EC2T creates sparse and ternary neural networks for resource-constrained devices.
problem Deploying deep neural networks on resource-constrained devices.
method Entropy-Constrained Trained Ternarization (EC2T) framework.
result EC2T creates sparse and ternary neural networks that are efficient in terms of storage and computation.
Smart Quantization adapts binary and ternary quantization for neural networks.
problem Resource constraints in deploying neural networks on devices with limited resources.
method Adaptive combination of binary and ternary quantization with a regularization function.
result Adapts quantization depth during training to maintain high model accuracy.
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.
GTC improves neural network compression and accuracy without multiplications.
problem Balancing accuracy and computational complexity in deep neural networks.
method Generalizes ternary connect to allow arbitrary levels and integer powers of two, learning optimal levels and weights end-to-end.
result GTC achieves comparable accuracy to binary networks with superior compression and hardware benefits.
New method optimizes weights and quantizers in ternary neural networks.
problem Reducing model size and computational cost in deep neural networks.
method Simultaneous optimization of weights and quantizers using truncated Gaussian approximation.
result 3.9-2.16% accuracy loss in ImageNet classification tasks.
Proposes volumization for neural networks to control bias-variance tradeoff.
problem Improving generalization and preventing memorization in neural networks.
method Defines a physical volume for weights, interpolating between L2 and L∞ regularization.
result Volumization interpolates between weight decay and clipping, improving generalization.
Binary and ternary weights simplify RNNs for mobile devices.
problem Complexity and memory intensity of RNNs on mobile devices.
method Learn binary and ternary weights during training.
result Significant memory saving and inference speedup on ASIC platform.
Hybrid neural-tree networks reduce IoT model size and computation by 52.2% and 11.1% respectively.
problem Power and storage constraints in IoT devices limit the deployment of modern neural networks.
method Combines neural and tree-based learning with ternary quantization.
result Significant reduction in model size and computation with minimal accuracy loss.
Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware, however, high precision real-time processing can still be a challenge. One approach to solving this problem is training networks with binary or…
Artificial neural networks predict quantum entanglement types.
problem Predicting entanglement types of quantum states.
method Supervised learning and deep neural networks on algebraic varieties.
result Trained neural networks can classify entanglement types for up to 5 binary qubits and 3 qutrits.
BinaryDuo improves BNNs by coupling binary activations, outperforming state-of-the-art models.
problem Gradient mismatch in BNNs due to binarizing activations.
method Using gradient of smoothed loss function to estimate gradient mismatch, proposing BinaryDuo scheme with coupled ternary activations.
result BinaryDuo outperforms state-of-the-art BNNs on various benchmarks.
The paper extends ternary algebra concepts using cube roots of unity.
problem Extending algebraic structures from binary to ternary multiplication.
method Introducing ternary associator, commutator, and Lie algebra at cube roots of unity.
result Derived an identity for ternary commutator based on GA(1,5). We define a homology for ternary groups using both associativity and skew elements. We describe the odd-even construction which yields many examples of ternary groups. We define the ternary knot group, consider its homomorphisms into ternary groups, and discuss the applications.
Selective classification improves trading strategies by abstaining from predictions.
problem Designing effective trading strategies using selective classification.
method Extends binary or multi-class classifiers to allow abstaining from predictions, evaluates across different feature sets and classifiers.
result Selective classifiers can improve trading performance by avoiding poor predictions.
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special attributes of such ternary groups, such as semi-commutativity, we construct a ternary invariant of curves immersed in compact surfaces, conside…
Novel ternary structures reveal new interpretations of linear connections.
problem Examining the ternary structure of Lie algebroid connections.
method Study of endomorphisms and explicit presentation of the endomorphism truss.
result Explicitly presented endomorphism truss of linear connections.
