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.
Analytical solution found for a three-layer network with a specific activation function.
New algorithm trains deep neural networks without global optimization.
Efficient active learning with abstention reduces label complexity exponentially.
Method extends option valuation for 2D Lévy models.
Active learning refers to the learning protocol where the learner is allowed to choose a subset of instances for labeling. Previous studies have shown that, compared with passive learning, active learning is able to reduce the label complexity exponentially if the data are linearly separable or satisfy the Tsybakov noi…
In the world of big data, large but costly to label datasets dominate many fields. Active learning, a semi-supervised alternative to the standard PAC-learning model, was introduced to explore whether adaptive labeling could learn concepts with exponentially fewer labeled samples. While previous results show that active…
Paper proposes a new activation function to reduce overfitting and large weight update issues.
We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise and are differentially-private. The framework is based on active learning algorithms that are statistical in the sense that they rely on estimates of expectations of functions of filtered random e…
New research explores using exponential activation functions in neural networks, achieving convergence with over-parameterization.
The problem of active diagnosis arises in several applications such as disease diagnosis, and fault diagnosis in computer networks, where the goal is to rapidly identify the binary states of a set of objects (e.g., faulty or working) by sequentially selecting, and observing, (noisy) responses to binary valued queries. …
Analytic networks with bounded coefficients can't outperform polynomial approximations.
Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models. Based on finite sample variances, confidence inte…
We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences.…
Activation functions influence behavior and performance of DNNs. Nonlinear activation functions, like Rectified Linear Units (ReLU), Exponential Linear Units (ELU) and Scaled Exponential Linear Units (SELU), outperform the linear counterparts. However, selecting an appropriate activation function is a challenging probl…
Three-hidden-layer neural networks can approximate Hölder continuous functions uniformly with exponential rate.
For any strictly positive martingale for which has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log strike. We illustrate the versatility of our expansion by computing t…
Rational neural networks approximate functions more efficiently with less depth.
Higher granularity in MoE models boosts expressivity exponentially.
Developing active inference agents for edge devices with limited resources.
Market activity scales near a constant of 0.632 in intrinsic time.
In this paper we address the problem of pool based active learning, and provide an algorithm, called UPAL, that works by minimizing the unbiased estimator of the risk of a hypothesis in a given hypothesis space. For the space of linear classifiers and the squared loss we show that UPAL is equivalent to an exponentially…
We investigate active learning with access to two distinct oracles: Label (which is standard) and Search (which is not). The Search oracle models the situation where a human searches a database to seed or counterexample an existing solution. Search is stronger than Label while being natural to implement in many situati…
New insights on eluder dimension for function approximation in machine learning.
Recently, self-normalizing neural networks (SNNs) have been proposed with the intention to avoid batch or weight normalization. The key step in SNNs is to properly scale the exponential linear unit (referred to as SELU) to inherently incorporate normalization based on central limit theory. SELU is a monotonically incre…
New study shows exponential sample growth for ReQU neural networks.
Study near-maturity convergence rates of American put prices in Lévy models.
New insights into neural network training efficiency.
Catapult phase in neural nets shows exponential loss growth before quick decrease.
PDBAL targets experiments for probabilistic models to maximize insights.
Annealed Entropic Allocation improves ranking and selection by mitigating hard switching and improving finite-budget discrimination.
We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous…
Upper bounds on fixed points in PWL neural networks with hyperplane analysis.
In this paper, the survival function of waiting times between orders and the corresponding trades in a double-auction market is studied both by means of experiments and of empirical data. It turns out that, already at the level of order durations, the survival function cannot be represented by a single exponential, thu…
This work achieves exponential concentration in heavy-tailed data over CAT(κ) spaces using the Fréchet median.
Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic. Bu…
Very deep CNNs achieve state-of-the-art results in both computer vision and speech recognition, but are difficult to train. The most popular way to train very deep CNNs is to use shortcut connections (SC) together with batch normalization (BN). Inspired by Self- Normalizing Neural Networks, we propose the self-normaliz…
New algorithm improves graph-based active learning by identifying unexplored regions.
We derive and analyze a new, efficient, pool-based active learning algorithm for halfspaces, called ALuMA. Most previous algorithms show exponential improvement in the label complexity assuming that the distribution over the instance space is close to uniform. This assumption rarely holds in practical applications. Ins…
Improved diffusion models for image synthesis with better training dynamics.
This research improves neural network performance with adaptive activation functions in sparse data settings.
Layer normalization with activations prevents Gram matrix rank collapse at initialization.
New algorithms reduce label collection for online prediction with expert advice.
FMMNN combines sine activations with multi-component, multi-layer structure for high-frequency function approximation.
Study fractal and regular geometry in deep neural networks.
We stabilize the activations of Recurrent Neural Networks (RNNs) by penalizing the squared distance between successive hidden states' norms. This penalty term is an effective regularizer for RNNs including LSTMs and IRNNs, improving performance on character-level language modeling and phoneme recognition, and outperfor…
Conventional learning with expert advice methods assumes a learner is always receiving the outcome (e.g., class labels) of every incoming training instance at the end of each trial. In real applications, acquiring the outcome from oracle can be costly or time consuming. In this paper, we address a new problem of active…
Solves large-scale metric constrained problems using Project and Forget algorithm.
We consider the problem of learning classifiers for labeled data that has been distributed across several nodes. Our goal is to find a single classifier, with small approximation error, across all datasets while minimizing the communication between nodes. This setting models real-world communication bottlenecks in the …