The paper defines matrices related to cluster transformations and proves certain quivers have no maximal sequences.
problem Proving quivers associated with once-punctured surfaces do not have maximal green or reddening sequences.
method Defining matrices related to cluster transformations and showing their relationships to the Jacobian and C-matrix.
result Quivers associated with once-punctured surfaces do not have maximal green or reddening sequences.
Study pinching sequences to understand degeneration of anti-de Sitter structures.
problem Understanding the degeneration of anti-de Sitter structures along pinching sequences.
method Parameterization of deformation space and analysis of pinching sequences.
result Regular anti-de Sitter structures appear as limiting points.
A faster method for optimizing DNA and protein sequences using machine learning.
problem Designing DNA and protein sequences with improved function.
method Activation maximization with a straight-through approximation and adaptive entropy variable.
result Fast SeqProp achieves up to 100-fold faster convergence and improved fitness optima.
The paper establishes conditions for optimal sampling configurations on complex manifolds.
problem Finding optimal sampling configurations on complex manifolds.
method Analyzes point configurations on compact complex manifolds using tensor powers of Hermitian ample line bundles.
result Necessary and sufficient conditions for the existence of asymptotically Fekete sequences.
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from…
Improves neural program synthesis by addressing aliasing and syntax issues.
problem Ignoring program aliasing and syntax in neural program synthesis.
method Reinforcement learning and direct syntax maximization training.
result Improved accuracy, especially with limited training data.
Proposes a curriculum learning algorithm to maximize cumulative return in reinforcement learning.
problem Maximizing cumulative return in reinforcement learning tasks.
method Task sequencing algorithm maximizing cumulative return, using curriculum learning to minimize suboptimal actions.
result Significantly better performance on cumulative return maximization compared to metaheuristic algorithms.
Paper clusters event sequences using a reinforcement learning approach with policy mixture model.
problem Clustering event sequences with varying temporal patterns.
method Reinforcement learning with a policy mixture model, decomposing sequences into states and actions.
result Effective clustering of event sequences into underlying policies, outperforming existing methods.
The goal of temporal alignment is to establish time correspondence between two sequences, which has many applications in a variety of areas such as speech processing, bioinformatics, computer vision, and computer graphics. In this paper, we propose a novel temporal alignment method called least-squares dynamic time war…
Expands Hidden Markov Model to include Markov chain observations.
problem Handling Markov chain observations in Hidden Markov Models.
method Developed Expectation-Maximization algorithm and Viterbi algorithm analogs.
result Estimates transition probabilities for hidden states and observations.
We recently discovered a relationship between the volume density spectrum and the determinant density spectrum for infinite sequences of hyperbolic knots. Here, we extend this study to new quantum density spectra associated to quantum invariants, such as Jones polynomials, Kashaev invariants and knot homology. We also …
This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on R converges to the exponential utility. Under a …
Enhances sequence memory capacity in neural networks.
problem Limited sequence capacity in Hopfield-like neural networks.
method Introducing a nonlinear interaction term and a generalized pseudoinverse rule.
result Significantly increased sequence capacity with novel scaling laws.
In the large financial market, which is described by a model with countably many traded assets, we formulate the problem of the expected utility maximization. Assuming that the preferences of an economic agent are modeled with a stochastic utility and that the consumption occurs according to a stochastic clock, we obta…
HARMLESS meta-learning method models short event sequences with relational information.
problem Learning heterogeneous point process models from short event sequence data.
method Hierarchical Bayesian mixture Hawkes process model with stochastic variational meta expectation maximization.
result HARMLESS outperforms existing methods in predicting future events.
A generic geodesic on a finite area, hyperbolic 2-orbifold exhibits an infinite sequence of penetrations into a neighborhood of a cone singularity, so that the sequence of depths of maximal penetration has a limiting distribution. The distribution function is the same for all such surfaces and is described by a fairly …
Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the volatility of asset prices (as well as the drift) varies. Degeneracies arise from …
Study calculates stable norm of slit tori using Farey sequence.
problem Computing the stable norm of slit tori.
method Explicit computations using the Farey sequence and gluing slit tori.
result Estimates the asymptotic counting of simple homology classes.