We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from ternary bialgebras are provided. We also describe ternary distributive algebraic structures com…
There is a pressing need to build an architecture that could subsume these networks under a unified framework that achieves both higher performance and less overhead. To this end, two fundamental issues are yet to be addressed. The first one is how to implement the back propagation when neuronal activations are discret…
New cohomology theories for heaps and ternary operations linked to group cohomology.
problem Defining and studying cohomology theories for heaps and ternary operations.
method Introduced para-associative and heap cohomology theories, and ternary self-distributive cohomology with abelian heap coefficients.
result Heap cohomology is related to group cohomology via a long exact sequence, and injects into ternary self-distributive cohomology.
Divide and conquer quantizes neural networks, improving accuracy.
problem Quantizing neural networks to reduce memory and compute.
method Divide a pretrained network into sections, train each section independently, then stitch them.
result Improves quantized training accuracy by 21.6% on average.
Introduces Lie semiheaps and their relation to Lie groups and bundles.
problem Defining and understanding Lie semiheaps and their properties.
method Introducing Lie semiheaps and proving their properties in relation to Lie groups and bundles.
result Established the existence of left-invariant vector fields on Lie semiheaps.
We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of Reidemeister, Yoshikawa, and Roseman moves. Our homology has a degenerate subcomplex. T…
Paper introduces compressibility loss for learning sparse neural network weights.
problem Learning highly compressible neural network weights.
method Applying a compressibility loss to minimize the negated sparsity of the signal.
result At critical points, weight vectors are ternary signals with a sparsity directly related to the objective value.
The paper constructs new algebraic structures from Lie algebras and ternary Nambu-Lie algebras, leading to Yang-Baxter operators.
problem Constructing new algebraic structures from Lie algebras and ternary Nambu-Lie algebras.
method Using compositions of binary Lie algebras, 3-Lie algebras, and ternary Nambu-Lie algebras, the paper constructs ternary self-distributive objects and Yang-Baxter operators.
result The constructed Yang-Baxter operators are not gauge equivalent to the transposition operator and can be deformed to new solutions.
New algebraic structure for vector bundles with special properties.
problem Developing new algebraic structures for vector bundles.
method Introducing para-associative algebroids and showing local triviality conditions.
result Existence of a differential connection is necessary and sufficient for local triviality.
We show that some ternary quasigroups appear naturally as invariants of classical links and links on surfaces. We also note how to obtain from them invariants of Yoshikawa moves. In our previous paper, we defined homology theory for algebras satisfying two axioms derived from the third Reidemeister move. In this paper,…
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…
New algorithm improves quantized neural networks for image classification.
problem Improving approximation capabilities of quantized neural networks.
method Proposed a novel gradient-based training algorithm for quantized neural networks.
result State-of-the-art performance on image classification benchmarks.
KD technique improves QDNN performance with reduced hyper-parameters.
problem Restoring performance loss in QDNNs due to quantization.
method Applied KD with reduced hyper-parameters, including a new coefficient reduction technique.
result Achieved 92.7% test accuracy on CIFAR-10 and 67.0% on CIFAR-100 with 2-bit weights.
FTTQ optimizes quantized networks in federated learning, reducing communication costs.
problem Redundant parameters in full-precision models lead to excessive communication costs in federated learning.
method FTTQ algorithm that optimizes quantized networks on clients through self-learning quantization factors.
result FTTQ reduces communication costs and can achieve slightly better performance on non-IID data.
Study of SO(3)-irreducible geometry in complex 5D and ternary Pauli exclusion principle.
problem Exploring SO(3)-irreducible geometry in complex 5D.
method Defined a ternary skew-symmetric tensor, split the 10D space into irreducible SO(3) subspaces, found invariants and defined geometric structures.
result Defined a SO(3)-irreducible geometric structure on a 5D complex Hermitian manifold.
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, one obtains the relations from the knot group, and from the core group. Using the ternary o…
Unified cosmological and Einstein polytope theories.
problem Unified understanding of cosmological and Einstein polytope theories.
method Unified combinatorial perspective of cosmological and Einstein polytope theories.
result Unified construction of cosmological and Einstein polytope theories.
