Quantizes Willmore energy in Riemannian manifolds with bounded energy and area.
problem Quantization of Willmore energy in bounded energy and area conditions.
method Uniform boundedness of Willmore energy and area, weak convergence of maps, and conformal structures in compact domain.
result Quantization of Willmore energy holds under specified conditions.
Energy quantization for surfaces with area, volume, and mean curvature constraints.
problem Energy quantization for constrained Willmore surfaces.
method Established through strong compactness under energy thresholds.
result Strong compactness of constrained Willmore surfaces, including minimizers.
The study quantizes energy for curves in symplectic manifolds.
problem Quantization of energy for pseudo-holomorphic curves.
method Extending Topping's theorem to almost everywhere immersed submanifolds and using it to prove energy quantization.
result Energy quantization for pseudo-holomorphic curves of all genus.
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.
problem Understanding Willmore flows and their singularities.
method Parametric approach to Willmore gradient flows.
result For small-energy weak immersions, a unique solution exists.
Proves energy quantization for surfaces with bounded index.
problem Energy quantization for Willmore surfaces with bounded index.
method Translated the question to the conformal Gauss map's perspective and showed convergence in specific regions.
result Conformal Gauss map converges to a light-like geodesic in De Sitter space in neck or collar regions.
Study quantizes energy for a specific fourth-order system in 4D.
problem Energy quantization for a fourth-order inhomogeneous system in 4D.
method Establishes angular energy quantization for the given system.
result Angular energy quantization proven for the system.
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…
The paper proposes a dataflow-based approach to reduce energy consumption in deep neural networks without sacrificing performance.
problem Reducing energy consumption in deep neural networks without performance drop.
method Dataflow-based joint quantization of weights and activations.
result Joint quantization improves performance and reduces energy consumption.
Paper improves DNN accelerator robustness against bit errors with energy savings.
problem Bit errors in quantized DNN weights reduce energy efficiency.
method Combines robust fixed-point quantization, weight clipping, and random bit error training.
result Significantly improves robustness against random bit errors with high energy savings.
Study quantizes energy distribution in inhomogeneous phase transitions.
problem Quantifying energy distribution in inhomogeneous Allen-Cahn phase transitions.
method Analysis of varifolds and convergence of integer rectifiable varifolds.
result Equidistribution of energy between Dirichlet and Potential energy in phase field limit.
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.
problem Quantizing conditional probability measures efficiently.
method DCMQ method using Huber-energy kernel and deep neural network.
result Promising results on various examples.
The paper tackles decision-oriented communications for energy-efficient resource allocation.
problem Maximizing utility functions under quantized information.
method Develops solutions for quantizing information to maximize utility functions under known and observed conditions.
result Quantizing the state roughly is optimal for sum-rate maximization but not for energy-efficiency metrics.
Quantizes semipositive line bundles on complex manifolds.
problem Quantize semipositive line bundles without ample representatives.
method Use adjoint Bergman kernels and non-pluripolar Monge-Ampère measures.
result Quantized energy converges to Monge-Ampère energy in semipositive setting.
Ternary MobileNets improve efficiency and accuracy on constrained devices.
problem Efficiently compressing MobileNets for real-time applications on constrained devices.
method Per-layer hybrid filter banks for ternary quantization of MobileNets.
result 27.98% energy savings and 51.07% reduction in model size with comparable accuracy.
Algorithm finds best Dirac mass approximation of target measure.
problem Finding optimal Dirac mass approximation of target measure.
method Minimizes statistical distance between original measure and quantized version using Huber-energy kernel.
result HEMQ algorithm robust and versatile, matches intuitive behavior.
AutoQ automatically optimizes quantization for CNNs, reducing latency and energy.
problem Efficiently quantizing CNN weights for low-power mobile devices.
method Hierarchical-DRL for kernel-wise quantization bitwidth selection.
result Reduces inference latency and energy consumption by 54.06% and 50.69% respectively.
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.
problem Energy quantization in Ginzburg-Landau vortices for higher dimensions.
method Analyzing normalized energy measures and vorticity sets.
result Energy quantization only holds when density is less than 2.
Paper analyzes solutions to equations on surfaces with boundary singularities.
problem Analyzing solutions to super-Liouville equations on surfaces with boundary singularities.
method Developed a new method to deduce the removability of boundary singularities due to the vanishing of the Pohozaev constant.
result Established energy quantization for solutions to super-Liouville type equations.
We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.
Improved SNNs with quantized activations outperform traditional networks.
problem Maintaining SotA accuracy in SNNs with limited bit precision.
method Interpolating between non-spiking and spiking regimes using signal processing tools.
result First hybrid SNN outperforms traditional RNNs in accuracy with reduced bit precision.
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.
