocol suits the case that the output state lies in the row space of the input matrix, of rank $r$, that is stored in the quantum random access memory. The quantum resources for decoding the state in $\ell_2$-norm with $\epsilon$ error require $\text{poly}(r,1/\epsilon)$ copies of the output state and $\text{poly}(r, \kappa^r,1/\epsilon)$ queries to the input oracles, where $\kappa$ is the condition number of the input matrix. With our read-out protocol, we completely characterise the end-to-end resources for quantum linear equation solvers and quantum singular value decomposition. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure, which we believe, will be of independent interest.Comment: Comments are welcome

Surprise and recency in novelty detection in the primate brain

Primates and other animals must detect novel objects. However, the neuronal mechanisms of novelty detection remain unclear. Prominent theories propose that visual object novelty is either derived from the computation of recency (how long ago a stimulus was experienced) or is a form of sensory surprise (stimulus unpredictability). Here, we use high-channel electrophysiology in primates to show that in many primate prefrontal, temporal, and subcortical brain areas, object novelty detection is intertwined with the computations of recency and sensory surprise. Also, distinct circuits could be engaged by expected versus unexpected sensory surprise. Finally, we studied neuronal novelty-to-familiarity transformations during learning across many days. We found a diversity of timescales in neurons\u27 learning rates and between-session forgetting rates, both within and across brain areas, that are well suited to support flexible behavior and learning in response to novelty. Our findings show that novelty sensitivity arises on multiple timescales across single neurons due to diverse but related computations of sensory surprise and recency and shed light on the computational underpinnings of novelty detection in the primate brain

Th17 i IL-17 osiągają wyższe stężenia w przebiegu martwicy głowy kości udowej i są dodatnio skorelowane z nasileniem bólu

Objective: Synovitis associated with osteonecrosis of the femoral head (ONFH) is responsible for several clinical symptoms. However, the mechanisms underlying synovitis and the inflammatory environment remain unclear. This study analyzed the proinflammatory mediation expression of IL-17 and Th17, which perform key functions in regulating inflammatory processes in the inflamed synovium and peripheral blood in ONFH. Methods: Synovial fluid from the hips of 23 patients and 5 controls was collected during surgery, and peripheral blood samples were obtained from 34 patients and 9 controls. The expression of IL-17 in the synovium was detected by immunohistochemistry, and the levels of Th17 and IL-17 in the blood were measured by flow cytometry and ELISA. Pain assessment was performed for all the patients and controls. Results: An inflamed synovium was characterized by increased leukocyte infiltration and IL-17 expression in comparison with the control. Preoperative levels of Th17 and IL-17 were significantly higher in the peripheral blood of the ONFH group than those in the controls. The symptoms were also positively correlated with the Th17 levels of the ONFH patients. Conclusion: Th17 cells were recruited to an inflamed synovium, and inflammatory cytokine IL-17 was expressed at an increased level in the hip synovium of ONFH patients, which possibly contributed to clinical syndrome development. Overall, this study will help in identifying new therapeutic strategies for ONFH, especially the targeting of IL-17 to decrease inflammation and pain. Wstęp: Zapalenie błony maziowej związane z martwicą głowy kości udowej (osteonecrosis of the femoral head; ONFH) odpowiada za kilka objawów klinicznych, jednak mechanizmy leżące u podstaw zapalenia błony maziowej oraz środowisko zapalne pozostają niejasne. W niniejszym badaniu poddano analizie ekspresję mediatora zapalenia IL-17 na limfocytach Th17, które pełnią kluczową rolę w regulowaniu procesów zapalnych w objętej stanem zapalnym błonie maziowej i krwi obwodowej w przebiegu ONFH. Materiał i metody: Podczas zabiegów operacyjnych pobrano maź stawową ze stawów biodrowych 23 pacjentów i 5 osób z grupy kon­trolnej, natomiast próbki krwi obwodowej uzyskano od 34 pacjentów i 9 osób z grupy kontrolnej. Ekspresję IL-17 w błonie maziowej wykrywano za pomocą metody immunohistochemicznej, a stężenie Th17 i IL-17 we krwi mierzono metodą cytometrii przepływowej i metodą ELISA. U wszystkich pacjentów i osób z grupy kontrolnej oceniono parametr bólu. Wyniki: Cechą charakterystyczną objętej stanem zapalnym błony maziowej był wzrost nacieczenia limfocytarnego i ekspresji IL-17 w porównaniu z grupą kontrolną. Stężenie Th17 i IL-17 przed wykonaniem zabiegów operacyjnych było znacząco wyższe we krwi obwodowej pacjentów z martwicą głowy kości udowej niż grupy kontrolnej. Również objawy były u tych pacjentów dodatnio skorelowane z poziomem Th17. Wnioski: Limfocyty Th17 były rekrutowane do objętej stanem zapalnym błony maziowej, a cytokina zapalna IL-17 ulegała ekspresji na zwiększonym poziomie w błonie maziowej stawu biodrowego pacjentów z martwicą głowy kości udowej, co prawdopodobnie przyczyniło się do rozwoju zespołu objawów klinicznych. Uogólniając, niniejsze badanie może pomóc zidentyfikować nowe strategie terapeutyczne w martwicy głowy kości udowej, w szczególności ukierunkowane na IL-17 w celu zmniejszenia stanu zapalnego i bólu