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In this work, a non-Gaussian cMERA tensor network for interacting quantum field theories (icMERA) is presented. This consists of a continuous tensor network circuit in which the generator of the entanglement renormalization of the wavefunction is nonperturbatively extended with nonquadratic variational terms. The icMERA circuit nonperturbatively implements a set of scale dependent nonlinear transformations on the fields of the theory, which suppose a generalization of the scale dependent linear transformations induced by the Gaussian cMERA circuit. Here we present these transformations for the case of self-interacting scalar and fermionic field theories. Finally, the icMERA tensor network is fully optimized for the $\lambda \phi^4$ theory in $(1+1)$ dimensions. This allows us to evaluate, nonperturbatively, the connected parts of the two- and four-point correlation functions. Our results show that icMERA wavefunctionals encode proper non-Gaussian correlations of the theory, thus providing a new variational tool to study phenomena related with strongly interacting field theories., Comment: v2: (43 pages) substantial improvement to the optimization procedure of the circuit for the $\phi^4$ model (Section 5.3). A new appendix is added to illustrate what are the features of the ground state of the $\lambda \phi^4$ theory that captured by the icMERA tensor network. Accepted for publication in JHEP

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This spreading can be analyzed with the spectral form factor, which is defined in terms of the analytic continuation of the partition function. The latter is equivalent to the survival probability of a thermofield double state under unitary dynamics. Using random matrices from the Gaussian unitary ensemble (GUE) as Hamiltonians for the time evolution, we obtain exact analytical expressions at finite N for the survival probability. Numerical simulations of the survival probability with matrices taken from the Gaussian orthogonal ensemble (GOE) are also provided. The GOE is more suitable for our comparison with numerical results obtained with a disordered spin chain with local interactions. Common features between the random matrix and the realistic disordered model in the chaotic regime are identified. The differences that emerge as the spin model approaches a many-body localized phase are also discussed.

The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the entanglement entropy of the half space for a free scalar theory through a Gaussian cMERA circuit. We obtain the correct entropy written in terms of the optimized cMERA variational parameter, the local density of disentanglers. Accordingly, using the entanglement entropy production per unit scale, we study local areas in the bulk of the tensor network in terms of the differential entanglement generated along the cMERA flow. This result spurs us to establish an explicit relation between the cMERA variational parameter and the radial component of a dual AdS geometry through the Ryu-Takayanagi formula. Finally, based on recent formulations of non-Gaussian cMERA circuits, we argue that the entanglement entropy for the half space can be written as an integral along the renormalization scale whose measure is given by the Fisher information metric of the cMERA circuit. Consequently, a straightforward relation between AdS geometry and the Fisher information metric is also established., Comment: 18 pages, 1 figure. Some references added in which v2 is the final version published in Fortschritte der Physik. Progress of Physics

A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through a class of variational non-Gaussian wavefunctionals for which expectation values of local operators can be efficiently calculated analytically and in a closed form. The method consists of a series of scale-dependent nonlinear canonical transformations on the fields of the theory under consideration. Here, the $\lambda\, \phi^4$ and the sine-Gordon scalar theories are used to illustrate how non-perturbative effects far beyond the Gaussian approximation are obtained by considering the energy functional and the correlation functions of the theory., Comment: 6 + 5 pages, 1 figure; v2: minor clarifications added, published version

The entanglement renormalization flow of a (1+1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity., 20 pages. v3 minor corrections. Accepted for publication in Physics Letters B

A universal relation is established between the quantum work probability distribution of an isolated driven quantum system and the Loschmidt echo dynamics of a two-mode squeezed state. When the initial density matrix is canonical, the Loschmidt echo of the purified double thermofield state provides a direct measure of information scrambling and can be related to the analytic continuation of the partition function. Information scrambling is then described by the quantum work statistics associated with the time-reversal operation on a single copy, associated with the sudden negation of the system Hamiltonian., Comment: 6 pages, 1 figure, published version

