arXiv research

Quantizes Willmore energy in Riemannian manifolds with bounded energy and area.

Energy quantization for surfaces with area, volume, and mean curvature constraints.

In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimension. This quantization is a consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We derive from this a…

A new parametric method studies Willmore flows and energy quantization.

Proves energy quantization for surfaces with bounded index.

Study quantizes energy for a specific fourth-order system in 4D.

We prove a bubble-neck decomposition together with an energy quantization result for sequences of Willmore surfaces into an arbitrary euclidian space with uniformly bounded energy and non-degenerating conformal type. We deduce the strong compactness of Willmore closed surfaces of a given genus modulo the Möbius group a…

Paper improves DNN accelerator robustness against bit errors with energy savings.

Study quantizes energy distribution in inhomogeneous phase transitions.

We establish an energy quantization result for sequences of Willmore surfaces when the underlying sequence of Riemann surfaces is degenerating in the moduli space. we notably exhibit a new residue which quantifies the potential loss of energy in collar regions. Thanks to these residues, we also prove compactness of Wil…

A new method quantizes conditional probability measures using deep learning.

Quantizes semipositive line bundles on complex manifolds.

Algorithm finds best Dirac mass approximation of target measure.

We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energ…

For Ginzburg-Landau vortices, energy quantization holds only when density is less than 2.

We first partially extend a theorem of Topping, on the relation between mean curvature and intrinsic diameter, from immersed submanifolds of $\mathbb{R} ^{n}$ to almost everywhere immersed, closed submanifolds of a compact Riemannian manifold. We use this to prove quantization of energy for pseudo-holomorphic closed c…

We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.

This paper addresses a challenging problem - how to reduce energy consumption without incurring performance drop when deploying deep neural networks (DNNs) at the inference stage. In order to alleviate the computation and storage burdens, we propose a novel dataflow-based joint quantization approach with the hypothesis…

In this paper, we introduce the problem of decision-oriented communications, that is, the goal of the source is to send the right amount of information in order for the intended destination to execute a task. More specifically, we restrict our attention to how the source should quantize information so that the destinat…

Improved SNNs with quantized activations outperform traditional networks.

MobileNets family of computer vision neural networks have fueled tremendous progress in the design and organization of resource-efficient architectures in recent years. New applications with stringent real-time requirements on highly constrained devices require further compression of MobileNets-like already compute-eff…

Memory-augmented neural networks (MANNs) refer to a class of neural network models equipped with external memory (such as neural Turing machines and memory networks). These neural networks outperform conventional recurrent neural networks (RNNs) in terms of learning long-term dependency, allowing them to solve intrigui…

Quantization needs evaluation of all of states of a quantized object rather than its stationary states with respect to its energy. In this paper, we have investigated moduli $\CMeP$ of a quantized elastica, a quantized loop with an energy functional associated with the Schwarz derivative, on a Riemann sphere $\PP$. The…

We prove the convergence of geodesic distance during the quantization of the space of Kähler potentials. As applications, this provides alternative proofs of certain inequalities about the K-energy functional in the projective case.

Network quantization is one of the most hardware friendly techniques to enable the deployment of convolutional neural networks (CNNs) on low-power mobile devices. Recent network quantization techniques quantize each weight kernel in a convolutional layer independently for higher inference accuracy, since the weight ker…

GOBO compresses 99.9% of BERT model parameters to 3 bits, improving inference efficiency.

In this paper, we develop the blow-up analysis and establish the energy quantization for solutions to super-Liouville type equations on Riemann surfaces with conical singularities at the boundary. In other problems in geometric analysis, the blow-up analysis usually strongly utilizes conformal invariance, which yields …

New method trains quantized neural networks to global optimality.

We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our approach enables storing a single set of weights that can be quantized on-deman…

Low-bit training framework reduces energy consumption in CNNs.

SmartDeal reduces energy and storage costs for deep neural networks.

Study on hyperbolic elastic flow, proving convergence and quantifying singularities.

Study of Dirac equation with non-local nonlinearity on spheres.

DQA efficiently quantizes deep neural network activations for resource-constrained devices.

The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle. The existence of reducible quantum structures leads to considering the…

SmartExchange trades memory for computation in neural networks.

We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from supersymmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless and divergence-free energy-momentum tens…

Let $M$ be an arbitrary complex manifold and let $L$ be a Hermitian holomorphic line bundle over $M$. We introduce the Berezin-Toeplitz quantization of the open set of $M$ where the curvature on $L$ is non-degenerate. The quantum spaces are the spectral spaces corresponding to $[0,k^{-N}]$ ($N>1$ fixed), of the Kodaira…

A hybrid neural network optimizes AI deployment on edge and cloud for energy efficiency.

The recent advent of `Internet of Things' (IOT) has increased the demand for enabling AI-based edge computing. This has necessitated the search for efficient implementations of neural networks in terms of both computations and storage. Although extreme quantization has proven to be a powerful tool to achieve significan…

Deep neural networks are the state-of-the-art methods for many real-world tasks, such as computer vision, natural language processing and speech recognition. For all its popularity, deep neural networks are also criticized for consuming a lot of memory and draining battery life of devices during training and inference.…

Stability of biharmonic maps in critical dimension proven.

Quantization can improve the execution latency and energy efficiency of neural networks on both commodity GPUs and specialized accelerators. The majority of existing literature focuses on training quantized DNNs, while this work examines the less-studied topic of quantizing a floating-point model without (re)training. …

Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only while training, but also when deployed at scales ranging from data centers all th…

Study exact Lagrangian cobordisms in cotangent bundles, proving bounds on sheaf interleaving distance and shadow distance.

In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kahler 2-form. We compare the geometric quantization framework wit…

As the will to deploy neural networks models on embedded systems grows, and considering the related memory footprint and energy consumption issues, finding lighter solutions to store neural networks such as weight quantization and more efficient inference methods become major research topics. Parallel to that, adversar…

We study a variational Ginzburg-Landau type model depending on a small parameter $\varepsilon>0$ for (tangent) vector fields on a $2$-dimensional Riemannian manifold $S$. As $\varepsilon\to 0$, these vector fields tend to have unit length so they generate singular points, called vortices, of a (non-zero) index if the g…