Verify spiral minimal product structure using Takahashi Theorem.
problem Verify spiral minimal product structure.
method Using Takahashi Theorem with full computational details.
result Verify spiral minimal product structure.
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48 results for “verification theorems”
Theoretical limits on verifying self-improving systems without risking unbounded utility.
problem Formalizing and proving the limits of safety verification for self-improving systems.
method Developed dual conditions and used Holder's inequality, NP counting method, and Lipschitz bounds to establish impossibility and ceiling results.
result A classifier-based safety gate cannot simultaneously permit unbounded beneficial self-modification and bounded cumulative risk.
Two impossibility theorems show formal alignment certification is impossible for AI systems.
problem Formal certification of AI alignment over open-ended domains is impossible.
method Two independent impossibility theorems: Semantic and Statistical barriers.
result No procedure can simultaneously satisfy soundness, completeness, and tractability.
We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelma…
Formalizes weak and strong verification for LLMs, controlling errors without assumptions.
problem Balancing cost and reliability in reasoning with LLMs.
method Formalizes weak-strong verification policies, introduces metrics, develops online algorithm.
result Optimal policies admit a two-threshold structure, and calibration and sharpness govern value of weak verifiers.
The paper analyzes a class of stochastic games involving moving free boundaries and Nash equilibria.
problem Analyzing interactions among players in stochastic games with moving free boundaries.
method Deriving sufficient conditions for Nash equilibrium through verification theorems, solving multi-dimensional free boundary problems, and Skorokhod problems.
result An intriguing connection between NE strategies and controlled rank-dependent stochastic differential equations.
Study consumption-investment problem in markets with rank-based returns.
problem Consumption-investment problem in markets with rank-based returns.
method Derives an HJB equation with Neumann boundary conditions for the value function and proves a corresponding verification theorem.
result Explicit solutions for unconstrained, open market constraints, and fully invested cases.
Continuous-time model shows how trading affects asset prices and optimizes investment strategies.
problem Modeling financial markets with transient price impact and optimal trading strategies.
method Establishes a continuous-time duality involving measures with martingales and a liquidity weighted norm.
result Optimality of buy-and-hold strategies for call options and utility maximizing investment strategies proved.
Formal framework verifies fairness, uniformity, and rationality in financial market trades.
problem Ensuring fairness, uniformity, and rationality in financial market trades.
method Formal definition and proof of properties in a theorem prover (Coq).
result Formal verification of double-sided auctions in financial markets.
We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system with one-dimensional slow variable . Our validation procedure is based on topological tools called isolatin…
We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibratio…
Study on PDEs in Heston model with unique solution and convergence proof.
problem Analyzing PDEs in the Heston model for financial applications.
method Regularity results, verification theorem, unique viscosity solution, convergence proof.
result Unique viscosity solution for wide initial and source data.
EEG signals enhance speaker verification system robustness.
problem Improving speaker verification in noisy environments.
method Used end-to-end deep learning model with EEG and speech features.
result EEG signals improve speaker verification robustness, especially in noisy conditions.
Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterionmath.OC
New approach to optimal dividend control with mean-variance criterion.
problem Balancing expected dividends and variability in a singular control framework.
method Game-theoretic approach to find time-consistent equilibrium strategies.
result Verification theorem for MV singular dividend control problem.
We improve neural network robustness verification by training for faster stability.
problem Efficient verification of adversarial robustness in deep networks.
method Co-design of weight sparsity and ReLU stability to simplify verification.
result Improving ReLU stability leads to a 4-13x speedup in verification times.
Develops first robustness verification for complex Transformers.
problem Certify prediction behavior of Transformers with complex self-attention layers.
method Resolves challenges of cross-nonlinearity and cross-position dependency in Transformers.
result Certified robustness bounds are significantly tighter than Interval Bound Propagation.
This research simplifies verification of machine learning systems using reparameterization.
problem Reduce or eliminate serious bugs in machine learning systems.
method Use proof assistants to construct machine-checked proofs of correctness, leveraging reparameterization to handle probabilistic claims.
result Demonstrates broad applicability of reparameterization to verify different types of machine learning systems.
