AdS (In)stability: Lessons From The Scalar Field

We argued in arXiv:1408.0624 that the quartic scalar field in AdS has features that could be instructive for answering the gravitational stability question of AdS. Indeed, the conserved charges identified there have recently been observed in the full gravity theory as well. In this paper, we continue our investigation of the scalar field in AdS and provide evidence that in the Two-Time Formalism (TTF), even for initial conditions that are far from quasi-periodicity, the energy in the higher modes at late times is exponentially suppressed in the mode number. Based on this and some related observations, we argue that there is no thermalization in the scalar TTF model within time-scales that go as $\sim 1/\epsilon^2$, where $\epsilon$ measures the initial amplitude (with only low-lying modes excited). It is tempting to speculate that the result holds also for AdS collapse.Comment: 10 pages, 4 figure

Complexity of compositional model checking of computation tree logic on simple structures

Temporal Logic Model Checking is one of the most potent tools for the veri.cation of .nite state systems. Computation Tree Logic (CTL) has gained popularity because unlike most other logics, CTL model checking of a single transition system can be achieved in polynomial time. However, in most real-life problems, specially in distributed and parallel systems, the system consist of a set of concurrent processes and the veri.cation problem translates to model check the composition of the component processes. Since explicit composition leads to state explosion, verifying the system without actually composing the components is attractive, even for possibly restrictive class of systems.We show that the problem of compositional CTL model checking is PSPACE complete for the class of systems composed of components that are tree-like transition structure and do not interact among themselves. For the simplest forms of existential and universal CTL formulas model checking turns out to be NP complete and coNP complete, respectively. The results hold for both synchronous and asynchronous composition

DietCNN: Multiplication-free Inference for Quantized CNNs

The rising demand for networked embedded systems with machine intelligence has been a catalyst for sustained attempts by the research community to implement Convolutional Neural Networks (CNN) based inferencing on embedded resource-limited devices. Redesigning a CNN by removing costly multiplication operations has already shown promising results in terms of reducing inference energy usage. This paper proposes a new method for replacing multiplications in a CNN by table look-ups. Unlike existing methods that completely modify the CNN operations, the proposed methodology preserves the semantics of the major CNN operations. Conforming to the existing mechanism of the CNN layer operations ensures that the reliability of a standard CNN is preserved. It is shown that the proposed multiplication-free CNN, based on a single activation codebook, can achieve 4.7x, 5.6x, and 3.5x reduction in energy per inference in an FPGA implementation of MNIST-LeNet-5, CIFAR10-VGG-11, and Tiny ImageNet-ResNet-18 respectively. Our results show that the DietCNN approach significantly improves the resource consumption and latency of deep inference for smaller models, often used in embedded systems. Our code is available at: https://github.com/swadeykgp/DietCNNComment: Supplementary for S. Dey, P. Dasgupta and P. P. Chakrabarti, "DietCNN: Multiplication-free Inference for Quantized CNNs," 2023 International Joint Conference on Neural Networks (IJCNN), Gold Coast, Australia, 2023, pp. 1-8, doi: 10.1109/IJCNN54540.2023.1019177

Discovering the input assumptions in specification refinement coverage

The design of a large chip is typically hierarchical - large modules are recursively expanded into a collection of sub-modules. Each expansion refines the design due to the addition of level specific details. We believe that a similar approach is necessary to scale the capacity of formal property verification technology - as the design gets refined from one level to another, the formal specification must also be refined to reflect the level specific design decisions. At the heart of this approach we propose a checker that identifies the input assumptions under which the refined specification "covers" the original specification. This enables the validation engineer to focus the verification effort on the remaining input scenarios thereby reducing the number of target coverage points for simulation

What lies between design intent coverage and model checking?

Practitioners of formal property verification often work around the capacity limitations of formal verification tools by breaking down properties into smaller properties that can be checked on the sub-modules of the parent module. To support this methodology, we have developed a formal methodology for verifying whether the decomposition is indeed sound and complete, that is, whether verifying the smaller properties on the submodules actually guarantees the original property on the parent module. In practice, however designers do not write properties for all modules and thereby our previous methodology was applicable to selected cases only. In this paper we present new formal methods that allow us to handle RTL blocks in the analysis. We believe that the new approach will significantly widen the scope of the methodology, thereby enabling the validation engineer to handle much larger designs than admitted by existing formal verification tools

Spin Dynamics of a J1-J2-K Model for the Paramagnetic Phase of Iron Pnictides

We study the finite-temperature spin dynamics of the paramagnetic phase of iron pnictides within an antiferromagnetic J_1-J_2 Heisenberg model on a square lattice with a biquadratic coupling $-K (S_i \cdot S_j)^2$ between the nearest-neighbor spins. Our focus is on the paramagnetic phase in the parameter regime of this J_1-J_2-K model where the ground state is a (\pi,0) collinear antiferromagnet. We treat the biquadratic interaction via a Hubbard-Stratonovich decomposition, and study the resulting effective quadratic-coupling model using both modified spin wave and Schwinger boson mean-field theories; the results for the spin dynamics derived from the two methods are very similar. We show that the spectral weight of dynamical structure factor S(q,\omega) is peaked at ellipses in the momentum space at low excitation energies. With increasing energy, the elliptic features expand towards the zone boundary, and gradually split into two parts, forming a pattern around (\pi,\pi). Finally, the spectral weight is anisotropic, being larger along the major axis of the ellipse than along its minor axis. These characteristics of the dynamical structure factor are consistent with the recent measurements of the inelastic neutron scattering spectra on BaFe_2As_2 and SrFe_2As_2.Comment: 13 pages, 11 figures, to be published in Phys. Rev.