Randomly chosen primary hidden units and derived secondary units reduce neural network complexity.
problem Large number of hidden units in neural networks.
method Introducing primary and secondary hidden units with random weights for primary units and derived weights for secondary units.
result Significant reduction in the number of hidden units without compromising accuracy.
Wasserstein t-SNE embeds hierarchical datasets considering within-unit distributions.
problem Exploring hierarchical datasets where units are compared based on means of sample distributions.
method Uses Wasserstein distance metric for 2D embeddings of units, approximating Gaussian distributions for efficiency.
result Demonstrates effective embedding of hierarchical datasets, uncovering meaningful structure.
Study calculates first p-widths of unit disk.
problem Computing first p-widths of the unit disk. method Regularity result for integral 1-varifolds on compact 2-manifolds with convex boundary, applied to unit disk.
result Computed first p-widths for p=1,...,4. A fast ML method solves complex combinatorial auction problems.
problem Solving winner determination in multi-unit combinatorial auctions.
method Graph Neural Network (GNN) with half-convolution operations for bid-item graph modeling.
result Approaches optimal performance with negligible revenue loss and low complexity.
IC-Network improves CNNs by integrating elastic collision units.
problem Designing more effective basic units in neural networks.
method Developed IC layer and IC block units combining the IC structure with convolution operations.
result Significant performance improvements in existing CNNs, reducing top-1 error from 22.85% to 21.49% on imagenet.
The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central processing units (CPUs), and thus provide a great deal of promise for computation…
A new method for optimizing regression problems with ReLU units converges.
problem Optimizing regression problems involving ReLU units in large language models.
method Introduced a greedy algorithm based on approximate Newton method, proving convergence in terms of the distance to optimal solution.
result The method converges in the sense of the distance to optimal solution under certain assumptions.
A novel quantum model improves RBM performance and is efficiently trainable.
problem Improving the performance of RBM models.
method Quantum model with parametrically coupled fermions to classical signals.
result The model outperforms classical RBM with the same number of hidden units.
The spectral k-support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank k matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral (k,p)-support norm, whose additional para…
Many state-of-the-art results obtained with deep networks are achieved with the largest models that could be trained, and if more computation power was available, we might be able to exploit much larger datasets in order to improve generalization ability. Whereas in learning algorithms such as decision trees the ratio …
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
problem Computational bottleneck in randomization step for large-scale linear algebra.
method Near constant-time linear random projections from LightOn OPUs.
result Significant acceleration of RandNLA algorithms with negligible precision loss.
This paper improves SVD for recommender systems using block-based matrix factorization.
problem Scalability and performance issues in recommender systems.
method Block-based Singular Value Decomposition (BMF) for matrix factorization.
result BMF paired with SVD enhances performance and scalability.
In this paper, we compute the covolume of the group of units of the quadratic form f_d^n(x) = x_1^2 + x_2^2 + . . . + x_n^2 - d x_{n+1}^2 with d an odd, positive, square-free integer. Mcleod has determined the hyperbolic Coxeter fundamental domain of the reflection subgroup of the group of units of the quadratic form f…
In this paper we propose and investigate a novel nonlinear unit, called Lp unit, for deep neural networks. The proposed Lp unit receives signals from several projections of a subset of units in the layer below and computes a normalized Lp norm. We notice two interesting interpretations of the Lp unit. First…
Frequency-based reservoir improves prediction accuracy and optimizes short-term forecasts.
problem Lack of precise explanation and optimization methods for reservoir computing.
method Inspired by brain's oscillatory dynamics, frequency-based reservoir uses an ensemble of independent oscillatory units.
result Frequency-based reservoir performs as well as or better than random reservoirs and can predict complex spatiotemporal dynamics.
GPU speeds up Monte Carlo simulations for large time steps.
problem Slow convergence and inaccurate solutions with large time steps in Monte Carlo simulations.
method Generalizes the Seven League scheme for GPU acceleration.
result Significantly improved computational speed.