Paper develops PAC verification for hypothesis classes and statistical algorithms.
problem Verifying machine learning models interactively.
method Develops interactive proof for PAC verification, proves lower bounds, and introduces a generalization.
result Improved protocol for verifying unions of intervals and statistical query algorithms.
Equilibrium singular dividend control under ambiguity aggregation of heterogeneous discount ratesmath.OC
A firm with heterogeneous shareholders optimizes dividends under ambiguity aggregation.
problem Optimizing dividends for a firm with heterogeneous shareholders under ambiguity aggregation.
method Characterizing equilibrium dividends using a partition of the state space.
result Time-homogeneous equilibrium dividend law characterized by a partition of the state space.
Paper optimizes hypothesis verification in sequential experiments.
problem Maximizing confidence in a verified hypothesis after exploration.
method Formulated as a confidence maximization problem in a POMDP, characterized optimal solutions, and proposed a heuristic.
result Heuristic performs better than existing methods in some scenarios.
Accelerates DNN robustness verification with target labels.
problem Improving the robustness of deep neural networks against adversarial attacks.
method Guiding robustness verification with target labels, reducing search space and using symbolic interval propagation and linear relaxation.
result Significantly improves DNN verification speed by 36X, especially when perturbation distance is reasonable.
New methods combat data poisoning attacks in bandit algorithms using limited verification.
problem Data poisoning attacks on bandit algorithms, especially in the UCB and ETC types.
method Verification-based mechanisms to restore optimal regret with limited verifications.
result A simple modified ETC type bandit algorithm can restore optimal regret with verifications.
Improved speaker verification with condition-aware backend.
problem Speaker verification calibration issues under unknown conditions.
method Discriminative PLDA model with joint training and condition integration.
result Out-of-the-box excellent calibration performance.
New algorithm speeds up robustness verification for tree-based models.
problem Formal robustness verification of tree-based models, especially ensembles.
method Reformulated as max-clique problem on a multi-partite graph with bounded boxicity; developed efficient multi-level verification algorithm.
result Tight lower bounds on robustness of decision tree ensembles, hundreds of times faster than previous approach.
Improves neural network verification by merging abstract domains and Lagrangian methods.
problem Prove provable bounds for neural network outputs given input ranges.
method Uses zonotopes within a Lagrangian decomposition to verify deep neural networks.
result Yields bounds that improve upon existing techniques in both time and tightness.
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the illiquid one can be traded only at discrete random times corresponding to the jumps …
This paper explores formal verification for autonomous systems, identifying limitations and proposing improvements.
problem Ensuring safety of autonomous systems like self-driving cars and drones.
method Formal verification techniques based on formal methods, analyzing three assumptions and their limitations.
result Preliminary work to improve the strength of evidence provided by formal verification.
Scalable verifier for recurrent neural networks using polyhedral abstractions.
problem Certifying the correctness of recurrent neural networks.
method Combining sampling, optimization, and Fermat's theorem for polyhedral abstractions; gradient descent for refinement.
result Successfully verified challenging recurrent models in various domains.
We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in term…
Paper develops a model for verifying facts in tables without pre-retrieved evidence.
problem Verification of factual claims in structured data, especially in open-domain settings.
method Joint reranking-and-verification model that fuses evidence documents.
result Model achieves comparable performance to closed-domain state-of-the-art on TabFact dataset.
Paper tackles speaker verification by removing reverberation using deep LSTM networks.
problem Improving speaker verification accuracy in reverberant environments.
method Dual-label deep LSTM networks trained to map reverberant to clean speech features.
result Evaluates performance using EERs, showing improved accuracy.
Unified approach to stochastic control, filtering, and stopping using rough paths.
problem Addressing gaps in classical problems of stochastic control, filtering, and stopping.
method Combining rough path theory with controlled rough paths to provide a pathwise deterministic framework.
result Established rigorous connection between candidate solutions and Hamilton-Jacobi-Bellman equation.
New neural network boosts authorship verification on social media.
problem Challenges in verifying authorship of short, diverse social media messages.
method Proposes a new neural network topology for similarity learning.
result Significantly improved performance on author verification tasks.