Using the path integral associated to a cMERA tensor network, we provide an operational definition for the complexity of a cMERA circuit/state which is relevant to investigate the complexity of states in quantum field theory. In this framework, it is possible to explicitly establish the correspondence (Minimal) Complexity $=$ (Least) Action. Remarkably, it is also shown how the cMERA complexity action functional can be seen as the action of a Liouville field theory, thus establishing a connection with two dimensional quantum gravity. Concretely, the Liouville mode is identified with the variational parameter defining the cMERA circuit. The rate of complexity growth along the cMERA renormalization group flow is obtained and shown to saturate limits which are in close resemblance to the fundamental bounds to the speed of evolution in unitary quantum dynamics, known as quantum speed limits. We also show that the complexity of a cMERA circuit measured through these complexity functionals, can be cast in terms of the variationally-optimized amount of left-right entanglement created along the cMERA renormalization flow. Our results suggest that the patterns of entanglement in states of a QFT could determine their dual gravitational descriptions through a principle of least complexity., Comment: 26 pages, improved presentation, new section on real time evolution, references added

Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling., Comment: 11+6pp, 5 figures. v3: version accepted for publication in Quantum

Quantum speed limits set an upper bound to the rate at which a quantum system can evolve and as such can be used to analyze the scrambling of information. To this end, we consider the survival probability of a thermofield double state under unitary time-evolution which is related to the analytic continuation of the partition function. We provide an exponential lower bound to the survival probability with a rate governed by the inverse of the energy fluctuations of the initial state. Further, we elucidate universal features of the non-exponential behavior at short and long times of evolution that follow from the analytic properties of the survival probability and its Fourier transform, both for systems with a continuous and a discrete energy spectrum. We find the spectral form factor in a number of illustrative models, notably we obtain the exact answer in the Gaussian unitary ensemble for any $N$ with excellent agreement with recent numerical studies. We also discuss the relationship of our findings to models of black hole information loss, such as the Sachdev-Ye-Kitaev model dual to AdS$_2$ as well as higher-dimensional versions of AdS/CFT., 33 pages, 6 figures, published version

We study a way of establishing a pure entangled state between two segments of a 1D ring using impenetrable bosons. The two bosons are initially simply placed at two positions on the ring which is an unentangled state. After some time evolution, we project the segments to a pure state through coarse grained measurements which ascertain whether there is a particle present in a given segment without revealing any information about its position within the segment. Subject to finding a particle in each segment, we quantify the entanglement established between the segments through the von Neumann entropy of a subsystem. We also investigate whether this entanglement increases with the number of particles and compare the entanglement in dynamical and ground states.

We investigate the spatio-temporal dynamics of hand preshaping during prehension through a biologically plausible neural model. The hand grip formation is generated through neural modulation of basic motor programs that can be rescaled to accommodate different task demands. The model assumes a timing role to propioceptive reafferent information generated by the reaching component of the movement, avoiding the need of a preorganized functional temporal structure for the timing of prehension as some previous models have proposed. Predictions of the model in both Normal and Altered initial hand aperture conditions match key kinematic features present in human data.

This paper proposes a neural network architecture for learning of grasping tasks. The multineural network model presented in this work, allows acquisition of different neural representations of the grasping task through a successive learning over two stages in a strategy that uses already learned representations for the acquisition of the subsequent knowledge. Systematic computer simulations have been carried out in order to test learning and generalization capabilities of the system. The neural activity at different subparts of the artificial neural network during its performance phase, is compared to the activity of populations of real neurons in areas AIP and F5 of the distributed parieto-frontal biological neural network involved in visual guidance of grasping. A more biologically plausible development of the model presented here is also discussed. The proposed model can be also used as a high level controller for a robotic dextrous hand during learning and execution of grasping tasks.

