Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
problem Phase transitions in multimodal models and their properties.
method Sharp coercivity estimate and constrained Lebedev--Milin inequality.
result Continuous phase transitions at critical coupling strengths for Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
Cut-DeepONet handles discontinuities and sharp transitions in neural operators.
problem Neural operators struggle with discontinuities and sharp transitions in PDEs.
method Two-stage training framework that explicitly models discontinuities via a lifting strategy and input-dependent discontinuity prediction.
result Cut-DeepONet outperforms state-of-the-art methods on benchmark PDEs with low-resolution datasets.
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.
Study phase transition in liquid crystal droplets using mathematical analysis.
problem Mathematical analysis of phase transition between isotropic and nematic states of liquid crystals.
method Rigorous mathematical analysis using the Ericksen model and Γ-convergence theory.
result Γ-limit provides geometric description and anchoring conditions for liquid crystal orientations.
Sharp concentration inequalities for sub-Orlicz random variables with phase transition at α=2.
problem Developing concentration inequalities for sub-Orlicz random variables with phase transition.
method New theoretical analysis framework involving variance and min/max functions of Orlicz tails.
result Sharp concentration inequalities with phase transition at α=2 for sub-Orlicz random variables.
We develop efficient and sharp bounds on policy value under perturbations in MDPs.
problem Evaluating policies under best- and worst-case perturbations in MDPs with transition observations.
method Proposed a perturbation model for MDPs, developed semiparametrically efficient estimator with asymptotic normality.
result Semiparametrically efficient and asymptotically normal estimator for policy value bounds.
Study phase transitions with prescribed mean curvature in Riemannian manifolds.
problem Understanding phase transitions with prescribed mean curvature in geometric settings.
method Analyzing solutions to inhomogeneous semilinear elliptic PDEs, establishing bounds and asymptotics.
result Established upper and lower bounds for eigenvalues of phase transition problems.
Tyler's M-estimator's phase transition at DS-SNR = 1 is resolved.
problem Robust Subspace Recovery
method Tyler's M-estimator
result TME converges exactly to the true subspace for DS-SNR >= 1 under a new stability condition.
LS4 models time-series with latent states, outperforming previous methods.
problem Learning sharp transitions in time-series data.
method State space ODE with convolutional representation to bypass hidden states.
result LS4 significantly outperforms previous models in various metrics.
Sharp results link DLN gradient flow to basis pursuit optimization and GHA phase transitions.
problem Understanding implicit regularization in Diagonal Linear Networks.
method Sharp convergence bounds and characterization of ℓ1 minimizers. result Gradient flow of DLNs with tiny initialization approximates minimizers of basis pursuit optimization problem.
Study phase transitions in noisy transformer dynamics on spheres.
problem Understanding phase transitions in noisy transformer dynamics on spheres.
method Sharp Beckner--Onofri/logarithmic HLS inequality, Funk--Hecke/Bessel coefficients, degree-two quartic obstruction.
result Sharp global-minimizer dichotomy and phase transitions in noisy transformer dynamics in arbitrary dimension.
We conduct a post hoc analysis of solar flare predictions made by a Long Short Term Memory (LSTM) model employing data in the form of Space-weather HMI Active Region Patches (SHARP) parameters calculated from data in proximity to the magnetic polarity inversion line where the flares originate. We train the the LSTM mod…
We show that reinforcement learning agents that learn by surprise (surprisal) get stuck at abrupt environmental transition boundaries because these transitions are difficult to learn. We propose a counter-intuitive solution that we call Mutual Information Minimising Exploration (MIME) where an agent learns a latent rep…
We show that the Morse index of every 2k-ended solution of the Allen-Cahn equation in R^2 is >= k-1. This bound is expected to be sharp.
Sharp feature transitions revealed in extensive-width networks.
problem Learning hierarchical features from noisy queries in large networks.
method Information-theoretic analysis and heuristic decoupling argument.
result Sequential phase transitions in feature learnability and effective width.
Flow on weighted graphs sharpens Bakry-Émery curvature.
problem Sharp curvature in weighted graphs.
method Bakry-Émery curvature flow on mixed weighted graphs.
result Limits of curvature flow are curvature sharp.
