Survey on quantization methods on Kähler manifolds.
problem None explicitly stated; focuses on methods.
method Deformation quantization, geometric quantization, Berezin-Toeplitz quantization, BV quantization.
result New relationships among quantization methods on Kähler manifolds.
The paper classifies quantizable functions and explores symmetry in quantization methods.
problem Classifying quantizable functions and understanding symmetry in quantization methods.
method Deformation quantization and geometric quantization methods are compared and classified.
result Formal quantizable functions are of a specific form and relate to Hamiltonian Killing vector fields.
This paper introduces a differentiable, scalable quantization method for neural networks.
problem Previous quantization methods lacked differentiability and scalability.
method The approach is differentiable and scalable, using bit-shifting and logarithmic quantization.
result The method achieves comparable accuracy to state-of-the-art approaches with less training time and lower inference cost.
StatQAT optimizes quantization for deep networks, reducing computational cost and memory usage.
problem Optimal quantization parameters selection for deep neural networks with diverse data distributions.
method Statistical error analysis framework for uniform and floating-point quantization, iterative and analytic quantizers designed for arbitrary and Gaussian-like distributions.
result Improved accuracy and stability in training low-precision neural networks.
This study optimizes quantized neural networks by considering model architecture and quantization types.
problem Optimizing quantized neural networks for low-power, high-throughput applications.
method Holistic approach including training methods and quantization-friendly architecture design.
result Deeper models are more sensitive to activation quantization, while wider models improve resilience to both weight and activation quantization.
Extends ONNX for quantized neural networks with new formats and operators.
problem Handling arbitrary-precision quantization in neural networks.
method Introduces new formats and operators in ONNX to represent quantized neural networks.
result Enabled representation of uniform quantization in neural networks.
New method for quantizing symplectic manifolds with Lagrangian bundles.
problem Quantization of symplectic manifolds with Lagrangian bundles.
method A new construction of strict deformation quantization.
result Established a correspondence between differential operators and principal symbols.
HMQ improves quantization for edge devices with mixed precision.
problem Efficient quantization for edge devices with uniform, power-of-two thresholds.
method Introduces HMQ, a mixed precision quantization block that repurposes Gumbel-Softmax for searching over quantization schemes.
result Achieves competitive and state-of-the-art results on ImageNet despite restrictions.
Introduces sheaf quantization, a topological approach to geometric quantization.
problem Topological realization of WKB-states in geometric quantization.
method Enhancement of constructible sheaves, Betti counterpart of Fukaya--Floer theory.
result Introduction to sheaf quantization as a topological realization of WKB-states.
Network quantization is an effective solution to compress deep neural networks for practical usage. Existing network quantization methods cannot sufficiently exploit the depth information to generate low-bit compressed network. In this paper, we propose two novel network quantization approaches, single-level network qu…
The article defines and compares two types of quantizations on compact manifolds.
problem Quantization on arbitrary compact smooth manifolds.
method Embedding into CP^n and inducing quantizations from there.
result Generalizations of earlier quantization methods.
We present Rotated Adaptive Tetra-iterated Quantizer (RATQ), a fixed-length quantizer for gradients in first order stochastic optimization. RATQ is easy to implement and involves only a Hadamard transform computation and adaptive uniform quantization with appropriately chosen dynamic ranges. For noisy gradients with al…
Quantized Adam reduces communication cost in deep learning training.
problem Reducing communication cost in distributed deep learning training.
method Gradient and weight quantization with error feedback in Adam.
result Proposed methods converge to first-order stationary points.
Quantizes neural networks using frame theory for improved accuracy.
problem Improving neural network efficiency and accuracy through quantization.
method Sigma-Delta (ΣΔ) quantization with finite unit-norm tight frames. result Error bound between original and quantized neural networks derived.
The paper studies quantization on symplectic manifolds with real polarizations, comparing different quantization methods.
problem Quantization on compact symplectic manifolds with real polarizations.
method Geometric quantization, Toeplitz operators, Fourier transforms, asymptotic expansion of traces.
result Deformation quantization is realized through asymptotic traces of Toeplitz operators.
