The study finds topological barriers for robustly transitive maps on surfaces.
problem Identifying necessary conditions for robustly transitive maps on surfaces.
method Analyzing partial hyperbolicity and homotopy to linear maps.
result Robustly transitive maps on surfaces are limited to torus and klein bottle, and homotopic to linear maps with eigenvalues > 1.
The paper proves properties of robust diffeomorphisms and their invariant sets.
problem Investigating robust diffeomorphisms and their invariant sets.
method Demonstrates the robust inverse shadowing property on chain recurrent and transitive sets.
result Proves that invariant sets are hyperbolic under robust inverse shadowing.
We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms f f f on compact 3 3 3 -manifolds with fundamental groups of exponential growth such that f n f^n f n is not homotopic to identity for all n > 0 n>0 n > 0 . These provide counterexamples to a classification conjecture of Pujals.
Study of transitivity in partially hyperbolic maps with expanding linear part.
problem Transitivity of partially hyperbolic endomorphisms with expanding linear part.
method Use of Blichfedt's theorem to analyze dynamical information from homology action.
result Robust transitivity condition and complete dichotomy for special cases.
In this paper we study how to learn stochastic, multimodal transition dynamics in reinforcement learning (RL) tasks. We focus on evaluating transition function estimation, while we defer planning over this model to future work. Stochasticity is a fundamental property of many task environments. However, discriminative f…
A new method identifies critical transitions in high-dimensional data.
problem Challenges in identifying critical transitions in high-dimensional time-series data.
method Spatial-temporal Principal Component Analysis (stPCA)
result Identifies tipping points before critical transitions reliably.
A new method learns robust policies from offline data with latent structures.
problem Conservative policies under unrealistic dynamics shifts.
method d-RRMDP framework with f f f -divergence regularization and R2PVI algorithm. result R2PVI learns robust policies with superior computational efficiency.
Weight decay stabilizes training dynamics by slowing progressive sharpening.
problem Understanding how weight decay affects training stability in deep learning models.
method Analyzing weight decay effects at the Edge of Stability, developing a mathematical framework.
result Weight decay dampens oscillations and stabilizes sharpness in CNNs, causing a phase transition in MLPs.
Model improves robustness of neural network sequences without transition failures.
problem Learning and generating complex sequences of motor primitives without interference.
method Inspired by thalamocortical circuit, uses specific module for motif transitions.
result Improved robustness of sequence generation with no transition failures.
VC classes can be robustly learned but only by misusing the learning method.
problem Learning adversarially robust predictors.
method Proves that VC classes are learnable with an improper learning rule.
result VC classes are robustly learnable with improper methods.
Study proposes a new early-warning framework for high-dimensional complex systems.
problem Predicting critical transitions in complex systems like epileptic seizures.
method Integrates manifold learning with stochastic dynamical system modeling, using Schrödinger bridge theory.
result Demonstrates higher sensitivity and robustness in epilepsy prediction.
New approach to robustly reliable learners against instance-targeted attacks.
problem Addressing data poisoning attacks on robustly reliable learners.
method Defining regularized robustly reliable learners and efficient algorithms.
result Efficient algorithms for robustly reliable learners with sublinear runtime.
Algorithm estimates mixtures of arbitrary Gaussians robustly in presence of corruptions.
problem Estimating mixtures of arbitrary Gaussians in the presence of a constant fraction of arbitrary corruptions.
method Polynomial-time algorithm using partial clustering and tensor decomposition.
result Resolves the main open problem in several previous works on algorithmic robust statistics.
Study shows pre-event L2 liquidity state predicts crypto futures liquidity better than event labels.
problem Understanding how crypto futures liquidity changes over time.
method Combining L2 order book data, trade-flow records, and macro-event windows to define discrete liquidity-state transitions and evaluate models.
result Pre-event L2 liquidity state predicts post-event liquidity regimes better than event labels, and order flow adds value only when layered on top of the state model.
Proposes robust graph embedding with noisy link weights.
problem Learning feature vectors from noisy link weights.
method β-graph embedding with empirical moment β-score.
result Computational tractability and local minimization of β-score.
Study analyzes bond price covariation robustly under no-arbitrage conditions.
problem Identifying the number of statistically relevant factors in the bond market.
method Nonparametric analysis of realized covariations in a general no-arbitrage setting.
result A high number of factors is needed to describe term structure evolution and term structure of volatility varies over time.
Adversarial examples arise from computational constraints in high-dimensional spaces.
problem Why classifiers in high dimensions are vulnerable to adversarial perturbations.
method Proved computational intractability of robust learning in high-dimensional space.
result Adversarial examples are due to computational limitations, not information theory.
