New MIP model and algorithms for Bayesian network learning.
problem Optimization problems with acyclic constraints on directed graphs.
method Mixed integer programming model and iterative algorithms based on topological orders.
result Significantly lower number of constraints and efficient search of topological orders.
DeepTMR reorders matrices without prior knowledge of structural patterns.
problem Matrix reordering without prior structural knowledge.
method DeepTMR uses a neural network to automatically extract features and reorder matrices.
result Trained network produces denoised mean matrix for visualization.
AutoLL uses neural networks to automatically reorder graph nodes for linear layouts.
problem Finding optimal node order in adjacency matrices without predefined features.
method Developed AutoLL-D and AutoLL-U neural network models for one-mode reordering of directed and undirected graphs.
result Demonstrated effectiveness of AutoLL through qualitative and quantitative evaluations.
Conditions for forming nontrivial knots from vector collections.
problem Conditions for forming nontrivial knots from vector collections.
method Analyzing vector collections and their reordering to form knots.
result For n ≥ 7 n \geq 7 n ≥ 7 , it's always possible to reorder vectors to form a nontrivial knot. New algorithm optimizes matrix reordering for noisy disordered matrices.
problem Optimizing matrix reordering for noisy disordered matrices in single-cell biology and metagenomics.
method Proposed a polynomial-time adaptive sorting algorithm to improve upon spectral seriation.
result Our algorithm achieves superior performance compared to existing methods in real datasets.
Maximal extractable value in CFMMs can degrade or improve routing quality, with reordering MEV showing logarithmic impact.
problem Maximal extractable value in constant function market makers (CFMMs) and its impact on routing quality.
method Game theoretic analysis of MEV in CFMMs, constructing price of anarchy and analyzing reordering MEV.
result Conditions under which reordering MEV shows logarithmic impact, and implications for MEV searchers and CFMM designers.
Researchers save memory on MCUs by reordering neural network operators.
problem Memory constraints on microcontrollers for neural network inference.
method Operator reordering to save memory, orthogonal to other compression methods.
result Reduced memory footprint of a CNN to deploy on an MCU with 512KB SRAM.
This work introduces uncertainty principles to mitigate Maximal Extractable Value in blockchain systems.
problem Maximal Extractable Value (MEV) in decentralized systems due to transaction submission privacy and monopolist power.
method Unified approaches via uncertainty principles, akin to harmonic analysis and physics, to quantify trade-offs between transaction flexibility and user economic payoff.
result Demonstrates a quantitative trade-off between transaction flexibility and user economic payoff, analogous to the Nyquist-Shannon sampling theorem.
Ethereum block builders can earn up to $14M/month by reordering transactions, harming users.
problem Block builders can exploit transaction reordering to earn significant profits, harming users.
method Estimation of MEV payments and analysis of reordering effects.
result Block builders can earn up to $14M/month by reordering transactions, skewing the distribution.
We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling e…
PRRO generates synthetic tabular data that improves SL performance and class distribution.
problem Low SL utility of synthetic data due to class imbalance and overlooked data relationships.
method Data pruning and column reordering to optimize SL utility.
result Synthetic data generated with PRRO enhances predictive performance and class distribution.
Study examines trading costs on Uniswap, finding adversarial slippage is significant for large trades and certain assets.
problem Analyzing costs and slippage in decentralized exchanges (DEXs).
method Empirical evaluation of Uniswap's USDC-ETH and PEPE-ETH pools, calculating slippage and reordering slippage.
result Adversarial slippage is significant for large trades and certain assets like PEPE.
Efficiently learns and transports posterior densities for real-time inference.
problem High computational cost of Bayesian inference for complex posterior densities.
method Tensor-train (TT) format for offline learning, conditional transport for online inference.
result Significant improvement in inference performance for high-dimensional problems.
NPMT translates phrases directly, outperforming NMT.
problem Improving machine translation quality and efficiency.
method Uses Sleep-WAke Networks (SWAN) for phrase modeling and soft local reordering.
result NPMT achieves superior performance on machine translation tasks.
Paper improves uncertainty estimation in LLM-as-a-judge systems.
problem Improving uncertainty estimation in LLM-as-a-judge frameworks.
method Generalised probabilistic modelling and improved uncertainty estimates.
result Proposed uncertainty estimates significantly improve system efficiency.
