A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Formally verifies fairness and uniformity in financial market trades.
Formal methods verify continuous auctions at exchanges.
We formalize and verify double auctions for multiple-quantity trades.
Formalizes vNM utility theorem using Lean 4, proving existence and uniqueness.
Proves formal self-adjointness of certain differential operators.
ViTaX provides formal guarantees for targeted explanations in safety-critical systems.
Neural networks are part of many contemporary NLP systems, yet their empirical successes come at the price of vulnerability to adversarial attacks. Previous work has used adversarial training and data augmentation to partially mitigate such brittleness, but these are unlikely to find worst-case adversaries due to the c…
Paper formalizes multi-dimensional FSD using geometric methods.
We introduce a formal framework for analyzing trades in financial markets. An exchange is where multiple buyers and sellers participate to trade. These days, all big exchanges use computer algorithms that implement double sided auctions to match buy and sell requests and these algorithms must abide by certain regulator…
Efficient verified double auctions improve matching speed and detect errors.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
This paper introduces a new classification tool named Silas, which is built to provide a more transparent and dependable data analytics service. A focus of Silas is on providing a formal foundation of decision trees in order to support logical analysis and verification of learned prediction models. This paper describes…
New method verifies formulas for causal interventional distributions.
PEREGRiNN verifies safety of ReLU NNs by penalizing relaxation in a greedy manner.
Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic approximation theorems typically possess assumptions which are difficult to communicate an…
This study extends verifiable learning to boosted tree ensembles, enabling efficient security verification.
This paper formalizes -learning and linear TD convergence using Lean 4.
Cactus improves auto-regressive decoding speed without sacrificing quality.
Revel tackles safe exploration in RL with verified symbolic policies.
The study develops a logic reasoner to verify MS case management specifications.
Framework evaluates AI proposals for drug discovery, finds no LLM advantage.
Formalizes weak and strong verification for LLMs, controlling errors without assumptions.
Paper formalizes Simon's satisficing through FFSD, proving its equivalence to expected utility theory.
Theoretical limits on verifying self-improving systems without risking unbounded utility.
This is a paper about geometry of (iterated) variations. We explain why no sources of divergence are built into the Batalin-Vilkovisky (BV) Laplacian, whence there is no need to postulate any ad hoc conventions such as "" and "" within BV-approach to quantisation of gauge systems. Remarkably, the ge…
This research simplifies verification of machine learning systems using reparameterization.
In this short note, we compute the Betti numbers of the moduli stack of flat SU(3)-bundles over a Klein bottle. We also handle the general compact group case over RP^2. In all cases the cohomology is found to be equivariantly formal, supporting a conjecture from the author's doctoral thesis. Our results also verify con…
Recent advances in machine learning and artificial intelligence are now being considered in safety-critical autonomous systems where software defects may cause severe harm to humans and the environment. Design organizations in these domains are currently unable to provide convincing arguments that their systems are saf…
Study improves understanding of why agentic theorem provers succeed.
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…
We study the problem of formally verifying the robustness to adversarial examples of support vector machines (SVMs), a major machine learning model for classification and regression tasks. Following a recent stream of works on formal robustness verification of (deep) neural networks, our approach relies on a sound abst…
Generalizes neural network verification by adding arbitrary cutting planes.
We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification f…
Language models help text classification tasks by predicting next words.
We address the problem of verifying neural-based perception systems implemented by convolutional neural networks. We define a notion of local robustness based on affine and photometric transformations. We show the notion cannot be captured by previously employed notions of robustness. The method proposed is based on re…
We consider an investor with constant absolute risk aversion who trades a risky asset with general Ito dynamics, in the presence of small proportional transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the leading-order optimal trading policy and the associated welfare impact of transaction costs. In th…
We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In particular, some necessary and sufficient conditions for the existence of abnorm…
Framework for verifying deep learning operators.
While neural networks are good at learning unspecified functions from training samples, they cannot be directly implemented in hardware and are often not interpretable or formally verifiable. On the other hand, logic circuits are implementable, verifiable, and interpretable but are not able to learn from training data …
This paper autoformalizes Euclidean geometry using LLMs and theorem provers.
New expressive losses improve adversarial robustness without sacrificing accuracy.
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable problem. While approximation methods exist, they do not come with guarantees, mak…
Despite the functional success of deep neural networks (DNNs), their trustworthiness remains a crucial open challenge. To address this challenge, both testing and verification techniques have been proposed. But these existing techniques provide either scalability to large networks or formal guarantees, not both. In thi…
Deep neural networks have achieved impressive performance in many applications but their large number of parameters lead to significant computational and storage overheads. Several recent works attempt to mitigate these overheads by designing compact networks using pruning of connections. However, we observe that most …
In various situations in Floer theory, one extracts homological invariants from "Morse-Bott" data in which the "critical set" is a union of manifolds, and the moduli spaces of "flow lines" have evaluation maps taking values in the critical set. This requires a mix of analytic arguments (establishing properties of the m…
Paper formalizes analogy between data sets and models using Hoare logic.
Formal verification of neural networks is essential for their deployment in safety-critical areas. Many available formal verification methods have been shown to be instances of a unified Branch and Bound (BaB) formulation. We propose a novel framework for designing an effective branching strategy for BaB. Specifically,…