Robustly combines supervised and bandit feedback for contextual bandits.
problem Learning from mixed supervised and bandit data with potentially misaligned costs.
method Developed no-regret algorithms robust to misaligned cost distributions.
result Our approach is feasible and helpful in practice, as shown by empirical evaluations.
Adversarially trained transformers can learn robustly across tasks with minimal tuning.
problem Adversarial attacks and the high cost of adversarial training.
method Adversarial pretraining followed by in-context learning.
result Single-layer linear transformers can generalize robustly to unseen tasks.
Robustly estimates mean in incomplete data with corrupted examples.
problem Estimating mean in data with missing values and outliers.
method Algorithms for robust estimation with optimal error guarantees in nearly-linear time.
result Information-theoretically optimal error guarantees for mean estimation.
Robustly computes intrinsic coordinates on point clouds using resampling and averaging.
problem Computing intrinsic coordinates on noisy or outlier-prone point clouds.
method Subsample data, vary hyperparameters, cluster candidate embeddings, identify representative embeddings, and average them using Procrustes analysis.
result Robust to noise and outliers, validated on synthetic and real data.
Robustly learns Ising models with corrupted data.
problem Learning Ising models corrupted by a constant fraction of adversarial samples.
method Develops a computationally efficient algorithm for robust learning.
result First near-optimal error guarantees for robust learning of Ising models.
New model selects robustly in adversarial reinforcement learning with unknown corruption.
problem Adversarial corruption in reinforcement learning with unknown total corruption amount.
method Model selection approach for finite-horizon tabular and linear MDPs.
result First worst-case optimal bound without knowledge of total corruption.
New spectral algorithm estimates random graph parameters robustly against corrupted nodes.
problem Estimating the parameter of an Erdős-Rényi random graph with adversarial corruption.
method Spectral algorithm designed for computational efficiency, with an inefficient but information-theoretic alternative.
result Achieves optimal error rate up to logarithmic factors, matching statistical lower bounds.
Robustly estimates posterior with adversarial outliers using Rob-ULA.
problem Estimating posterior distribution in the presence of adversarial outliers.
method Proposes Rob-ULA, a robust variant of ULA, and provides finite-sample analysis.
result Sampling from p T p_T p T with e x t d i s t ( p T , p ∗ ) ≤ ε e x t s f a c c + i l d e O ( ε ) ext{dist}(p_T, p^*) \leq \varepsilon_{ extsf{acc}} + ilde{\mathcal{O}}(ε) e x t d i s t ( p T , p ∗ ) ≤ ε e x t s f a cc + i l d e O ( ε ) after T = i l d e O ( d / ε e x t s f a c c ) T= ilde{\mathcal{O}}(d/\varepsilon_{ extsf{acc}}) T = i l d e O ( d / ε e x t s f a cc ) iterations. The paper explores the difficulty of robust machine learning models.
problem Understanding the vulnerability of machine learning models to adversarial attacks.
method The study uses computational learning theory to analyze the feasibility of robust learning from both sample and computational complexity perspectives.
result No non-trivial concept class can be robustly learned in the distribution-free setting against a single-bit adversary, and the class of monotone conjunctions cannot be robustly learned under the uniform distribution against an adversary that can perturb ω ( log n ) ω(\log n) ω ( log n ) bits. New approach to algorithmic fairness for human-AI collaboration considers compliance with human decisions.
problem Current fairness approaches assume perfect human compliance, but real-world compliance is often poor.
method Defines compliance-robustly fair algorithms and proposes an optimization strategy to improve fairness.
result Algorithmic recommendations can improve fairness even if humans do not fully comply with fair algorithms.
Study improves CI tests for relational data to robustly discover causal structures.
problem Learning causal relationships from relational data.
method Conduct CI tests against relational data to robustly recover causal structure.
result Effective approach demonstrated through experiments.
Paper proposes a method to robustly estimate volatility from OTM options.
problem Accurately measuring volatility in real-world markets with limited option trading.
method Constructs an arbitrage-free continuous option pricing function from bid-ask spreads of OTM options.
result Robustly calculates volatility indices with theoretical consistency, even in low-liquidity markets.
Framework for causal signals in non-stationary financial markets.
problem Constructing causal signals in non-stationary financial time series.
method Combines normalized indicators and causally computed derivatives, with hysteresis-based decision mapping.
result Demonstrates risk-reshaping effect with smoother trajectories and reduced drawdowns.
Transformers learn to use induction heads or shortcuts based on data diversity.
problem How data diversity influences the behavior of transformers.
method Gradient-based training of a single-layer transformer on a minimal task.
result Data diversity steers transformers toward induction heads or shortcuts.
New algorithms learn model complexity and stochasticity robustly in online prediction.
problem Learning model complexity and stochasticity in online prediction.
method Probabilistic structural risk minimization integrated into adaptive algorithms.
result Competitive regret bounds for model and stochasticity adaptivity.