Hyperfitting improves LLM generation quality by enhancing diversity, contrary to simple temperature scaling.
problem Improving open-ended generation quality of LLMs with minimal fine-tuning effort.
method Demonstrates that hyperfitting, a phenomenon where LLMs are fine-tuned to near-zero training loss, enhances generation quality and mitigates repetition.
result Hyperfitting is distinct from temperature scaling and involves a dynamic, context-dependent rank reordering mechanism in the final transformer block.
In (exploratory) factor analysis, the loading matrix is identified only up to orthogonal rotation. For identifiability, one thus often takes the loading matrix to be lower triangular with positive diagonal entries. In Bayesian inference, a standard practice is then to specify a prior under which the loadings are indepe…
Seq2Tens uses tensors to efficiently represent sequences, improving performance on time series and video tasks.
problem Challenges in analyzing sequential data due to complex dependencies and non-commutativity.
method Uses tensor algebra to capture dependencies and low-rank tensor projections to manage computational complexity.
result State-of-the-art performance on multivariate time series classification and video generation benchmarks.
We study the space $\nua{m}{d}$ of clouds in $\bbr^d$ (ordered sets of m m m points modulo the action of the group of affine isometries). We show that $\nua{m}{d}$ is a smooth space, stratified over a certain hyperplane arrangement in $\bbr^m$ . We give an algorithm to list all the chambers and other strata (this is indep…
New method reduces summary points for datasets while maintaining quality.
problem Thinning datasets to reduce summary points while maintaining quality.
method Low-rank analysis of sub-Gaussian thinning.
result Guarantees high-quality compression for any distribution and kernel.
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder t…
Janossy pooling averages permutation-sensitive functions over all sequences to create invariant functions.
problem Creating deep, invariant functions for variable-size inputs.
method Janossy pooling: average permutation-sensitive functions over all reorderings.
result Improved performance over state-of-the-art methods.
Proposes tPARAFAC2 for tracking evolving patterns in time-evolving data.
problem Lack of temporal regularization in tensor factorizations for capturing evolving patterns.
method Temporal PARAFAC2 (tPARAFAC2) with temporal regularization.
result tPARAFAC2 accurately captures evolving patterns better than existing methods.
Quantum algorithm samples from SDEs using DQCs and quantile mechanics.
problem Sampling from solutions of stochastic differential equations.
method Differentiable quantum circuits (DQCs) encoding latent variables, quantile mechanics.
result Quantum algorithm generates time-series from SDEs.
KQSP method prevents crossing issues in probabilistic K-line forecasts.
problem Quantile and K-line crossing issues in probabilistic K-line forecasts.
method Parameter-free and training-free reconciliation method (KQSP).
result KQSP reduces crossing rates to zero for all test data.
Research analyzes ethical concerns around MEV on blockchain and social media.
problem Fairness issues in transaction ordering on blockchain.
method Applied NLP methods to analyze topics in tweets on MEV.
result Tweets discussed ethical concerns like security, equity, and solutions to MEV.
PRESTIGE improves privacy in stochastic optimization by combining private sampling and CL.
problem Privacy leakage in stochastic optimizations for large-scale sensitive data.
method Introduces PRESTIGE, a robust stochastic optimization framework that combines private sampling and gradual curriculum learning.
result PRESTIGE achieves a good tradeoff between privacy preservation and robustness over baselines.
New model optimizes portfolios with realistic transaction costs.
problem Real-world transaction costs impact portfolio profitability.
method DPGRGT model with 2D relative-attentional Gated Transformer.
result Model outperforms baseline models in U.S. stock market data.
Paper introduces Deep Sets for Symmetric Elements (DSS) layers for learning sets of symmetric elements.
problem Learning sets of symmetric elements is underexplored.
method Characterized equivariant layers, showed DSS layers are universal approximators, and demonstrated their effectiveness.
result DSS layers improve set-learning architectures across various data types.
Analyzes tt*-structures from A D E ADE A D E -type Stokes data.
problem Classifying tt*-structures over C ∗ \mathbb{C}^* C ∗ . method Isomonodromic deformations with upper unitriangular real Stokes matrices.
result Establishes a direct analytic realization of the A D E ADE A D E classification. Patch ranking improves CNN performance by focusing on object content, not location.
problem CNNs lack rotation and translation invariance, limiting model capacity.
method Patch ranking before convolution and pooling to encode invariance.
result Patch ranking module improves CNN performance on various tasks.
Unified framework connects different neural network models.
problem Understanding the geometry of neural network loss landscapes.
method Unified framework capturing four symmetry classes.
result First discovery of low- and zero-barrier linear interpolation paths.
