Study shows optimal RL with transition look-ahead is NP-hard for ℓ≥2.
problem Optimal reinforcement learning with transition look-ahead is computationally hard.
method Proved NP-hardness for ℓ≥2 using linear programming. result There is a precise boundary between tractable and intractable cases for RL with look-ahead.
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…
Sequence-to-sequence text-to-speech (TTS) is dominated by soft-attention-based methods. Recently, hard-attention-based methods have been proposed to prevent fatal alignment errors, but their sampling method of discrete alignment is poorly investigated. This research investigates various combinations of sampling methods…
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.
Unified approach to tensor PCA and related problems using tensor cumulants.
problem Statistical inference on invariant distributions, particularly tensor PCA.
method Definition and analysis of tensor cumulants to unify and extend previous results.
result Unified explanation of hardness and subexponential-time algorithms for tensor PCA.
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.
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.
New algorithm for planning in observable POMDPs in quasi-polynomial time.
problem Planning in POMDPs is computationally hard.
method Assumption of well-separated distributions on states and observations leads to quasi-succinct descriptions of near-optimal policies.
result Quasipolynomial-time algorithm for planning in observable POMDPs.
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.
Manually authoring transition animations for a complete locomotion system can be a tedious and time-consuming task, especially for large games that allow complex and constrained locomotion movements, where the number of transitions grows exponentially with the number of states. In this paper, we present a novel approac…
Many optimization problems can be cast into the maximum satisfiability (MAX-SAT) form, and many solvers have been developed for tackling such problems. To evaluate a MAX-SAT solver, it is convenient to generate hard MAX-SAT instances with known solutions. Here, we propose a method of generating weighted MAX-2-SAT insta…
Curiosity-Critic improves world model training by focusing on cumulative prediction error.
problem Training world models with intrinsic rewards that consider cumulative prediction error.
method Curiosity-Critic uses a surrogate reward based on the difference between current and asymptotic prediction errors, estimated online by a co-trained critic.
result Curiosity-Critic outperforms other methods in training speed and final world model accuracy.
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.
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…
This work interprets GELU and related activations via a first-order loss function.
problem Understanding and optimizing activation functions in neural networks.
method Complementary interpretation using the Gaussian first-order loss function.
result Calibrated or learned uniform-threshold gates are competitive and often outperform GELU, ReLU, and SiLU/Swish.
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.
This research develops an efficient reinforcement learning method for undercomplete POMDPs.
problem Learning undercomplete Partially Observable Markov Decision Processes (POMDPs) is computationally hard.
method OOM-UCB algorithm for episodic finite undercomplete POMDPs.
result Achieves optimal sample complexity of ildeO(1/ε2) for finding an ε-optimal policy. Paper tackles instance-dependent label noise by approximating it with part-dependent noise.
problem Learning with instance-dependent label noise is challenging.
method Approximate instance-dependent label noise with part-dependent noise. Use transition matrices for parts to model noise.
result Method outperforms state-of-the-art approaches for instance-dependent label noise.
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…
Paper proposes DG-ETC for online submodular maximization with stochastic bandit feedback.
problem Online unconstrained submodular maximization with stochastic bandit feedback.
method Double-Greedy - Explore-then-Commit (DG-ETC) approach.
result DG-ETC achieves logarithmic regret O(dlog(dT)) for 1/2-approximate pseudo-regret. China and EU race to develop hydrogen for energy transition.
problem Developing hydrogen for sustainable energy systems.
method Comparative analysis framework using key factors.
result Customized solutions for local hydrogen industries.
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.
Paper establishes new lower bounds for MDPs with changing transition kernels.
problem Minimizing sample complexity and regret in non-stationary MDPs.
method Developed novel lower bounds and constructed hard MDPs.
result Proved Ω((H3SA/ε2)log(1/δ)) sample complexity lower bound. New algorithm learns POMDPs without computational oracles.
problem Learning near-optimal policies in POMDPs with computationally hard oracles.
method Quasipolynomial-time algorithm using barycentric spanners for policy covers.
result First oracle-free learning algorithm for observable POMDPs.
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'.