This paper is concerned with an optimal stock selling rule under a Markov chain model. The objective is to find an optimal stopping time to sell the stock so as to maximize an expected return. Solutions to the associated variational inequalities are obtained. Closed-form solutions are given in terms of a set of thresho…
An End-to-End Text-independent Speaker Verification Framework with a Keyword Adversarial Networkeess.AS
End-to-end speaker verification framework reduces text dependency.
problem Improving text-independent speaker verification.
method Jointly trains SE and ASR networks with triplet loss and adversarial gradient.
result Lower equal error rate and better text-independency compared to other approaches.
Paper proposes an ensemble model for writer-independent offline signature verification using deep learning.
problem Difficulty in distinguishing genuine signatures from skilled forgeries in writer-independent offline signature verification.
method Used an ensemble model with two CNNs for feature extraction, RGBT for classification, and stacking for final prediction.
result Achieved state-of-the-art performance on various datasets.
Efficiently verifies neural networks by handling neuron splits, improving speed and accuracy.
problem Handling neuron split constraints in incomplete neural network verification.
method β-CROWN, which optimizes parameters β to encode neuron splits and uses them in bound propagation.
result β-CROWN significantly speeds up verification while maintaining high accuracy.
Formal methods verify continuous auctions at exchanges.
problem Ensuring fairness and correctness in continuous auctions.
method Formal specification, design, and verification of continuous double auctions.
result A verified algorithm satisfies natural properties of auctions.
In this study, we introduce an explicit trading-volume process into the Almgren-Chriss model, which is a standard model for optimal execution. We propose a penalization method for deriving a verification theorem for an adaptive optimization problem. We also discuss the optimality of the volume-weighted average-price st…
Semantify-NN verifies neural network robustness against semantic perturbations.
problem Verifying robustness of neural networks against semantic adversarial attacks.
method Inserting semantic perturbation layers (SP-layers) into neural networks to verify robustness.
result Semantify-NN significantly improves robustness verification performance over -norm-based methods.
Proposes a new neural network for text-dependent speaker verification.
problem Improves speaker verification by encoding phrase and speaker information.
method Uses differentiable alignment models to produce supervectors from utterances.
result Achieves competitive performance in text-dependent speaker verification tasks.
Researchers find floating point errors can mislead neural network verifiers.
problem Floating point arithmetic inaccuracies mislead neural network verifiers.
method Efficiently searches inputs and constructs neural network architectures to exploit verification errors.
result Floating point errors can systematically mislead neural network verifiers.
New technique reduces verification time for neural networks.
problem Verifying neural networks for safety-critical applications.
method Shadow prices for more efficient input partitioning.
result Significant reduction in computation times for verification.
This study extends verifiable learning to boosted tree ensembles, enabling efficient security verification.
problem Efficiently verifying the robustness of boosted tree ensembles against norm-based attackers.
method Formal verification of robustness for large-spread boosted tree ensembles, considering -norm and pseudo-polynomial time for -norm verification.
result Polynomial time verification for -norm attackers, NP-hard for other norms, and pseudo-polynomial time for -norm verification.
Accelerating Speculative Diffusions via Block Verification
problem Adapting speculative decoding for continuous diffusion models
method Introducing a novel speculative sampling mechanism for diffusion models
result Improves acceptance rate and speeds up inference
Unified convex relaxation framework for neural network robustness verification.
problem Inability to achieve tight verification of neural networks against adversarial attacks.
method Unified convex relaxation framework for neural networks of various architectures and nonlinearities.
result Exact solution to convex-relaxed problem does not significantly improve verification gap.
This paper tackles robustness of ensemble stumps and trees under general ℓ_p norm perturbations.
problem The vulnerability of ensemble stumps and trees to small input perturbations under the ℓ_∞ norm.
method Developed dynamic programming algorithms for robustness verification and certified defense under general ℓ_p norm perturbations.
result First certified defense method for ensemble stumps and trees under ℓ_p norm perturbations.
A new method for verifying deep learning architectures on FPGAs is proposed.
problem Design-time verification of deep learning architectures on FPGAs.
method 2-Level 3-Way (2L-3W) hardware-software co-verification methodology.
result Layer-by-layer similarity scores of 99% accuracy for successful mappings.