Unified finetuning of all quantization degrees of freedom achieves state-of-the-art 4-bit quantization.
problem Achieving high accuracy in quantized neural networks while maintaining speed and resource constraints.
method Quantization-aware finetuning (QFT) that jointly optimizes all quantization degrees of freedom.
result 4-bit weight quantization results on-par with state-of-the-art (SoTA) within PTQ constraints.
Neural network models are resource hungry. It is difficult to deploy such deep networks on devices with limited resources, like smart wearables, cellphones, drones, and autonomous vehicles. Low bit quantization such as binary and ternary quantization is a common approach to alleviate this resource requirements. Ternary…
Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf is quantized.
Meta learning optimizes neural network quantization for efficient inference.
problem Uniform bitwidth quantization is sub-optimal for neural network compression.
method Meta learning to automatically generate hybrid quantization policies.
result Meta learning outperforms uniform quantization and RL approaches.
Study quantization effects on high-dimensional linear regression learning.
problem Understanding quantization's impact on learning high-dimensional linear regression models.
method Analyzes stochastic gradient descent for high-dimensional linear regression under various quantization targets.
result Establishes precise bounds on excess risk for different quantization schemes.
We present an overview of techniques for quantizing convolutional neural networks for inference with integer weights and activations. Per-channel quantization of weights and per-layer quantization of activations to 8-bits of precision post-training produces classification accuracies within 2% of floating point networks…
FrostNet improves INT8 quantization efficiency in mobile networks.
problem The importance of network architecture for optimal INT8 quantization.
method Quantization-aware training (QAT) with StatAssist and GradBoost, hardware-aware NAS.
result FrostNets achieve higher recognition accuracy with comparable latency when quantized.
Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers an alternative approach with improved tolerance to different classes of data-type…
Quantizes symplectic manifolds with bounded geometry using Berezin-Toeplitz method.
problem Quantization of symplectic manifolds with bounded geometry.
method Berezin-Toeplitz quantization theory.
result Correct semiclassical limit achieved.
Quantization-aware training can recover accuracy lost by post-training quantization.
problem Post-training quantization (PTQ) can fail sharply at aggressive bitwidths.
method A unified geometric framework that explains PTQ failure and QAT recovery.
result QAT has a useful bias that steers iterates back into the basin.
This study analyzes quantization in deep learning models using statistical physics methods.
problem The computational resource requirements for large-scale data analysis models.
method Typical case analysis from statistical physics, specifically the replica method.
result Optimal quantization width minimizes error and delays overfitting.
Neural network quantization is becoming an industry standard to efficiently deploy deep learning models on hardware platforms, such as CPU, GPU, TPU, and FPGAs. However, we observe that the conventional quantization approaches are vulnerable to adversarial attacks. This paper aims to raise people's awareness about the …
Paper develops a statistical framework for quantized training of deep neural networks.
problem Lack of theoretical understanding of gradient quantization in FQT.
method Presented a statistical framework for analyzing FQT algorithms, viewing quantized gradient as a stochastic estimator of QAT gradient.
result Developed two novel gradient quantizers with smaller variance than existing per-tensor quantizer.
In [3], the authors showed the existence and the uniqueness of a sl(m+1,\R)-equivariant quantization in the non-critical situations. The curved generalization of the sl(m+1,\R)-equivariant quantization is the natural and projectively equivariant quantization. In [1] and [7], the existence of such a quantization was pro…
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in the sheaf cohomology of the geometric quantization line bundle. The correspondin…
A new method for robust product Markovian quantization overcomes numerical instabilities.
problem Numerical instabilities in the PMQ algorithm limit its adoption, especially for stochastic volatility models.
method Reformulated PMQ as standard vector quantization, applying accelerated Lloyd's algorithm for robustness.
result The method overcomes numerical instabilities and extends applicability to stochastic volatility models.