In this paper, the problem of precision reaching applications in robotic systems for scenarios with static and non-static objects has been considered and a solution based on a modular neural architecture has been proposed and implemented. The goal of this solution is to combine robustness and capability mapping trajectories from two biologically plausible neural network sub-modules: Hyper RBF and AVITE. The Hyper Basis Radial Function (HypRBF) neural network solves the inverse kinematic in redundant robotic systems, while the Adaptive Vector Integration to End-Point (AVITE) visuo-motor neural model quickly maps the difference vector between current and desired position in both spatial (visual information) and motor coordinates (propioceptive information). The anthropomorphic behaviour of the proposed architecture for reaching and tracking tasks in presence of spatial perturbations has been validated over a real arm-head robotic platform.

In this paper, a solution based on hyper radial basis functions networks (HRBF) for learning inverse kinematics in redundant robots is presented. This model has been implemented in two different visuo-motor robotic platforms for reaching and grasping applications. The obtained results allow to verify the robustness and accuracy capabilities of this neural model for reaching and tracking objects as well as to give a solution when redundant robots are considered. Therefore, the invariance of the proposed visuo-motor architecture for different arm-head relative configurations is demonstrated.

We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a quantum quench are also analyzed. To this end, a full tensor network representation of the action of local unitary operations on the bridge state is proposed. This amounts to a tensor network which grows in size by adding succesive layers of bridge states. Finally, we discuss on the holographic interpretation of the tensor network through a notion of distance within the network which emerges from its entanglement distribution., 23 pages, 8 figures, JHEP style, Comments are wellcome

We investigate a recent conjecture connecting the AdS/CFT correspondence and entanglement renormalization tensor network states (MERA). The proposal interprets the tensor connectivity of the MERA states associated to quantum many body systems at criticality, in terms of a dual holographic geometry which accounts for the qualitative aspects of the entanglement and the correlations in these systems. In this work, some generic features of the entanglement entropy and the two point functions in the ground state of one dimensional gapped systems are considered through a tensor network state. The tensor network is builded up as an hybrid composed by a finite number of MERA layers and a matrix product state (MPS) acting as a cap layer. Using the holographic formula for the entanglement entropy, here it is shown that an asymptotically AdS metric can be associated to the hybrid MERA-MPS state. The metric is defined by a function that manages the growth of the minimal surfaces near the capped region of the geometry. Namely, it is shown how the behaviour of the entanglement entropy and the two point correlators in the tensor network, remains consistent with a geometric computation which only depends on this function. From these observations, an explicit connection between the entanglement structure of the tensor network and the function which defines the geometry is provided., 25 pages, 6 Postscript figures. The v2 is a major revisioned version with a new title and results to be published in JHEP

In this paper we formulate the $xp$ model on the AdS$_2$ spacetime. We find that the spectrum of the Hamiltonian has positive and negative eigenvalues, whose absolute values are given by a harmonic oscillator spectrum, which in turn coincides with that of a massive Dirac fermion in AdS$_2$. We extend this result to generic $xp$ models which are shown to be equivalent to a massive Dirac fermion on spacetimes whose metric depend of the $xp$ Hamiltonian. Finally, we construct the generators of the isometry group SO(2,1) of the AdS$_2$ spacetime, and discuss the relation with conformal quantum mechanics., Comment: 24 pages, 1 figure, some comments and new references added

Several parameters related to the timing, grip force and load force involved in a precision grasping task were studied in patients with Parkinson's disease (PD) at different moments of medication and healthy controls, using a sensorized anthropomorphic device which was totally adapted to the human hand. The aim of this work was to carry out an accurate study of the reach-load-grip-hold-place-release subtasks to identify any physical motor impairment, its relation to medication and Parkinsonian strategies. Twenty seven patients in ON and OFF-like medication moments, and twenty seven age-matched controls took part in the experiment, which consisted of using the index finger and the thumb to perform a precision motor task involving different experimental objects. Visual cues were used as distracting elements. Results showed several motor parameters impaired in OFF-like medication moment but attenuated in ON state, suggesting a medication effect on the performance of the task.