Paper uses PPO and PPO-dynamic for sequence generation tasks, improving stability and performance.
problem Intractable backpropagation issue in sequence generation tasks.
method Replaces policy gradient with PPO and proposes a dynamic approach for PPO (PPO-dynamic).
result PPO and PPO-dynamic outperform policy gradient in sequence generation tasks.
In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse Baum-Connes assembly map is an isomorphism for the associated metric space X. As discussed in the first paper in this s…
Deep models generate and optimize DNA sequences for protein binding.
problem Designing DNA sequences with desired properties.
method Three approaches: GAN for synthetic sequences, activation maximization for design, and a combined method.
result Generated DNA sequences have superior properties to those in training data.
Optimizes profit in targeted marketing across multiple markets with varying marketing expenditures.
problem Maximizing profit in a sequential marketing strategy with multiple markets and varying marketing costs.
method Near-optimal algorithms in an adversarial bandit setting, proving regret bounds for different demand curve types.
result Proved near-optimal regret bounds for the profit-maximization problem in targeted marketing.
In this paper we prove that if we consider the standard real metric on simplicial rooted trees then the category Tower-Set of inverse sequences can be described by means of the bounded coarse geometry of the naturally associated trees. Using this we give a geometrical characterization of Mittag-Leffler property in inve…
BestChanID identifies the channel with maximal capacity using training sequences.
problem Identifying the channel with maximal capacity among several discrete memoryless channels.
method Formulated as a multi-armed bandit problem, proposed a capacity estimator, and developed gap-elimination algorithms.
result Guaranteed to output the DMC with the largest capacity with a desired confidence.
Deep Convolutional Neural Networks (DCNN) has shown excellent performance in a variety of machine learning tasks. This manuscript presents Deep Convolutional Neural Fields (DeepCNF), a combination of DCNN with Conditional Random Field (CRF), for sequence labeling with highly imbalanced label distribution. The widely-us…
QATS efficiently decodes HMMs with polylogarithmic complexity.
problem Efficiently decoding hidden Markov models from noisy observations.
method Divide-and-conquer procedure with polylogarithmic sequence complexity and cubic state space complexity.
result QATS outperforms Viterbi and PMAP in speed and accuracy.
LES optimizes designs by sampling descent sequences, achieving strong sample efficiency.
problem Optimizing large, complex design spaces is infeasible and unnecessary.
method LES uses Bayesian optimization to target solutions reachable by iterative optimizers.
result LES achieves strong sample efficiency compared to existing methods.
We prove that the Yang-Mills α-functional satisfies the Palais-Smale condition. This guarantees the existence of critical points, which are called Yang-Mills α-connections. It was shown by Hong, Tian and Yin in [10] (to appear in Comm. Math. Helv.) that as α→1, a sequence of Yang-Mills α-connections converge…
New method combines personal and reference genomes for better machine learning in DNA sequencing.
problem Improving accuracy of genetic variant calls in sequencing data.
method Interlaces personal and reference genomes to generate images for machine learning.
result Significant improvement in germline variant calling and somatic variant calling across tumor/normal data.
In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of t…
We discuss the geometry of some arithmetic orbifolds locally isometric to a product of real hyperbolic spaces of dimension two and three, and prove that certain sequences of non-uniform orbifolds are convergent to this space in a geometric ("Benjamini--Schramm") sense for hyperbolic three--space and a product of hyperb…
Generative Bridging Network improves sequence prediction models by penalizing confidence and smoothing language.
problem Data sparsity and overfitting in sequence prediction tasks.
method Introduces a bridge module to extend ground truth and minimize KL-divergence between bridge distribution and generator.
result Significant improvements over strong baselines in machine translation and text summarization tasks.
The paper proves the existence of boundary minimal hypersurfaces in compact manifolds with boundary.
problem Existence of boundary minimal hypersurfaces in compact manifolds with boundary.
method Min-max theory applied to local maximizers of width in conformal classes.
result Existence of a sequence of properly embedded equidistributed boundary minimal hypersurfaces.