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…
Quantizes contact structures using dynamical methods.
problem Quantizing contact structures in a flat connection.
method Constructs a dynamical quantization using a flat connection on a Hilbert tractor bundle.
result Determines a contact tractor connection whose parallel sections determine a distinguished choice of Reeb dynamics.
Paper proposes a new binary quantization method for faster DNN inference.
problem Accelerating deep neural network inference on resource-limited devices.
method Quantized Compressed Sensing (QCS) for binary quantization.
result The proposed method preserves benefits of standard methods while reducing quantization error.
LSQ+ improves quantization of neural nets with Swish activations, achieving state-of-the-art results.
problem Quantization of neural nets with Swish activations, especially negative activations, leads to significant performance loss.
method Introduces learnable scale and offset parameters for asymmetric quantization, and uses MSE-based initialization for quantization parameters.
result Significantly outperforms LSQ for low-bit quantization of neural nets with Swish activations, achieving up to 5.6% gain with W2A2 quantization of EfficientNet-B0.
BatchNorm helps train quantized networks by avoiding gradient explosion.
problem Training quantized neural networks is difficult due to gradient issues.
method Investigated the impact of BatchNorm on both full-precision and quantized networks.
result BatchNorm avoids gradient explosion in quantized networks, contrary to expectations.
Paper quantizes heavy-tailed data for near optimal estimation rates.
problem Estimating parameters from heavy-tailed data with quantization.
method Truncate and dither data, then uniformly quantize; achieves near minimax rates.
result Near optimal estimation rates achievable with quantized data.
For arbitrary compact quantizable Kaehler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic expansion) due to Bordemann, Meinrenken and Schlichenmaier are used in an essential man…
Neural network quantization procedure is the necessary step for porting of neural networks to mobile devices. Quantization allows accelerating the inference, reducing memory consumption and model size. It can be performed without fine-tuning using calibration procedure (calculation of parameters necessary for quantizat…
Although deep neural networks are highly effective, their high computational and memory costs severely challenge their applications on portable devices. As a consequence, low-bit quantization, which converts a full-precision neural network into a low-bitwidth integer version, has been an active and promising research t…
Study quantization schemes on Kähler manifolds linking star products and BV quantizations.
problem Quantization of structures on Kähler manifolds.
method Construct Fedosov's star products and Batalin-Vilkovisky (BV) quantizations.
result One-loop exactness of BV quantizations, leading to a cochain level formula.
In order to quantize the gate parameters of the LSTM (Long Short-Term Memory) neural network model with almost no recognition performance degraded, a new quantization method named Quantization Loss Re-Learn Method is proposed in this paper. The method does lossy quantization on gate parameters during training iteration…
Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
Symmetries of Poisson manifolds are in general quantized just to symmetries up to homotopy of the quantized algebra of functions. It is therefore interesting to study symmetries up to homotopy of Poisson manifolds. We notice that they are equivalent to Poisson principal bundles and describe their quantization to symmet…
Quantizes functions on Kähler manifolds without formal deformation.
problem Deforming smooth functions on Kähler manifolds to non-formal quantization.
method Using Fedosov connections and prequantum line bundles.
result Quantizable functions form a sheaf of twisted differential operators.
We propose a generalization of quantization as a categorical way. For a fixed Poisson algebra quantization categories are defined as subcategories of R-module category with the structure of classical limits. We construct the generalized quantization categories including matrix regularization, strict deformation quantiz…
This paper evaluates quantization techniques for deep learning inference.
problem Reducing the size and improving inference of deep neural networks.
method Review and empirical evaluation of quantization parameters for various neural network models.
result 8-bit quantization maintains accuracy within 1% of floating-point models.
BiQGEMM efficiently multiplies quantized DNN weights using lookup tables.
problem Efficiently multiplying quantized DNN weights on CPUs/GPUs with limited memory.
method BiQGEMM pre-computes and stores redundant intermediate results in lookup tables.
result BiQGEMM achieves lower overall computations and higher performance.