Reformulation of the No-Free-Lunch Theorem for Entangled Datasets.

The no-free-lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training dataset. With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process with quantum training data. However, in the quantum setting, the training data can possess entanglement, a strong correlation with no classical analog. In this Letter, we show that entangled datasets lead to an apparent violation of the (classical) NFL theorem. This motivates a reformulation that accounts for the degree of entanglement in the training set. As our main result, we prove a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. We employ Rigetti's quantum computer to test both the classical and quantum NFL theorems. Our Letter establishes that entanglement is a commodity in quantum machine learning.

Inference-Based Quantum Sensing.

In a standard quantum sensing (QS) task one aims at estimating an unknown parameter θ, encoded into an n-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response R(θ) (i.e., changes in the measurement outcomes). For simple cases the form of R(θ) is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this Letter, we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, R(θ) can be fully characterized by only measuring the system response at 2n+1 parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than δ, if one measures the system response with a number of shots that scales only as Ω(log^{3}(n)/δ^{2}). Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.

Barren Plateaus Preclude Learning Scramblers.

Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. We prove a no-go theorem for learning an unknown scrambling process with QML, showing that it is highly probable for any variational Ansatz to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. This implies that the required resources scale exponentially even when strategies to avoid such scaling (e.g., from Ansatz-based barren plateaus or no-free-lunch theorems) are employed. Furthermore, we numerically and analytically extend our results to approximate scramblers. Hence, our work places generic limits on the learnability of unitaries when lacking prior information.

A Mechanism for Synaptic Copy Between Neural Circuits.

Cortical oscillations are central to information transfer in neural systems. Significant evidence supports the idea that coincident spike input can allow the neural threshold to be overcome and spikes to be propagated downstream in a circuit. Thus, an observation of oscillations in neural circuits would be an indication that repeated synchronous spiking may be enabling information transfer. However, for memory transfer, in which synaptic weights must be being transferred from one neural circuit (region) to another, what is the mechanism? Here, we present a synaptic transfer mechanism whose structure provides some understanding of the phenomena that have been implicated in memory transfer, including nested oscillations at various frequencies. The circuit is based on the principle of pulse-gated, graded information transfer between neural populations.

Mutual Information and Information Gating in Synfire Chains.

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains-SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains.

Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Recently experimental evidence has been presented suggesting that neural information is encoded and transferred in packets, i.e., in stereotypical, correlated spiking patterns of neural activity. Due to their relevance to coherent spiking, synfire chains are one of the main theoretical constructs that have been appealed to in order to describe coherent spiking and information transfer phenomena. However, for some time, it has been known that synchronous activity in feedforward networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to propagate. This has limited the classical synfire chain's ability to explain graded neuronal responses. Recently, we have shown that pulse-gated synfire chains are capable of propagating graded information coded in mean population current or firing rate amplitudes. In particular, we showed that it is possible to use one synfire chain to provide gating pulses and a second, pulse-gated synfire chain to propagate graded information. We called these circuits synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded information can rapidly cascade through a neural circuit, and show a correspondence between this type of transfer and a mean-field model in which gating pulses overlap in time. We show that SGSCs are robust in the presence of variability in population size, pulse timing and synaptic strength. Finally, we demonstrate the computational capabilities of SGSC-based information coding by implementing a self-contained, spike-based, modular neural circuit that is triggered by streaming input, processes the input, then makes a decision based on the processed information and shuts itself down.

A mechanism for graded, dynamically routable current propagation in pulse-gated synfire chains and implications for information coding.

Neural oscillations can enhance feature recognition (Azouz and Gray Proceedings of the National Academy of Sciences of the United States of America, 97, 8110-8115 2000), modulate interactions between neurons (Womelsdorf et al. Science, 316, 1609-01612 2007), and improve learning and memory (Markowska et al. The Journal of Neuroscience, 15, 2063-2073 1995). Numerical studies have shown that coherent spiking can give rise to windows in time during which information transfer can be enhanced in neuronal networks (Abeles Israel Journal of Medical Sciences, 18, 83-92 1982; Lisman and Idiart Science, 267, 1512-1515 1995, Salinas and Sejnowski Nature Reviews. Neuroscience, 2, 539-550 2001). Unanswered questions are: 1) What is the transfer mechanism? And 2) how well can a transfer be executed? Here, we present a pulse-based mechanism by which a graded current amplitude may be exactly propagated from one neuronal population to another. The mechanism relies on the downstream gating of mean synaptic current amplitude from one population of neurons to another via a pulse. Because transfer is pulse-based, information may be dynamically routed through a neural circuit with fixed connectivity. We demonstrate the transfer mechanism in a realistic network of spiking neurons and show that it is robust to noise in the form of pulse timing inaccuracies, random synaptic strengths and finite size effects. We also show that the mechanism is structurally robust in that it may be implemented using biologically realistic pulses. The transfer mechanism may be used as a building block for fast, complex information processing in neural circuits. We show that the mechanism naturally leads to a framework wherein neural information coding and processing can be considered as a product of linear maps under the active control of a pulse generator. Distinct control and processing components combine to form the basis for the binding, propagation, and processing of dynamically routed information within neural pathways. Using our framework, we construct example neural circuits to 1) maintain a short-term memory, 2) compute time-windowed Fourier transforms, and 3) perform spatial rotations. We postulate that such circuits, with automatic and stereotyped control and processing of information, are the neural correlates of Crick and Koch's zombie modes.