This paper resolves the all-or-nothing phase transition in graph matching.
problem Recovering vertex correspondence between edge-correlated random graphs.
method Analysis of mutual information, truncated second-moment computation, and maximum likelihood estimator.
result Sharp thresholds for correct matching in both dense and sparse graphs.
Sharp theory of neural network scaling laws for hierarchical targets.
problem Learning hierarchical multi-index models in neural networks.
method Sharp information-theoretic scaling laws derived for two-layer neural networks.
result Optimal rates achieved by a simple spectral estimator.
We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. Under some general conditions, we show that this transition is sharp for the hinge loss. In the whole over-parametrized regime, poor minima of the loss are not encounte…
Study uses MTD model to optimize portfolios by capturing complex financial asset relationships.
problem Capturing nonlinear and directional relationships in financial markets.
method Directed and weighted financial networks using Mixture Transition Distribution (MTD) model.
result Portfolio optimization with network-based assortativity measures outperforms classical methods.
Differentiable relaxation for inferring partial orders from noisy linear data.
problem Inference of partial orders from linear data with noisy observations.
method Introducing a differentiable relaxation to model noisy linear extensions, replacing discontinuous precedence and feasibility with smooth surrogates.
result Smooth posterior that preserves partial-order semantics, supports gradient-based inference, and converges to hard likelihood.
We show that the martingale component in the long-term factorization of the stochastic discount factor due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) is highly volatile, produces a downward-sloping term structure of bond Sharpe ratios, and implies that the long bond is far from growth optimality. In…
We introduce a scalable measure of curvature for analyzing training dynamics of large language models.
problem Analyzing the training dynamics of large language models due to high computational cost of measuring Hessian sharpness.
method We introduce critical sharpness and relative critical sharpness as computationally efficient measures capturing Hessian sharpness phenomena.
result We provide the first demonstration of sharpness phenomena at scale up to 7B parameters.
High-dimensional models become unstable when sample size falls below a critical level, leading to a phase transition.
problem Instability in high-dimensional learning models when sample size is insufficient.
method Proved the necessity of a Fisher eigenvalue threshold for stability, introduced Fisher floor for verification.
result A sharp phase transition between reliable concentration and inevitable failure in high-dimensional learning.
Study on estimating signals from shifted and noisy copies in high dimensions, revealing a phase transition.
problem Estimating a signal in high-dimensional space from its circularly-shifted and noisy copies.
method Analysis of sample complexity in the high-dimensional regime, focusing on the parameter α.
result A phase transition phenomenon governed by α, with different sample complexities based on α values.
A model predicts how hyperparameters affect pruning performance.
problem Predicting the impact of hyperparameters on pruning performance.
method Phenomenological model using temperature-like and load-like parameters.
result A sharp transition phenomenon in pruning performance.
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a multivariate counting process with stochastic intensities. The interest rate, drift, …
Solves complex clustering and rotation synchronization problem.
problem Challenges in classifying and synchronizing rotated objects into multiple categories.
method Semidefinite programming relaxations to solve the joint problem of community detection and synchronization.
result Exact recovery of community detection and synchronization when extending stochastic block model.
Reward hacking exploits misspecified rewards, affecting agent capabilities and true performance.
problem Reward hacking in RL models exploiting reward misspecifications.
method Constructed four RL environments with misspecified rewards; analyzed agent capabilities and behavior.
result More capable agents exploit reward misspecifications, achieving higher proxy reward but lower true reward.
New method improves feasibility of fitting Gaussian vectors to an ellipsoid.
problem Feasibility of fitting n Gaussian vectors to an ellipsoid boundary. method Improved concentration of Gram matrices using Bartl & Mendelson (2022) results.
result Feasibility of (P) with high probability when n≤d2/C. Study explores grokking in neural networks, revealing transition from memorization to generalization.
problem Understanding the transition from memorization to generalization in over-parameterized neural networks.
method Extensive experiments and exploration of various viewpoints on grokking mechanism.
result Sharp transition from no generalization to perfect generalization observed during prolonged training.