Truncated CauchyNMF robustly learns subspaces from noisy data.
problem Outliers in non-negative matrix factorization (NMF) cause failure.
method Proposes Truncated CauchyNMF loss to handle outliers.
result Theoretical analysis and experimental validation show Truncated CauchyNMF's robustness.
Develops methods to simulate rare transitions in molecular systems.
problem Rare transitions between metastable states in molecular systems are difficult to study due to limited data.
method Two novel methods: chain-based and midpoint-based approaches.
result Demonstrates effectiveness of methods in both data-rich and data-scarce scenarios.
The paper models market crashes as phase transitions, finding dynamic transitions offer better predictions.
problem Understanding and predicting extreme financial events like market crashes.
method Employing phase transition theory, focusing on endogenous crashes, and comparing DPT, CPT, and SPT.
result Dynamic phase transitions provide more accurate predictions of market crashes compared to critical and stochastic models.
This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.
problem Understanding and characterizing transitive double Lie algebroids.
method Using core diagrams and equivalence of transitive core diagrams with transitive double Lie groupoids.
result Transitive double Lie algebroids are completely determined by their core diagrams.
Paper analyzes and improves DNNs trained with noisy labels.
problem Training deep neural networks with noisy labels.
method Characterize test accuracy as a function of noise ratio, apply cross-validation, and use Co-teaching strategy.
result Our strategy consistently improves DNNs' generalization performance.
In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for L 2 , 1 L_{2,1} L 2 , 1 norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column outliers, we reformulate the batch mode matrix L 2 , 1 L_{2,1} L 2 , 1 norm minimization with…
This paper shows semi-equivelar toroidal maps are vertex-transitive covers.
problem Understanding the relationship between semi-equivelar and vertex-transitive toroidal maps.
method Proving semi-equivelar toroidal maps are quotients of vertex-transitive toroidal maps.
result Each semi-equivelar toroidal map has a finite vertex-transitive cover.
DynBRO learns robustly from dynamic Byzantine workers.
problem Fault-tolerant distributed learning with dynamic Byzantine workers.
method Multi-level Monte Carlo (MLMC) gradient estimation and adaptive learning rate.
result DynaBRO nearly matches static setting's convergence rate with O ( T ) \mathcal{O}(\sqrt{T}) O ( T ) Byzantine worker changes. Novel algorithm detects causal macrovariables from high-dimensional data.
problem Leveraging high-dimensional observational datasets for coarse-grained causal models.
method Inspired by information bottlenecks, novel algorithm detects macrovariables and investigates causal relationships through additive noise models.
result Algorithm robustly detects and infers causal relationships in both synthetic and real climate datasets.
Two-dimensional transition rates improve life insurance reserve calculations.
problem Calculating life insurance reserves with Markov assumptions.
method Introducing two-dimensional forward and backward transition rates.
result Two-dimensional transition rates enable more accurate reserve calculations.
Machine learning approximates phase transitions using Fisher information.
problem Understanding phase transitions from data using machine learning.
method Information geometry and Fisher information.
result Machine learning indicators approximate the square root of Fisher information.
Paper shows how to identify and reconstruct degree-d PTFs robustly from their Fourier coefficients.
problem Identifying and reconstructing degree-d polynomial threshold functions (PTFs) from their Fourier coefficients.
method Proves a robust version of the theorem that degree-d Chow parameters uniquely characterize degree-d PTFs, and uses this to develop efficient algorithms.
result Boolean degree-d PTFs are robustly identifiable from their degree-d Chow parameters.
Dual-T method improves transition matrix estimation in noisy label learning.
problem Large estimation error in noisy class posterior leads to poor transition matrix estimation.
method Introducing an intermediate class to avoid direct estimation of noisy class posterior, factorizing the transition matrix into two easier-to-estimate matrices.
result The dual-T estimator leads to better classification performances.
Double-well transitions are stiffer than minimal surfaces.
problem Rigidity of double-well phase transitions compared to minimal hypersurfaces.
method Comparison of rigidity properties between double-well phase transitions and minimal hypersurfaces.
result Double-well phase transitions exhibit more rigidity than minimal hypersurfaces.
Defines SETR to measure carbon transition risk for investors.
problem Difficulty in measuring the magnitude of carbon transition risk for investors.
method Defines Single Event Transition Risk (SETR) and illustrates its use.
result SETR can approximate the magnitude of low-carbon transition risk.
SubSearch detects graph outliers and estimates SBM parameters robustly.
problem Real-world graphs often deviate from ideal SBM assumptions.
method Subgraph search to find subgraphs that align with SBM assumptions.
result SubSearch accurately estimates SBM parameters and detects outliers.