DBQ quantizes lightweight networks efficiently for resource-constrained devices.
problem High computational and storage complexity of deep neural networks on resource-constrained devices.
method A differentiable non-uniform quantizer that can be mapped onto efficient ternary-based dot product engines.
result Achieves state-of-the-art results with minimal training overhead and best accuracy-complexity trade-off.
Quantum invariant derived from ternary cohomology of self-distributive structures.
problem Defining and proving a quantum invariant from ternary cohomology.
method Constructing a ribbon category from a TSD set, showing it coincides with the cocycle invariant.
result The ribbon cocycle invariant is a quantum invariant.
New knot coloring layers simplify homology calculations.
problem Complex knot homology calculations.
method Inductive ternary quasigroup colorings and higher degree homology.
result More efficient homology group access.
Paper ranks stocks by compression risk, not volatility.
problem Investment risk not correlated with stock price volatility.
method Binary-ternary compressive coding of price change time series.
result Compression risk is a better indicator of stock investment risk.
New inequality for ternary variables improves on existing measures.
problem Analyzing excess losses and weighted majority votes with ternary random variables.
method Developed a split-kl inequality and its PAC-Bayes extension.
result Outperforms existing inequalities in certain regimes.
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guara…
FQ-Conv quantizes CNNs for efficient inference with low-precision weights and activations.
problem Reducing precision in DNNs leads to reduced accuracy.
method Fully quantized convolutional neural networks (FQ-Conv) using novel quantization and training techniques.
result Ternary-weight CNNs perform nearly as well as full-precision networks.
A Triangle Generative Adversarial Network (Δ-GAN) is developed for semi-supervised cross-domain joint distribution matching, where the training data consists of samples from each domain, and supervision of domain correspondence is provided by only a few paired samples. Δ-GAN consists of four neural networks, two ge…
Algorithm identifies Copeland winners in dueling bandits with ternary feedback.
problem Identifying Copeland winners in dueling bandits with indifferences.
method Proposed POCOWISTA algorithm with a sample complexity close to lower bound.
result Algorithm shows excellent performance, even for conventional dueling bandits.
Characterizes knot-theoretic flocks up to 64 elements.
problem Classifying ternary quasigroups for knot theory.
method Group action on flock colorings to improve knot-theoretic invariant.
result Enumerated and characterized knot-theoretic flocks up to 64 elements.
UniPhyNet improves cognitive load classification accuracy using EEG, ECG, and EDA signals.
problem Classifying cognitive load using multimodal physiological data.
method Unified network architecture integrating multiscale parallel convolutional blocks, ResNet-type blocks, and channel block attention module. Uses bidirectional gated recurrent unit for temporal dependencies.
result Improves raw signal classification accuracy from 70% to 80% (binary) and 62% to 74% (ternary) on CL-Drive dataset.
Study examines null vector fields on Lorentzian manifolds.
problem Understanding the structure of null vector fields on Lorentzian manifolds.
method Investigates the bundle structure and ternary product of nowhere vanishing null vector fields.
result Null tangent bundle is a non-polynomial graded bundle with a para-associative ternary product.
The group of C1-diffeomorphisms of any sparse Cantor subset of a manifold is countable and discrete (possibly trivial). Thompson's groups come out of this construction when we consider central ternary Cantor subsets of an interval. Brin's higher dimensional generalizations nV of Thompson's group V arise…
Heap theory applied to framed links yields new invariants.
problem Developing invariants for framed links using heap theory.
method Introducing fundamental heap, defining cocycle invariant using ternary cohomology.
result Found cocycles and computed invariants for specific link families.
Lectures explore how differential methods improve understanding of algebraic group orbit spaces.
problem Understanding structure of invariants and orbit spaces of algebraic Lie groups.
method Combines algebraic and differential viewpoints to study orbit spaces.
result Differential approach provides deeper insights into invariants and orbit spaces.