A new algorithm optimizes softmax units in large language models.
problem Efficiently computing gradients for large-scale language models.
method Zero-th Order method for approximating gradients.
result The algorithm converges and efficiently computes gradients.
FasTR efficiently solves sparse and unit-rank tensor regression problems.
problem Sparse and unit-rank tensor regression problems in tensor data analysis.
method FasTR decomposes tensor coefficients into component vectors and estimates each with ℓ1 regularized regression, solving in parallel. result FasTR computes better solutions faster than baseline models.
The Funk-Finsler structure is constructed in hyperbolic models, including the Klein unit disc.
problem Constructing Funk-Finsler structures in hyperbolic models.
method Using Finsler isometries and explicit computations, the Funk-Finsler structure is constructed in various hyperbolic models.
result The Funk-Finsler structure in the Klein unit disc is a Randers metric.
Researchers calculate quasi-local mass on unit spheres at infinity.
problem Computing quasi-local mass on unit spheres at spatial infinity.
method Developed new techniques to evaluate quasi-local mass.
result Leading order term of quasi-local mass recovers stress-energy tensor for vacuum spacetime.
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the…
We present a new blow-up method that allows for establishing the first general formula to compute the perimeter measure with respect to the spherical Hausdorff measure in noncommutative nilpotent groups. This result leads us to an unexpected relationship between the area formula with respect to a distance and the profi…
PALMS reconstructs large-scale networks efficiently with parallel computing.
problem Reconstructing large-scale latent networks from observed dynamics is computationally challenging.
method PALMS (Parallel Adaptive Lasso with Multi-directional Signals) framework for distributed network reconstruction.
result PALMS substantially reduces computational complexity and storage requirements.
The paper evaluates three variants of the Gated Recurrent Unit (GRU) in recurrent neural networks (RNN) by reducing parameters in the update and reset gates. We evaluate the three variant GRU models on MNIST and IMDB datasets and show that these GRU-RNN variant models perform as well as the original GRU RNN model while…
Study on Klein bottle's cotangent bundle using contact homology.
problem Understanding symplectic embeddings of toric domains into the Klein bottle's cotangent bundle.
method Combinatorial description of embedded contact homology, pseudoholomorphic curves.
result Obstruction theorem for symplectic embeddings and computation of Gromov width.
Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
In adversarial attacks to machine-learning classifiers, small perturbations are added to input that is correctly classified. The perturbations yield adversarial examples, which are virtually indistinguishable from the unperturbed input, and yet are misclassified. In standard neural networks used for deep learning, atta…
Geometric structures on quaternionic unit ball for slice regular Möbius transformations.
problem No new problem introduced.
method Introducing Hermitian, Riemannian, and Kähler-like structures on quaternionic unit ball using regular Möbius transformations.
result Geometric structures are natural generalizations of complex setup and solve problems not achieved by other geometries.
We describe a method to compute the norm on the cotangent space to the moduli space of Riemann surfaces associated to the Finsler Teichmüller metric. Our method involves computing the periods of abelian double covers and is easy to implement for Riemann surfaces presented as algebraic curves using existing tools for ap…
A dynamic ResNet model learns different routes for images from different classes.
problem Fixed structure in ResNet-like architectures limits their adaptability to diverse inputs.
method Develops a ResNet-based model that dynamically selects Computational Units for each input image.
result Achieves better results on CIFAR-10 test set compared to the original ResNet-38 architecture.
Lipschitz RNNs improve stability and performance in various tasks.
problem Improving stability and performance of RNNs.
method Introduced a Lipschitz recurrent unit with a linear and Lipschitz nonlinear component for stability analysis.
result Lipschitz RNNs outperform existing units on benchmark tasks.
Study of Riemannian geometry on quaternionic unit ball linked to Sp(1,1) group.
problem Understanding the geometry induced by slice Riemannian metric.
method Developed Lie theoretic study, computed isometry group, compared with quaternionic Poincaré geometry.
result Isometry group of slice Riemannian metric is built from symmetries of Sp(1,1) group.