We quantify the extractable entanglement of excited states of a Lieb-Liniger gas that are obtained from coarse-grained measurements on the ground state in which the boson number in one of two complementary contiguous partitions of the gas is determined. Numerically exact results obtained from the coordinate Bethe ansatz show that the von Neumann entropy of the resulting bipartite pure state increases monotonically with the strength of repulsive interactions and saturates to the impenetrable boson limiting value. We also present evidence indicating that the largest amount of entanglement can be extracted from the most probable projected state having half the number of bosons in a given partition. Our study points to a fundamental difference between the nature of the entanglement in free-bosonic and free-fermionic systems, with the entanglement in the former being zero after projection, while that in the latter (corresponding to the impenetrable boson limit) being non-zero., 7 pages, 6 PDF figures. Minor revisions, appendix added, references updated, typos corrected

In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual information is computed using the Ryu-Takayanagi formula. As an explicit example, we use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system not only show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value but also provide an intuitive entropic argument accounting for the source of this instability. We discuss the robustness of this transition when finite temperature and finite size effects are taken into account., 21 pages, 5 figures. Abstract and Figure 1 has been modified. Minor modifications in Section 1 and Section 5

We compute the entanglement between separated blocks in certain spin models showing that at criticality this entanglement is a function of the ratio of the separation to the length of the blocks and can be written as a product of a power law and an exponential decay. It thereby interpolates between the entanglement of individual spins and blocks of spins. It captures features of correlation functions at criticality as well as the monogamous nature of entanglement. We exemplify invariant features of this entanglement to microscopic changes within the same universality class. We find this entanglement to be invariant with respect to simultaneous scale transformations of the separation and the length of the blocks. As a corollary, this study estimates the entanglement between separated regions of those quantum fields to which the considered spin models map at criticality., 4 pages, 3 figures; comments welcome