Efficient hybrid networks improve AI performance at the edge.
problem Achieving AI performance at the edge with minimal energy and memory usage.
method Proposed hybrid networks combining binary and full-precision layers.
result Hybrid networks achieve close to full-precision performance with up to 21.8x memory compression.
GOBO compresses 99.9% of BERT model parameters to 3 bits, improving inference efficiency.
problem Efficient execution of attention-based NLP models, especially in terms of latency and energy consumption.
method GOBO quantizes 32-bit floating-point parameters to 3 bits without fine-tuning, using hardware compression and co-designed architectures.
result GOBO maintains model accuracy while significantly reducing inference latency and energy consumption.
New method trains quantized neural networks to global optimality.
problem Training optimal quantized neural networks is intractable due to combinatorial non-convex optimization.
method Convex optimization strategy using hidden convexity, semidefinite lifting, and Grothendieck's identity.
result Quantized NN problems can be solved to global optimality in polynomial-time.
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…
Study of vortex interactions in Ginzburg-Landau models on 2D Riemannian manifolds.
problem Characterize and quantify interactions between vortices in Ginzburg-Landau models.
method Variational Ginzburg-Landau model, Γ-limit analysis, flux quantization constraints.
result Renormalized energy between vortices determined as a Γ-limit.
Low-bit training framework reduces energy consumption in CNNs.
problem Reducing energy consumption in convolutional neural networks.
method Low-bit training framework using MLS tensor format with dynamic quantization.
result Achieves superior trade-off between accuracy and bit-width.
SmartDeal reduces energy and storage costs for deep neural networks.
problem Heavy parameterization of deep neural networks leads to inefficient use of DRAM.
method SmartDeal decomposes weights into a small basis matrix and a structurally sparse coefficient matrix, quantized to power-of-2.
result Up to 2.44x energy efficiency improvement in inference and 10.56x reduction in training energy.
Study on hyperbolic elastic flow, proving convergence and quantifying singularities.
problem Understanding singularities and convergence of elastic flow in hyperbolic plane.
method Analyzes closed and open curves with clamped boundary conditions, proving convergence without small energy assumption.
result Each singularity carries an energy cost of at least 8, and blow-ups are explicitly classified.
Study of Dirac equation with non-local nonlinearity on spheres.
problem Conformally invariant Dirac equation with non-local nonlinearity.
method Investigation of compactness, bubbling, and energy quantization of energy functional; characterization of ground state solutions; proof of Aubin-type inequality and Brezis-Nirenberg type result.
result Existence of solutions to the conformal Einstein-Dirac problem in dimension 4.
DQA efficiently quantizes deep neural network activations for resource-constrained devices.
problem Efficiently quantizing deep neural network activations for resource-constrained devices.
method DQA uses simple shifting-based operations and Huffman coding for sub-6-bit quantization.
result DQA achieves significantly better accuracy than direct quantization and state-of-the-art methods.
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.
problem Energy-efficient inference of deep neural networks.
method Algorithm-hardware co-design framework integrating sparsification, decomposition, and quantization.
result SmartExchange reduces energy consumption and improves performance.
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…
This paper proposes a method to improve neural network quantization without retraining.
problem Handling outliers in quantized DNN weights and activations.
method Outlier Channel Splitting (OCS) which duplicates channels containing outliers and halves their values.
result OCS outperforms state-of-the-art clipping techniques with minimal overhead.
A hybrid neural network optimizes AI deployment on edge and cloud for energy efficiency.
problem Energy and resource constraints in edge devices for deep learning models.
method Conditionally deep hybrid neural network with quantized layers at edge and full-precision layers at cloud.
result Early classification at the edge reduces energy consumption by 5.5x on CIFAR-10 dataset.
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…
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.…
Quantized neural networks are vulnerable to adversarial attacks.
problem Adversarial robustness of quantized neural networks.
method Investigated adversarial robustness of quantized neural networks under different threat models.
result Quantization does not offer robust protection and results in gradient masking.
Paper presents CeNN quantization for efficient CPS applications.
problem Efficient processing for CPS applications, especially in telemedicine and ADAS.
method Incremental quantization of CeNNs with various strategies.
result Achieved up to 7.8x speedup with no performance loss.
Stability of biharmonic maps in critical dimension proven.
problem Stability of biharmonic maps between manifolds in critical dimension.
method Generalization of Morse stability theory to biharmonic maps, development of strong energy quantization method.
result Strong energy quantization in a wide class of problems in geometric analysis.
Paper proposes a new method for quantizing channel state information to optimize resource allocation.
problem Optimizing resource allocation for a receiver sending quantized channel state information to a transmitter.
method Introducing a task-oriented approach where the receiver sends the right amount of information to the transmitter.
result Analytical solution for optimal task-oriented CSI quantizer found for a specific energy-efficient power control problem.
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…