The Effect of Examiner Variability on Multiple Canine Stifle Kinematic Gait Collections in a 3-Dimensional Model.

OBJECTIVE: To evaluate examiner variability in a superficial skin marker model of canine stifle kinematics. STUDY DESIGN: Experimental. ANIMALS: Six clinically normal dogs. METHODS: Dogs had 11 retroreflective markers fixed to the skin on the right hindlimb. Dogs were trotted 5 times through the calibrated testing space and this was repeated on 4 different testing days. Examiner A applied all markers to a dog and collected 6 good trials for analysis. The markers were then removed and Examiner B immediately repeated the process on the same dog. This was repeated for each dog on the 4 testing days. The dogs were trotted at a velocity of 1.70-2.10 m/s through the testing space to obtain the dynamic data sets. Comparisons were performed with Fourier analysis and Generalized Indicator Function Analysis (GIFA). Significance was set at P < .05 for all comparisons. RESULTS: Fourier analysis and GIFA found differences within and between examiners. Fourier analysis found no differences in sagittal and transverse planes for the experienced (A) and novice examiner (B), respectively. Fourier analysis detected fewer differences for the experienced examiner (A). CONCLUSION: Variability occurs within and between examiners using the same kinematic model. Transverse and frontal plane kinematics produce variable results between examiners. Prior experience with the model reduces the amount of variability and results in consistent and repeatable sagittal plane kinematic data collection.

Out-of-distribution generalization for learning quantum dynamics.

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.

Improved dimensionally-reduced visual cortical network using stochastic noise modeling.

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.

Drosophila TRPA channel modulates sugar-stimulated neural excitation, avoidance and social response.

Drosophila melanogaster postfeeding larvae show food-averse migration toward food-free habitats before metamorphosis. This developmental switching from food attraction to aversion is regulated by a neuropeptide Y (NPY)-related brain signaling peptide. We used the fly larva model to delineate the neurobiological basis of age-restricted response to environmental stimuli. Here we provide evidence for a fructose-responsive chemosensory pathway that modulates food-averse migratory and social behaviors. We found that fructose potently elicited larval food-averse behaviors, and painless (pain), a transient receptor potential channel that is responsive to noxious stimuli, was required for the fructose response. A subset of pain-expressing sensory neurons have been identified that show pain-dependent excitation by fructose. Although evolutionarily conserved avoidance mechanisms are widely appreciated for their roles in stress coping and survival, their biological importance in animal physiology and development remains unknown. Our findings demonstrate how an avoidance mechanism is recruited to facilitate animal development.

Quantum simulation of operator spreading in the chaotic Ising model.

There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a four-spin Ising model as a function of space, time, and integrability. Reaching four spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of a ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.

Generalization in quantum machine learning from few training data.

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as [Formula: see text]. When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to [Formula: see text]. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

The effect of marker location variability on noninvasive canine stifle kinematics.

OBJECTIVE: Evaluate the effect of marker placement on kinematics of the canine stifle in 3 distinct hindlimb models. STUDY DESIGN: In vivo biomechanical study. ANIMALS: Normal adult mixed-breed dogs (n=5). METHODS: Ten retroreflective markers were affixed to the skin on the right rear leg of each dog to establish normal stifle kinematics. Four additional markers were placed around the greater trochanter (GT), 2 m cranial, caudal, dorsal, and ventral to evaluate single marker placement variability on kinematic model data. Dogs were walked and trotted 5 times through the calibrated space. Sagittal flexion and extension angle waveforms were acquired during each trial with 3 models that were produced simultaneously during each gait. The GT marker was reassigned to 1 of the 4 additional locations (cranial, caudal, dorsal, and ventral) to alter the kinematic model. Comparison of sagittal flexion and extension angle waveforms was performed with Generalized Indicator Function Analysis. RESULTS: Each model provided consistent equivalent sagittal flexion-extension data. Analysis revealed statistically significant differences between all GT locations. The differences were greatest in the cranial and caudal locations for all models. CONCLUSIONS: Deviation of the GT marker in the cranial/caudal direction from an anatomically normal position produces a greater degree of difference than deviation in a dorsal/ventral direction.

Time-resolved NMR: extracting the topology of complex enzyme networks.

