Hard phase in inference problems is glassy and hard to reconstruct.
problem Hard phase in inference problems that are hard to solve algorithmically.
method Study of metastable states and their entropy in low-rank matrix factorization.
result AMP algorithm performance is not improved by considering glassy states.
Proves well-posedness for hard phase model in general relativity.
problem Modeling fluid dynamics in curved spacetime.
method A priori estimates and well-posedness in Sobolev spaces, coupled interior-boundary system of wave equations.
result Proves existence and uniqueness of solutions in Sobolev spaces.
We find optimal learning rate schedules for a random feature model.
problem Choosing optimal learning rates for deep learning models.
method We analyze a powerlaw random feature model trained with SGD, considering optimal schedules as numerical and analytical problems.
result We discover two regimes: easy and hard phases, with different optimal learning rate schedules.
Meta-learning strategy improves few-shot classification performance.
problem Few-shot classification with deep neural networks struggles when labeled samples are limited.
method Proposes an easy-to-hard expert meta-training strategy to arrange training tasks based on task hardness.
result Meta-learners achieve better results with the proposed expert training strategy.
Study examines the excluded area between two-dimensional hard particles, identifying key factors affecting its magnitude.
problem Determining the excluded area between two-dimensional hard particles with various orientations and shapes.
method Used principal component analysis and Monte Carlo simulations to analyze randomly generated non-self-intersecting polygons and star lines.
result The minimum excluded area is achieved when particles are antiparallel, and elongation of the particle shape significantly affects the excluded area.
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.
Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solution…
Study shows it's impossible to count communities without finding them.
problem Determining the number and sizes of communities in random graph models.
method Hypothesis testing between models with different community structures, using low-degree polynomial framework.
result Testing between two different planted distributions is as hard as finding the communities.
Boolean logic used for neural network training and inference, with convergence analysis.
problem Discrete optimization in neural networks with Boolean logic.
method Boolean logic backpropagation with convergence analysis.
result First convergence analysis for Boolean logic in neural networks.
Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently-discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to the network topology…
Paper proposes a new method for sparse phase retrieval with fewer measurements.
problem Sparse phase retrieval in various fields.
method Stochastic alternating minimizing method (StormSpar) with HTP algorithm.
result The method recovers sparse signals from fewer measurements than existing methods.
Paper eliminates warm-up phase for PO in linear MDPs, achieving optimal regret.
problem Costly warm-up phase in PO algorithms for linear MDPs.
method Simple contraction mechanism replaces warm-up phase.
result Achieves rate-optimal regret with improved dependence on problem parameters.
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.
A new method generates MAX-2-SAT instances with adjustable hardness.
problem Creating hard MAX-SAT instances for evaluating MAX-SAT solvers.
method Inspired by frustrated-loop algorithm, extends to bipartite couplings, tuning hardness through frustration index.
result Generated instances can be tuned through a central parameter (frustration index), showing double phase transition behavior.
End-to-end speech separation with improved phase reconstruction.
problem Cocktail party problem: separating multiple speakers in a single-channel recording.
method End-to-end approach using deep learning with unfolded phase reconstruction iterations and novel activation functions.
result State-of-the-art performance on SI-SDR and SDR metrics.
Deep neural network estimates support of sparse signals for improved phase retrieval.
problem Sparse phase retrieval from Fourier magnitudes with support estimation.
method Trained deep neural network (DNN) provides extended support estimate E larger than the support T. result DNN-based support estimation improves signal reconstruction performance with lower complexity.
We consider the problem of estimating the phases of K mixed complex signals from a multichannel observation, when the mixing matrix and signal magnitudes are known. This problem can be cast as a non-convex quadratically constrained quadratic program which is known to be NP-hard in general. We propose three approaches t…
Study reveals phase transition in neural networks near interpolation.
problem Understanding generalization and learning transitions in neural networks.
method Effective theory for approximating Bayes-optimal generalisation error.
result Unveils a discontinuous phase transition between universal and specialisation phases.
AIHT improves online high-dimensional quantile regression by separating support discovery and refinement.
problem Online high-dimensional quantile regression with structural sparsity.
method Adaptive Iterative Hard Thresholding (AIHT) alternates stochastic updates with adaptive hard-thresholding steps.
result AIHT achieves logarithmic regret for the sliding-window objective in high-dimensional settings.
Optimal learning rates decay to zero in easy tasks and maintain a warmup phase in hard tasks.
problem Optimizing learning rates under functional scaling laws for model training.
method Deriving optimal learning-rate schedules based on exponents s and β. result Sharp phase transition between easy and hard tasks, with different decay behaviors.
Reduces learning periodic neural networks to lattice problems, proving hardness under cryptographic assumptions.
problem Learning single periodic neurons in noisy environments.
method Reduction to worst-case lattice problems, using LLL algorithm.
result Polynomial-time algorithms for learning these functions are hard under cryptographic assumptions.
Stochastic Gradient Descent phases explained for deep networks.
problem Understanding the different regimes of SGD in deep learning.
method Teacher-student perceptron model, phase diagram analysis.
result SGD phases separated by batch size B∗, scaling with training set size P. Study on InstaHide's security, linking to phase retrieval problem.
problem Security of InstaHide scheme for private dataset sharing.
method Design of a provable algorithm for private vector recovery.
result Private vectors can be recovered using synthetic vectors and public vectors.
New PSDMF algorithms derived from PR and ARM methods.
problem Positive semidefinite matrix factorization (PSDMF) challenges.
method Design PSDMF algorithms based on phase retrieval (PR) and affine rank minimization (ARM) methods.
result New PSDMF algorithms inherit numerical properties from PR and ARM methods.