A new regularizer boosts long-range dependency in sequence data.
problem Improving long-range dependency in sequence data models.
method Developed a mutual information regularizer to enhance sequence learning.
result The approach increases mutual information and likelihood on holdout data.
New algorithm for quickly deciding on tech innovations to maximize ROI.
problem Maximizing ROI in repeated decision-making for tech innovations.
method Developed a novel algorithm for learning optimal decision-making policies over innovation proposals.
result Algorithm converges to optimal policy with a rate of order min{1/(NΔ2),N−1/3}. The decorated hypercube found in the construction of Khovanov homology for links is an example of a Boolean lattice equipped with a presheaf of modules. One can place this in a wider setting as an example of a coloured poset, that is to say a poset with a unique maximal element equipped with a presheaf of modules. In t…
Empirical Bayes method improves Gaussian sequence model inference.
problem Estimating parameters in correlated Gaussian sequence models.
method Maximum Composite Marginal Likelihood (CML) estimator, leveraging geometric Brascamp-Lieb inequality.
result CML estimator converges at rate \( n_*^{-1/2} \) in weighted Hellinger distance.
In this paper, we prove that a normal subgroup N of an n-dimensional crystallographic group G determines a geometric fibered orbifold structure on the flat orbifold E^n/G, and conversely every geometric fibered orbifold structure on E^n/G is determined by a normal subgroup N of G, which is maximal in its commensurabili…
Study eigenvalues and shapes, proving sharp inequalities for Steklov eigenvalues.
problem Eigenvalue continuity and shape optimization for Laplace and Steklov problems.
method Variational eigenvalue analysis, Sobolev space convergence, shape optimization techniques.
result Sharp isoperimetric inequalities for Steklov eigenvalues, upper bound 8πk for k-th perimeter-normalized eigenvalue. The study extracts market direction from transaction data.
problem Extracting market direction from transaction data.
method Dynamic equation with time scale selection from past transactions.
result Automatic determination of time scale for price calculation.
Binary sequence correlation estimation fails but trinary data succeeds.
problem Estimating correlation in binary sequences generated by thresholding a hidden continuous sequence.
method Formal analysis and numerical experiments on likelihood maximization and discretization effects.
result Consistent estimation of correlation is possible with trinary data but not with binary data.
Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.
problem Classifying CR hypersurfaces with maximal symmetry in low dimensions.
method Introduced modified CR symbols to organize local invariants, classified hypersurfaces through modified symbols, and used Lie group structures.
result Found nine model structures among locally homogeneous 2-nondegenerate hypersurfaces in C4. Differentiable submodular maximization combines learning and optimization.
problem Learning and optimizing submodular functions separately.
method Interpreting greedy maximization as distributions, smoothing, and differentiating.
result The approach optimizes submodular functions with theoretical guarantees.
Algorithm optimizes biological sequences using bootstrapped training with a score-conditioned generator.
problem Optimizing biological sequences for a black-box score function.
method Bootstrapped training of score-conditioned generator (BootGen) algorithm.
result Our method outperforms competitive baselines on biological sequential design tasks.
A new model uses normalizing flows for discrete sequences, improving generation speed.
problem Modeling discrete sequences like text using normalizing flows poses challenges.
method Proposes a VAE-based model with autoregressive and non-autoregressive flow architectures.
result Flow-based models can match or improve on autoregressive baselines for discrete sequence tasks.
Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is represented by a nonuniquely ergodic ending lamination, and (3) the sequence divides into a finite set of subsequences, each of wh…
MASA discovers motifs in noisy time series data.
problem Discovering common sequences of states in noisy time series data.
method MASA uses an expectation-maximization approach to solve a large optimization problem.
result MASA outperforms state-of-the-art baselines by up to 38.2%.
Modeling disease progression using irregular time intervals in EHRs.
problem Challenges in analyzing temporal data from EHRs.
method Developed a Markovian generative model using EHR data.
result Model accurately recovers underlying disease progression patterns from irregular time intervals.