Study reconstructs hidden perfect matchings in random graphs with specific edge weights.
problem Reconstructing hidden perfect matchings in random weighted bipartite graphs.
method Analyzes the maximum likelihood estimator for matching reconstruction under different probability distributions of edge weights.
result Sharp threshold and infinite-order phase transition in reconstruction error for different probability distributions.
The paper tackles joint learning of linear systems, improving accuracy with pooled data.
problem Estimating transition matrices of multiple related linear systems more accurately.
method Developed novel techniques to bound estimation errors and establish high probability bounds for singular values.
result Significant gains in accuracy achieved by pooling data across systems.
SVM and linear regression models coincide in high dimensions.
problem Understanding the connection between SVM and linear regression in high-dimensional data.
method Analyzing feature models and proving lower bounds on dimensionality.
result A sharp phase transition in Gaussian feature models, with support vector proliferation occurring only in very high dimensions.
New optimization method improves generalization across various tasks.
problem Improving zeroth-order optimization for better generalization.
method Exponential tilting objective to connect zeroth-order optimization with sharpness-aware minimization.
result Achieves better generalization compared to vanilla zeroth-order baselines.
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary curve hMLE, parameterized by two scalars measuring the overall magnitu…
Fewer degrees of freedom can train deep networks, showing a sharp phase transition.
problem Training deep networks with fewer degrees of freedom than parameters.
method Examined success probability of hitting training loss sub-level sets within random subspaces.
result Threshold training dimension increases as desired final loss decreases.
New insights into neural networks reveal unexpected phase transitions.
problem Understanding how overparameterized neural networks learn and generalize.
method Statistical physics of disordered systems applied to non-convex binary neural networks.
result Atypical phase transitions lead to better generalization in neural networks.
PLS-SVD struggles with missing data in multimodal datasets, showing a phase transition in performance.
problem Missing data in PLS-SVD for multimodal datasets.
method Replica-symmetric analysis of spiked rectangular random matrices with missing entries.
result PLS-SVD performance transitions from uninformative to informative singular vectors at a critical signal-to-noise threshold.
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, a…
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
problem Emergence of scaling laws from feature learning in multi-layer networks.
method Layer-wise spectral algorithm adapted to compositional structure, sequential feature detection.
result Sequential detection of latent features, leading to explicit power-law decay of prediction error.
Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
If the face-cycles at all the vertices in a map on a surface are of same type then the map is called semi-equivelar. There are eleven types of Archimedean tilings on the plane. All the Archimedean tilings are semi-equivelar maps. If a map X on the torus is a quotient of an Archimedean tiling on the plane then the map…
Sharp statistical theory for conditional diffusion models.
problem Lack of theoretical foundation for conditional diffusion models.
method Sharp statistical theory with approximation of conditional score function.
result Sample complexity bound that adapts to data distribution smoothness.
This work analyzes how transformers learn common linear regression tasks.
problem Understanding how in-context learning operates in real-world applications with common task structures.
method Analyzing a linear attention model trained on low-rank regression tasks.
result Statistical fluctuations in finite pre-training data induce an implicit regularization, leading to a sharp phase transition in generalization error.
The study provides precise asymptotic theory for in-context learning by Transformers.
problem Understanding the sample complexity, pretraining task diversity, and context length for successful in-context learning.
method An exactly solvable model of linear regression task by linear attention, deriving sharp asymptotics.
result Double-descent learning curve with increasing pretraining examples, phase transition between low and high task diversity regimes.
ML PCA detects phase transitions in muon spectroscopy data.
problem Detecting phase transitions in materials using muon spectroscopy data.
method Unsupervised Machine Learning (PCA) applied to asymmetry functions.
result PCA method effectively detects phase transitions in muon spectroscopy experiments.
New algorithm reduces suboptimality in imitation learning to nearly optimal levels.
problem Statistical limits of imitation learning in MDPs with known transitions.
method Mimic-MD algorithm and reduction to value estimation problem.
result Upper bound of O(∣S∣H3/2/N) for suboptimality, with efficient computation.