A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Floating Gossip improves continuous machine learning in a decentralized manner.
Distributing Neural Network training is of particular interest for several reasons including scaling using computing clusters, training at data sources such as IOT devices and edge servers, utilizing underutilized resources across heterogeneous environments, and so on. Most contemporary approaches primarily address sca…
Paper proposes robust gossip algorithms for mean and trimmed mean estimation.
The paper gives bounds for how long it takes for gossip protocols to spread information in networks.
AsylADMM improves gossip-based learning for non-smooth objectives.
New gossip algorithms improve robustness of rank-based statistics in decentralized systems.
Multiple gossip steps improve decentralized optimization convergence.
Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.
Decentralized ranking consensus via gossip for robust and scalable systems.
We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over machines that can only communicate to their neighbors on a fixed communication graph. To reduce the communication bottleneck, the nodes compress (e.g. quantize or sparsi…
Consider a network of agents connected by communication links, where each agent holds a real value. The gossip problem consists in estimating the average of the values diffused in the network in a distributed manner. We develop a method solving the gossip problem that depends only on the spectral dimension of the netwo…
For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to a new spherical area measure, the floating area. Remarkably, this floating area…
This paper proposes a gossip-based algorithm for distributed bilevel optimization over networks.
Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries. Results on weighted best and random approximation and the new approach to floati…
We address the issue of speeding up the training of convolutional neural networks by studying a distributed method adapted to stochastic gradient descent. Our parallel optimization setup uses several threads, each applying individual gradient descents on a local variable. We propose a new way of sharing information bet…
We carry out a systematic investigation on floating bodies in real space forms. A new unifying approach not only allows us to treat the important classical case of Euclidean space as well as the recent extension to the Euclidean unit sphere, but also the new extension of floating bodies to hyperbolic space. Our main re…
Multi-simulator training has contributed to the recent success of Deep Reinforcement Learning by stabilizing learning and allowing for higher training throughputs. We propose Gossip-based Actor-Learner Architectures (GALA) where several actor-learners (such as A2C agents) are organized in a peer-to-peer communication t…
Unified framework for Byzantine robust gossip algorithms with guaranteed performance.
Hamiltonian method applied to floating barrier options pricing.
We address the issue of speeding up the training of convolutional networks. Here we study a distributed method adapted to stochastic gradient descent (SGD). The parallel optimization setup uses several threads, each applying individual gradient descents on a local variable. We propose a new way to share information bet…
Introduces new weighted floating functions and affine surface areas.
The wide adoption of DNNs has given birth to unrelenting computing requirements, forcing datacenter operators to adopt domain-specific accelerators to train them. These accelerators typically employ densely packed full precision floating-point arithmetic to maximize performance per area. Ongoing research efforts seek t…
We establish a connection between capillary floating in neutral equilibrium and the billiard ball problem. This allows us to reduce the question of floating in neutral equilibrium at any orientation with a prescribed contact angle for infinite homogeneous cylinders to a question about billiard caustics for their orthog…
Paper examines floating exercise boundaries for American options in time-inhomogeneous models.
In the era of big data, an important weapon in a machine learning researcher's arsenal is a scalable Support Vector Machine (SVM) algorithm. SVMs are extensively used for solving classification problems. Traditional algorithms for learning SVMs often scale super linearly with training set size which becomes infeasible …
Researchers find floating point errors can mislead neural network verifiers.
The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.
Study spherical convex bodies using -floating areas and curvature entropy.
We investigate weighted floating bodies of polytopes. We show that the weighted volume depends on the complete flags of the polytope. This connection is obtained by introducing flag simplices, which translate between the metric and combinatorial structure. Our results are applied in spherical and hyperbolic space. This…
Floating geodesic planes in Hitchin manifolds have fractal closures with non-integer dimensions.
For successful deployment of deep neural networks on highly--resource-constrained devices (hearing aids, earbuds, wearables), we must simplify the types of operations and the memory/power resources used during inference. Completely avoiding inference-time floating-point operations is one of the simplest ways to design …
We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications on an arbitrary connected graph. We develop two no…
Unique floating and buoyancy surfaces identify convex polytopes.
Paper tightens lower bounds on decentralized training complexity.
We compare the results of our earlier paper on the floating in neutral equilibrium at arbitrary orientation in the sense of Finn-Young with the literature on its counterpart in the sense of Archimedes. We add a few remarks of personal and social-historical character.
Constructs minimal immersions with singularities.
The emerging concern about data privacy and security has motivated the proposal of federated learning, which allows nodes to only synchronize the locally-trained models instead their own original data. Conventional federated learning architecture, inherited from the parameter server design, relies on highly centralized…
GOAT learns multiple node representations from graph structure alone.
Conventional hardware-friendly quantization methods, such as fixed-point or integer, tend to perform poorly at very low word sizes as their shrinking dynamic ranges cannot adequately capture the wide data distributions commonly seen in sequence transduction models. We present AdaptivFloat, a floating-point inspired num…
Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of -statistics, relying on more expensive averaging over pairs of observations, is…
Recently, the posit numerical format has shown promise for DNN data representation and compute with ultra-low precision ([5..8]-bit). However, majority of studies focus only on DNN inference. In this work, we propose DNN training using posits and compare with the floating point training. We evaluate on both MNIST and F…
IntSGD compresses SGD gradients without floats, converging as SGD.
In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing unit. In this paper, we address the problem of decentralized minimization of pairw…
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of performance and energy efficiency. In the first part of this paper, the behaviour of …
Geometric mechanics approach to constrained and floating multibody systems using Hamel's equations.
A new approach corrects bias in federated learning due to varying communication links.
The paper proves a conjecture about the shape of floating bodies.
Low-precision DNNs have been extensively explored in order to reduce the size of DNN models for edge devices. Recently, the posit numerical format has shown promise for DNN data representation and compute with ultra-low precision in [5..8]-bits. However, previous studies were limited to studying posit for DNN inference…