Study online RL with mismatched dynamics, achieving sublinear regret.
problem Exploration challenges in online RL with mismatched training and deployment dynamics.
method Introduce supremal visitation ratio, propose efficient algorithm with f-divergence. result Achieves sublinear regret in online RMDPs with optimal dependence on supremal visitation ratio and interaction episodes.
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.
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.
New insights on offline RL with state aggregation and trajectory data.
problem Understanding sample complexity in offline policy evaluation.
method Analyzing concentrability coefficient in aggregated Markov Transition Model.
result Sample complexity depends on concentrability coefficient in aggregated model.
PHINN: A generative model for rare-event time series using persistent homology
problem Generating rare events in time series
method Flow-matching framework with dynamic Betti curves and persistence landscape loss
result Outperforms statistical and diffusion baselines in topological fidelity and tail coverage
An agent learning through interactions should balance its action selection process between probing the environment to discover new rewards and using the information acquired in the past to adopt useful behaviour. This trade-off is usually obtained by perturbing either the agent's actions (e.g., e-greedy or Gibbs sampli…
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement map…
Generative model learns to mimic time-series behavior to generate accurate trajectories.
problem Learning generative models for time-series data with accurate multi-step trajectories.
method Contrastive imitation framework combining autoregressive and adversarial elements.
result The method generates accurate and useful samples from real-world datasets.
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.
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 lower bound shows RL with linear approximations is computationally hard.
problem Computational hardness in reinforcement learning with linear function approximation.
method Reduction from Unique-Sat to MDPs with linear optimal value functions.
result No randomized polynomial time algorithm exists for RL with linear function approximation unless NP=RP.
New algorithm optimizes resource allocation in non-stationary networks.
problem Optimal resource allocation in non-stationary RMABs is computationally hard.
method Sliding-Window Online Whittle (SW-Whittle) policy for non-stationary transition kernels.
result Sub-linear dynamic regret achieved with unknown variation budget.
New method detects global factors near BBP phase transition in high-dimensional data.
problem Detecting the number of global factors in noisy high-dimensional correlation matrices.
method Iterative Global Factor (IGF) algorithm combining adaptive edge recalibration and PR delocalization filter.
result IGF algorithm successfully detects global factors near BBP transition, improving over eigenvalue-only methods.
Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.
problem Estimating a planted signal in a nested matrix-tensor model.
method Comparing tensor-based and matrix-based approaches for best rank-one approximation of tensor data.
result Derives precise algorithmic threshold for the unfolding approach and shows BBP-type transition behavior.
Model-free reinforcement learning methods such as the Proximal Policy Optimization algorithm (PPO) have successfully applied in complex decision-making problems such as Atari games. However, these methods suffer from high variances and high sample complexity. On the other hand, model-based reinforcement learning method…
Paper tackles matrix estimation under arbitrary noise, achieving minimax optimality.
problem Noisy low-rank-plus-sparse matrix recovery under arbitrary dependence.
method Incoherent-constrained least-square estimator, novel energy spreading result.
result Achieves minimax optimality in estimating structured Markov transition kernels.
The tree reconstruction problem is to collect and analyze massive data at the nth level of the tree, to identify whether there is non-vanishing information of the root, as n goes to infinity. Its connection to the clustering problem in the setting of the stochastic block model, which has wide applications in machin…
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.
We tackle the Multi-task Batch Reinforcement Learning problem. Given multiple datasets collected from different tasks, we train a multi-task policy to perform well in unseen tasks sampled from the same distribution. The task identities of the unseen tasks are not provided. To perform well, the policy must infer the tas…
We consider a sparse high dimensional regression model where the goal is to recover a k-sparse unknown vector β∗ from n noisy linear observations of the form Y=Xβ∗+W∈Rn where X∈Rn×p has iid N(0,1) entries and W∈Rn has iid N(0,σ2) entries. Under certa…
Proposes a new model for community detection using neural priors.
problem Community detection in graphs with node attributes.
method Neural-prior stochastic block model with belief propagation and approximate message passing algorithm.
result Identifies phase transitions and algorithmically hard regions for community detection.