[SPA] En esta Tesis Doctoral se proponen y desarrollan nuevos modelos neuronales de inspiración biológica para el control y aprendizaje de tareas de agarre por parte de dispositivos robóticos antropomorfos. En la primera parte de la Tesis se lleva a cabo una revisión exhausta de los aspectos más relevantes del comportamiento humano y animal durante movimientos de agarre de objetos en la que se resaltan las características invariantes de dicho movimiento, establecidas a través de numerosos experimentos psicofísicos con humanos y primates. A continuación se realiza un repaso al estado actual del conocimiento relativo a la neurobiología que subyace a los comportamientos motrices descritos anteriormente. Con esta base, la Tesis presenta un modelo para la organización del movimiento de agarre que mimetiza las interacciones entre distintas áreas del córtex y los ganglios basales durante la planificación y ejecución del movimiento de agarre en condiciones normales y en condiciones de déficit motor parkinsoniano. El modelo genera trayectorias realistas de agarre a través de la computación y actualización continúa de las señales que codifican la diferencia entre los programas motores que se establecen para la realización de la tarea, y el estado actual de los efectores finales del movimiento involucrados en la ejecución de dicha tarea. Las principales hipótesis del modelo son: (1) el control del transporte de la mano y de la apertura de los dedos se lleva a cabo a través de la acción de señales de paso talámicas cuya modulación corre a cargo de los circuitos neuronales de los ganglios basales. Dichas señales permiten la ejecución coordinada de los distintos subobjetivos que componen una tarea de agarre. (2) La disrupción del programa motriz detectado en la enfermedad de Parkinson, se debe a la modificación en la funcionalidad de la red de interneuronas colinérgicas del estriado ante una deflexión de dopamina estriatal. En estas condiciones, dicha red de interneuronas pierde la habilidad para mantener segregada la información procesada en bucles cortico ganglio basles paralelos y como consecuencia se producen acoplamientos entre distintos canales cortico subcorticales que afectan a los patrones cinemáticos prototípicos del movimiento de agarre. (3) La aplicación de este modelo a un sistema en el que los efectores finales de los movimientos son antropomorficamente realistas, implica el desarrollo, a partir de los resultados de experiencias psicofísicas expresamente diseñadas en esta Tesis Doctoral, de un esquema de control biológicamente plausible para la reducción de la dimensionalidad en el problema de la coordinación del gesto de la mano, durante el movimiento de agarre. Este esquema de control es lo que se define en la Tesis como Biblioteca de Gestos.(4) El aprendizaje que permite el establecimiento de los programas motores tras la percepción del objeto se lleva a cabo a través de una novedosa arquitectura neuronal multi red inspirada en la conectividad cortical entre áreas del córtex parietal posterior y córtex promotor que, tras una serie de etapas de aprendizaje, es capaz de generar movimientos de agarre correctos para un conjunto brazo mano robot antropomorfo cuando a éste sistema se le presentan objetos de distinta forma y tamaño, independientemente de su localización u orientación en el espacio. La Tesis presenta numerosos resultados referentes a la simulación de los modelos en distintas situaciones así como resultados relativos a la implantación de dichos modelos sobre una plataforma robótica antropomorfa orientada al agarre de objetos. Dichos resultados sustentan las hipótesis teóricas que fundamentan esta investigación y por otra parte muestran las capacidades de los modelos desarrollados para actuar como controladores de alto nivel en el guiado de tareas de agarre manipuladores robóticos humanoides. [ENG] Robotics has become into a traditional field in which research is made by engineers and scientist from different science disciplines such as mathematics, physics, medicine, neurosciences etc. It is evident that in the last years , robotics has evolve to be a multidisciplinary area getting closer and closer to everyday life of human beings such as in the cases of robotics applied to rehabilitation or surgery. It also has been established the use of robotics as a tool for the study of the Man and other biological systems or even to construct artificial anthropomorphic components such as, arms, sensors or cognitive – behavioural schemas able to substitute their biological counterparts in some situations. In the last years, it has been established within the robotics community, the idea about that the understanding of the nervous system of humans and monkeys has also a potential industrial or productive interest. The artificial intelligence industrial devices are more and more inspired in Biology. The brain operates in way very different to the way an actual robot actually operates. The mechanisms for information processing are vastly more complex and subtle in brain neural circuits than in the electronic circuits of the actual robots. The interactions within groups of neurons modify the properties of neural firing of these neurons in their interaction with sensory signals from the external world. An elemental learning such as avoiding behaviours with negative consequences, imply millions of neuronal events, including the reconfiguration and establishment of new neuronal connections. This is what is called ‘adaptability to environment’ of the biological systems. Neuro – Robotics constitutes an emergent and new field which represents, in its objectives, a huge challenge for science ad technology: the transference of fundamental principles of the neurobiology that drives the human behaviour to the diversity of disciplines of the engineering that constitute the Robotics (signal processing, robust and adaptive control, non linear systems, pattern recognition, mechatronics, etc…). If Robotics always has been a multidisciplinary field basically at the technological level, the need to push this field into major advances, requires a stronger interaction between the roboticians and scientist from another fields such as neurosciences, physiology or psychology. The ideas exposed above are the general reference frame in which the work of this PhD Thesis is developed. Concretely, it could be said that, major objectives of this PhD coincide with major objectives of two basic research projects funded by European Commission: BRITE-SYNERAGH (Systems neuroscience and engineering research for anthropomorphic grasping and handling, 1998-2001, BRE-2-CT980797) project and IST/FET-PALOMA (Progressive and adaptive learning for object manipulation: a biologically inspired multi-network architecture, 2001-2004, IST-2001-33073) project. The author of this PhD Thesis is ascribed to NeuroTechnology, Control and Robotics research group of the Universidad Politécnica de Cartagena. This research group and the author of this Thesis, have been intensively involved in the development of the two mentioned European projects. Universidad Politécnica de Cartagena Programa de doctorado en Tecnologías Industriales. Subprograma Neurotecnología, Control y Robótica

