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 theorem”
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.
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.
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…
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.
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.
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.
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.
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.
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.
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.
Hypothesis testing is an important problem with applications in target localization, clinical trials etc. Many active hypothesis testing strategies operate in two phases: an exploration phase and a verification phase. In the exploration phase, selection of experiments is such that a moderate level of confidence on the …
We explore the concept of co-design in the context of neural network verification. Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more easily. To this end, we identify two properties of network models - weight sparsity a…
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.
In this paper we demonstrate that performance of a speaker verification system can be improved by concatenating electroencephalography (EEG) signal features with speech signal features or only using EEG signal features. We use state-of-the-art end-to-end deep learning model for performing speaker verification and we de…
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.
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.
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 …
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.
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…
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.
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.
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…
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…
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.
We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existin…
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
Verifying robustness of neural networks given a specified threat model is a fundamental yet challenging task. While current verification methods mainly focus on the -norm threat model of the input instances, robustness verification against semantic adversarial attacks inducing large -norm perturbations,…
We consider a spread financial market defined by the multidimensional Ornstein--Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions in the base of stochastic dynamical programming method. We show a special Verification Theorem for this case. We find the solution…
In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop equilibrium consumption-investment pair in terms of a coupled forward-backward …
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.
GPUPoly verifies large neural networks robustly on GPUs.
problem Proving robustness of deep neural networks is crucial but challenging.
method Custom polyhedra algorithms on GPUs.
result GPUPoly can verify 1M neuron networks in 34.5 ms.
New spoofing strategies show PoL verification is more vulnerable than previously thought.
problem Vulnerability of Proof-of-Learning verification mechanisms.
method Developed new spoofing strategies that can be reproduced across different configurations and are more cost-effective.
result Current PoL verification is not robust to adversaries and requires further understanding of optimization in deep learning.
We present a scoring approach for speaker verification that mimics the standard PLDA-based backend process used in most current speaker verification systems. However, unlike the standard backends, all parameters of the model are jointly trained to optimize the binary cross-entropy for the speaker verification task. We …
NeuroDiff: Scalable Differential Verification of Neural Networks using Fine-Grained Approximationcs.LG
NeuroDiff improves neural network equivalence verification with fine-grained approximations.
problem Verifying the equivalence of compressed neural networks.
method Symbolic and fine-grained approximation technique for differential verification.
result NeuroDiff achieves up to 1000X speedup and 5X accuracy improvement.
FPGAs have become a popular choice for deploying deep learning architectures (DLA). There are many researchers that have explored the deployment and mapping of DLA on FPGA. However, there has been a growing need to do design-time hardware-software co-verification of these deployments. To the best of our knowledge this …
Novel approach using Lagrangian Decomposition for neural network verification.
problem Computing tight bounds on neural network outputs.
method Lagrangian Decomposition, efficient supergradient ascent, proximal algorithm.
result Proves tighter bounds than previous dual algorithms.
Validates neural networks inputs to protect against adversarial examples.
problem Ensuring neural networks robustness against adversarial attacks.
method Runtime local robustness verification based on normal distribution of robustness radii.
result Improves neural network accuracy and protects against adversarial examples.
Paper improves speaker verification with federated learning and differential privacy.
problem Improving speaker verification accuracy using private data.
method Combining federated learning and differential privacy to train an auxiliary model that predicts vocal characteristics.
result 6% relative improvement in equal error rate over a baseline system.
An End-to-End Text-independent Speaker Verification Framework with a Keyword Adversarial Networkeess.AS
This paper presents an end-to-end text-independent speaker verification framework by jointly considering the speaker embedding (SE) network and automatic speech recognition (ASR) network. The SE network learns to output an embedding vector which distinguishes the speaker characteristics of the input utterance, while th…
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm adversarial perturbations, for example). Most previous work on this topic was limi…