The use of nondestructive NMR spectroscopy for enzymatic studies offers unique opportunities to identify nearly all enzymatic byproducts and detect unstable short-lived products or intermediates at the molecular level; however, numerous challenges must be overcome before it can become a widely used tool. The biosynthesis of acetyl-coenzyme A (acetyl-CoA) by acetyl-CoA synthetase is used here as a case study for the development of an analytical NMR-based time-course assay platform. We describe an algorithm to deconvolve superimposed spectra into spectra for individual molecules, and further develop a model to simulate the acetyl-CoA synthetase enzyme reaction network using the data derived from time-course NMR. Simulation shows indirectly that synthesis of acetyl-CoA is mediated via an enzyme-bound intermediate (possibly acetyl-AMP) and is accompanied by a nonproductive loss from an intermediate. The ability to predict enzyme function based on partial knowledge of the enzymatic pathway topology is also discussed.

Dimensionally-reduced visual cortical network model predicts network response and connects system- and cellular-level descriptions.

Systems-level neurophysiological data reveal coherent activity that is distributed across large regions of cortex. This activity is often thought of as an emergent property of recurrently connected networks. The fact that this activity is coherent means that populations of neurons may be thought of as the carriers of information, not individual neurons. Therefore, systems-level descriptions of functional activity in the network often find their simplest form as combinations of the underlying neuronal variables. In this paper, we provide a general framework for constructing low-dimensional dynamical systems that capture the essential systems-level information contained in large-scale networks of neurons. We demonstrate that these dimensionally-reduced models are capable of predicting the response to previously un-encountered input and that the coupling between systems-level variables can be used to reconstruct cellular-level functional connectivities. Furthermore, we show that these models may be constructed even in the absence of complete information about the underlying network.

Comparison of canine stifle kinematic data collected with three different targeting models.

OBJECTIVE: To model the kinematics of the canine stifle in 3 dimensions using the Joint Coordinate System (JCS) and compare the JCS method with linear and segmental models. STUDY DESIGN: In vivo biomechanical study. ANIMALS: Normal adult mixed breed dogs (n=6). METHODS: Dogs had 10 retroreflective markers affixed to the skin on the right pelvic limb. Dogs were walked and trotted 5 times through the calibrated space and the procedure was repeated 5 days later. Sagittal flexion and extension angle waveforms acquired during each trial with all 3 models (JCS, Linear, and Segmental) were produced simultaneously during each gait. The JCS method provided additional internal/external and abduction/adduction angles. Comparison of sagittal flexion and extension angle waveforms was performed with generalized indicator function analysis (GIFA) and Fourier analysis. A normalization procedure was performed. RESULTS: Each model provided consistent equivalent sagittal flexion-extension data. The JCS provided consistent additional internal/external and abduction/adduction. Sagittal waveform differences were found between methods and testing days for each dog at a walk and a trot with both GIFA and Fourier analysis. After normalization, differences were less with Fourier analysis and were unaltered with GIFA. CONCLUSIONS: Whereas all methods produced similar flexion-extension waveforms, JCS provided additional valuable data. CLINICAL RELEVANCE: The JCS model provided sagittal plane flexion/extension data as well as internal/external rotation and abduction/adduction data.

Variational consistent histories as a hybrid algorithm for quantum foundations.

Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the Consistent Histories formalism, which has previously been employed to study quantum cosmology, quantum paradoxes, and the quantum-to-classical transition. We present a variational hybrid quantum-classical algorithm for finding consistent histories, which should revitalize interest in this formalism by allowing classically impossible calculations to be performed. In our algorithm, the quantum computer evaluates the decoherence functional (with exponential speedup in both the number of qubits and the number of times in the history) and a classical optimizer adjusts the history parameters to improve consistency. We implement our algorithm on a cloud quantum computer to find consistent histories for a spin in a magnetic field and on a simulator to observe the emergence of classicality for a chiral molecule.

Imaging neural events in zebrafish larvae with linear structured illumination light sheet fluorescence microscopy.

Light sheet fluorescence microscopy (LSFM) is a powerful tool for investigating model organisms including zebrafish. However, due to scattering and refractive index variations within the sample, the resulting image often suffers from low contrast. Structured illumination (SI) has been combined with scanned LSFM to remove out-of-focus and scattered light using square-law detection. Here, we demonstrate that the combination of LSFM with linear reconstruction SI can further increase resolution and contrast in the vertical and axial directions compared to the widely adopted root-mean square reconstruction method while using the same input images. We apply this approach to imaging neural activity in 7-day postfertilization zebrafish larvae. We imaged two-dimensional sections of the zebrafish central nervous system in two colors at an effective frame rate of 7 frames per second.

The evolution of fidelity in sensory systems.

We investigate the effect that noise has on the evolution of measurement strategies and competition in populations of organisms with sensory systems of differing fidelities. We address two questions motivated by experimental and theoretical work on sensory systems in noisy environments: (1) How complex must a sensory system be in order to face the need to develop adaptive measurement strategies that change depending on the noise level? (2) Does the principle of competitive exclusion for sensory systems force one population to win out over all others? We find that the answer to the first question is that even very simple sensory systems will need to change measurement strategies depending on the amount of noise in the environment. Interestingly, the answer to the second question is that, in general, at most two populations with different fidelity sensory systems may co-exist within a single environment.