Deep model learns protein interfaces from high-order interactions.
problem Predicting protein interfaces from amino acid pairs.
method Graph neural networks and convolutional neural networks for 2D dense predictions.
result Our method consistently improves interface prediction performance.
We propose several novel methods for enhancing the multi-class SVMs by applying the generalization performance of binary classifiers as the core idea. This concept will be applied on the existing algorithms, i.e., the Decision Directed Acyclic Graph (DDAG), the Adaptive Directed Acyclic Graphs (ADAG), and Max Wins. Alt…
Unified optimization framework for matrix seriation.
problem Discovering latent structure in relational data.
method Mathematical optimization models for seriation.
result Optimization models enhance solution quality and interpretability.
New analysis reveals gaps in selective classifiers, guiding improvements.
problem Improving selective classifiers to match perfect-ordering oracle performance.
method Formalized selective classification gap, decomposed into five sources of looseness.
result Monotone post-hoc calibration has limited impact on closing the gap.
CTD efficiently decomposes tensors for fast, accurate, and interpretable patterns.
problem Finding patterns and anomalies in tensors efficiently and interpretably.
method CTD: a sampling-based tensor decomposition method.
result CTD-S is 17-83x more accurate and 5-86x faster than state-of-the-art methods.
Proves Weinstein conjecture for specific contact manifolds.
problem Proving the Weinstein conjecture for a specific class of contact manifolds.
method Introduced iterated planar Lefschetz fibrations and open book decompositions to prove the conjecture.
result Contact manifolds supporting iterated planar open book decompositions satisfy the Weinstein conjecture.
Paper analyzes iterates in high-dimensional linear models and proposes estimators for their generalization error.
problem Analyzing iterates in high-dimensional linear models with comparable feature and sample sizes.
method Novel estimators for generalization error, debiasing corrections, and valid confidence intervals.
result Estimators are n \sqrt{n} n -consistent and can be used for early stopping. cGAP visualizes high-dimensional categorical data with interpretable geometric structure.
problem Lack of visualization tools for high-dimensional categorical data.
method cGAP uses Homogeneity Analysis (HOMALS) to embed data in a 3D space and maps it to colors.
result cGAP reveals coherent clusters, outliers, and local-to-global structure in categorical data.
cGAP visualizes high-dimensional categorical data with interpretable geometric structure.
problem Lack of visualization tools for high-dimensional categorical data.
method cGAP uses Homogeneity Analysis (HOMALS) to embed data in a 3D space and maps it to colors for visualization.
result cGAP reveals coherent clusters, outliers, and local-to-global structure in categorical data.
Paper analyzes iterative learning for concept classes and learns half-spaces.
problem Learning concept classes efficiently with iterative learners.
method Analyzes various settings of iterative learning and provides a constructive algorithm for half-spaces.
result Constructive iterative algorithm for learning half-spaces from informant.
WaveFit uses fixed-point iteration to create high-quality neural vocoders.
problem Creating high-quality neural vocoders with fast inference.
method Integrates GANs' adversarial training into a DDPM-like iterative framework based on fixed-point iteration.
result WaveFit synthesizes speech with naturalness comparable to human speech, and is significantly faster than existing methods.
Last iterate of Extragradient algorithm converges slower than averaged iterates in saddle point problems.
problem Smooth convex-concave saddle point problems
method Analysis of Extragradient (EG) algorithm convergence rates
result The last iterate of EG converges at a rate of O(1/√T), compared to O(1/T) for averaged iterates
We prove that an iterated torus knot type fails the uniform thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot …
Sharp analysis of power iteration for tensor PCA, improving convergence and stopping criteria.
problem Analyzing the power iteration algorithm for tensor PCA to improve convergence and stopping criteria.
method Sharp bounds on the number of iterations, revealing a smaller algorithmic threshold, proposing a stopping criterion.
result Sharp bounds on the number of iterations required for power method to converge, revealing a smaller algorithmic threshold than previously conjectured.
New estimators reduce computation for Kendall's tau and conditional Kendall's tau matrices under structural assumptions.
problem Efficient estimation of Kendall's tau and conditional Kendall's tau matrices for large dimensions.
method Averaging pairwise estimates over blocks or conditional estimates, exploiting structural assumptions.
result Improved estimators with reduced computational cost and similar error level.
Paper proves exponential lower bounds for policy iteration in MDPs.
problem Proving lower bounds for policy iteration in multi-action MDPs.
method Generalized previous results to k-action MDPs, constructed families of MDPs.
result Proved novel exponential lower bound of (3+k)2^(N/2-3) iterations.