Maximizes Rényi entropy for efficient exploration in reward-free RL.
problem Challenges of exploration in reward-free reinforcement learning.
method Maximizes Rényi entropy over state-action space in exploration phase; uses batch RL for planning phase.
result Effective and sample-efficient exploration leading to superior policies.
New AMP algorithms reveal phase transitions in tensor recovery.
problem Understanding algorithmic behavior of low-rank tensor decompositions.
method Derive Bayesian AMP algorithms and use dynamic mean field theory.
result Reveals phase transitions between easy, hard, and impossible inference regimes.
This paper studies the problem of detecting the presence of a small dense community planted in a large Erdős-Rényi random graph G(N,q), where the edge probability within the community exceeds q by a constant factor. Assuming the hardness of the planted clique detection problem, we show that the computatio…
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive results are developed on both the statistical and computational limits for tensor …
This paper develops the Jungle model in a credit portfolio framework. The Jungle model is able to model credit contagion, produce doubly-peaked probability distributions for the total default loss and endogenously generate quasi phase transitions, potentially leading to systemic credit events which happen unexpectedly …
Adaptive algorithm identifies best arm with abstention, showing phase transition from polynomial to exponential error probability.
problem Bayesian best-arm identification with abstention to reduce undetected error.
method Adaptive algorithm PGWS that optimally uses abstention budget.
result Introducing any positive abstention budget induces an exponential decay in undetected error probability.
Classification and regression tasks in overparameterized models show different generalization properties.
problem Comparing classification and regression in overparameterized models.
method Comparison of least-squares minimum-norm interpolation and hard-margin SVM using different loss functions.
result Interpolating solutions generalize well with 0-1 loss but not with square loss.
New findings show sampling vs optimization are incomparable in non-convex cases.
problem Comparing sampling and optimization in non-convex Bayesian learning.
method Simpler and stronger separation of sampling and optimization.
result Provable incomparability of sampling and optimization in non-convex cases.
The Bethe free energy approximation is reliable when convex on a submanifold, the 'Bethe box'.
problem Accuracy of the Bethe free energy approximation in probabilistic inference.
method Analysis of convexity and verification conditions based on the Bethe Hessian matrix.
result The Bethe approximation is mostly accurate if it is convex on a submanifold, the 'Bethe box'.
Paper shows how to integrate quantization into neural compression models.
problem Integrating quantization into neural compression models.
method Integrates uniform noise channel at test time using universal quantization.
result Eliminates mismatch between training and test phases while maintaining differentiability.
Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of q=2 groups. However, analytic calculations using the cavity method are challenging since they require us to understand p…
A local search algorithm successfully recovers sparse vectors in high-dimensional regression.
problem Recovering a sparse vector from noisy linear observations.
method Local search algorithm based on improvement rule.
result Simple algorithm successfully recovers sparse vectors and infers their support for large enough sample sizes.
Neural networks learn simpler features first, then more complex ones; Fourier analysis reveals this pattern.
problem Understanding the learning dynamics of neural networks, especially with natural image data.
method Fourier analysis of translation-invariant and power-law spectra to study feature learning.
result Simple neural networks first rely on amplitude information, then phase information, and power-law spectra can accelerate learning phase information.
Optimal feature transfer identified through bias-variance analysis.
problem Optimizing feature transfer in transfer learning.
method Simple linear model with fine-grained bias-variance decomposition.
result Optimal pretrained feature transform is naturally sparse.
Paper explores limits of high-order clustering with planted structures.
problem Statistical and computational limits of high-order clustering with planted structures.
method Developed methods for detection and recovery of clusters, identified signal-to-noise ratio boundaries.
result Sharp boundaries of signal-to-noise ratio for statistical and computational feasibility.
Study local convergence of GDA for training GANs with kernel-based discriminators.
problem Analyzing the local dynamics of GDA for GANs with kernel-based discriminators.
method Linearization of a non-linear dynamical system, under an isolated points model assumption.
result Showed phase transitions indicating convergence, oscillation, or divergence of GDA.
Tensor PCA problem analyzed with statistical query lower bounds.
problem Estimating the expected value of a rank-1 tensor from Gaussian samples.
method Sharp analysis of optimal sample complexity in the Statistical Query model.
result SQ algorithms with polynomial query complexity fail in the conjectured hard phase and have sub-optimal sample complexity.
Polynomial-time algorithm solves random parity games with high probability.
problem Solving random parity games efficiently.
method SWCP algorithm based on cycles in subgraphs.
result Polynomial-time solution for large-degree games with high probability.
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.
New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.
problem Resolving algorithmic hardness in asymmetric binary perceptrons.
method Fully lifted random duality theory (fl RDT) and large deviation upgrade (sfl LD RDT).
result Local entropy breaks down for constraint densities in (0.77, 0.78) interval, matching current solver limits.
Quantum computing techniques improve graph analysis and community detection.
problem Analyzing large graphs efficiently and accurately.
method Used quantum annealing and quantum gate computers for community detection and regularity checking.
result Demonstrated the effectiveness of quantum computing in solving complex graph problems.
TREK uses distillation to help students solve hard problems.
problem Stalled progress on hard prompts when current policy lacks useful reasoning trajectories.
method TREK combines distillation and reinforcement learning to expand student support.
result TREK significantly improves student performance on mathematical reasoning and agentic tasks.
GE finds failures in autonomous systems without domain heuristics.
problem Finding failures in autonomous systems without domain-specific heuristics.
method Adaptive stress testing using go-explore (GE) algorithm.
result GE finds failures in scenarios other RL techniques cannot solve.
DiTSNe-Ia model accurately reconstructs supernovae spectra from light curves.
problem Difficult identification and interpretation of diverse sub-populations of supernovae.
method Variational diffusion-based generative model conditioned on light curves.
result DiTSNe-Ia achieves significantly more accurate reconstructions than SALT3 across all phases.