In this paper, two solutions for learning to reach targets in 3D space with redundant robots are presented. Fist of them is based on Hyper Radial Basis Functions networks (HRBF) that learn to compute a locally linear approximation of the Jacobian pseudoinverse at each robot joint configuration. The second one, is an alternative solution that is inspired in human ability to project the sensorial stimulus over the motor actuators on joints, sending motor commands to each articulation and avoiding, in most phases of the movement, the feedback of the visual information. These models have been implemented on a visuo-motor robotic platform for reaching and grasping applications. The obtained results allow to compare the robustness and accuracy capabilities of both neural models for reaching and tracking objects as well as to give a solution when redundant robots are considered.

The question of how the transport and grasp components in prehension are spatio-temporally coordinated is addressed in this paper. Based upon previous works by Castiello [1] we hypothesize that this coordination is carried out by neural networks in basal ganglia that exert a sophisticated gating / modulatory function over the two visuomotor channels that according to Jeannerod [2] and Arbib [3] are involved in prehension movement. Spatial dimension and temporal phasing of the movement are understood in terms of basic motor programs that are re-scaled both temporally and spatially by neural activity in basal ganglia thalamocortical loops. A computational model has been developed to accommodate all these assumptions. The model proposes an interaction between the two channels, that allows a distribution of cortical information related with arm transport channel, to the grasp channel. Computer simulations of the model reproduce basic kinematic features of prehension movement.

In this paper two neural models of basal ganglia function during motor sequential behaviour are presented. Two connectionist models of neuron - like elements that mimic some aspects of anatomy and physiology of cortico - basal ganglia - thalamo - cortical loops have been developed. The aim of this work is to report a new computaional model of motor sequence learning guided by reinforcement signals from neuronal systems that evaluate behaviours. The models are partially recurrent neural networks known as Jordan networks trained under a reinforcement learning paradigm. To validate these models, experimental findings of Tanji Shima [5] on monkeys have been reviewed. The hypothesis that cortico -- basal ganglionic loops learn and perform sequences successfully driven by reinforcement signals has been demonstrated in computer simulations of the models presented in this paper.

We thank Santiago Oviedo-Casado, Javier Molina-Vilaplana, Matthias Volk, Sukhbinder Singh, and Michael Kastoryano for insightful discussions, as well as Alexander Jahn, Jens Eisert and Glen Evenbly for their feedback on the manuscript. J.P. is grateful for financial support from Ministerio de Ciencia, Innovación y Universidades (SPAIN), including FEDER (Grant no. PGC2018-097328-B-100) together with Fundación Séneca (Murcia, Spain) (Project no. 19882/GERM/15)., M.S. wrote the main manuscript text. J.P. supervised and reviewed the manuscript., Hyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence. Although this new class of tensor network shows much potential for simulating conformal field theories arising from hyperbolic bulk manifolds with quasiperiodic boundaries, many issues are unresolved. In this manuscript we analyze the challenges related to optimizing tensors in a hyMERA with respect to some quasiperiodic critical spin chain, and compare with standard approaches in MERA. Additionally, we show two new sets of tensor decompositions which exhibit different properties from the original construction, implying that the multitensor constraints are neither unique, nor difficult to find, and that a generalization of the analytical tensor forms used up until now may exist. Lastly, we perform randomized trials using a descending superoperator with several of the investigated tensor decompositions, and find that the constraints imposed on the spectra of local descending superoperators in hyMERA are compatible with the operator spectra of several minimial model CFTs., SPAIN, Fundación Séneca 19882/GERM/15, Ministerio de Ciencia, Innovación y Universidades, European Regional Development Fund PGC2018-097328-B-100