The stability of the 3-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle, is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of t…
Paper derives Thiele's equation for unit-linked policies in a stochastic volatility model.
problem Deriving pricing formula for unit-linked policies in a stochastic volatility model.
method Derives Thiele's differential equation for a unit-linked policy in the Heston-Hawkes model.
result Established a method to compute reserves in life insurance via solving Thiele's equation.
Study causal effects on humans in mixed human-AI systems with unobserved unit types.
problem Estimating causal effects on humans in systems with unobserved unit types and interaction networks.
method Assumed human-AI prior, causal message passing (CMP) framework, subpopulation analysis.
result Consistently recover human-specific causal effects using subpopulations with varying expected human composition and treatment exposure.
New LTC RNNs can approximate any continuous system with fewer units.
problem Approximating continuous dynamical systems with neural networks.
method Introducing LTC RNNs with variable time-constant synaptic transmission.
result LTC RNNs can approximate any n-dimensional continuous dynamical system. We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we pro…
TPUs speed up financial Monte Carlo simulations.
problem High computational cost of Monte Carlo simulations in finance.
method Empirical experiments comparing TPUs to GPUs for financial Monte Carlo tasks.
result TPUs provide accurate and fast estimators for financial Monte Carlo tasks.
The paper disproves Kaplansky's unit conjecture for certain groups.
problem Disproving Kaplansky's unit conjecture for specific groups.
method Introducing a process called 'left alignment' and recursively constructing taikos to find counterexamples.
result There are no counterexamples to the conjectures for certain groups.
A method to train neural networks that are robust to pruning.
problem Training neural networks to be amenable to pruning.
method Targeted dropout: a simple self-reinforcing sparsity criterion to select units or weights to be dropped.
result Trained networks are robust to post hoc pruning of weights or units.
Quantum computing improves graph neural network aggregation.
problem Limitations of classical GNNs in processing global graph features.
method Quantum computer-generated aggregation weights for graph neural networks.
result Quantum-enhanced GNN performs similarly to classical models on standard datasets.
ReLU activations lead to smoother learning curves compared to sigmoidal activations in neural networks.
problem Comparing the performance of ReLU and sigmoidal activations in neural networks.
method Analytical computation of learning curves in shallow networks with different activation functions.
result ReLU networks exhibit continuous transitions in performance, while sigmoidal networks show discontinuous transitions.
Algorithm removes units and layers of neural networks without losing accuracy.
problem Deploying large neural networks under limited resources.
method Mixed-Integer Linear Programming (MILP) and L1 regularization.
result Lossless compression of neural networks is achieved.
A new method for the unsupervised learning of sparse representations using autoencoders is proposed and implemented by ordering the output of the hidden units by their activation value and progressively reconstructing the input in this order. This can be done efficiently in parallel with the use of cumulative sums and …
Paper proves existence of a CMC hypertorus in 4D sphere using numerical methods.
problem Proving the existence of a constant mean curvature (CMC) hypertorus in \(S^4\).
method Employed the round Taylor method with rational arithmetic and the Poincare-Miranda theorem.
result Existence of a constant mean curvature (CMC) hypertorus in \(S^4\).
ARU adapts deep forecasting models in streaming data with efficient updates.
problem Adapting deep globally trained models for streaming data efficiently.
method ARU combines deep global models with closed-form linear models for per-series adaptation.
result ARU outperforms local adaptation methods on various datasets.
Gating is a key technique used for integrating information from multiple sources by long short-term memory (LSTM) models and has recently also been applied to other models such as the highway network. Although gating is powerful, it is rather expensive in terms of both computation and storage as each gating unit uses a…
Paper proves rigidity and index of Y-cones in unit ball.
problem Proving rigidity and index of Y-cones in the unit ball.
method Analyzes conformal and minimal immersions of Y-cones meeting the boundary orthogonally.
result Y-cones are the only free boundary minimal surfaces with Morse index 2(n-2).