This report synthesizes research advances in integrating machine learning with visual analytics.
problem Underexplored combination of machine learning and data visualization in visual analytics.
method Synthesizing research advances to highlight the progress and challenges.
result Opportunities and challenges identified for future research in machine learning and visual analytics.
The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.
problem Analyzing finite-time singularities in Spin(7)-structure flows.
method Proves Shi-type derivative estimates and shows that Λ(x,t) must blow up at finite-time singularities.
result Establishes a general analytic framework for studying Spin(7)-structure flows.
It is commonly believed that increasing the interpretability of a machine learning model may decrease its predictive power. However, inspecting input-output relationships of those models using visual analytics, while treating them as black-box, can help to understand the reasoning behind outcomes without sacrificing pr…
Survey on automating geometry problem solving with large models.
problem Automating geometric problem solving with spatial understanding and logical reasoning.
method Synthesizes GPS advancements through benchmark construction, parsing, and reasoning paradigms.
result Unified analytical paradigm and emerging opportunities identified.
A simple, yet reasonably accurate, analytical technique is proposed for multi-factor structural credit portfolio models. The accuracy of the technique is demonstrated by benchmarking against Monte Carlo simulations. The approach presented here may be of high interest to practitioners looking for transparent, intuitive,…
System uses machine learning and automated reasoning to speed up PBE synthesis.
problem Slow synthesis in PBE due to domain-specific knowledge and large training datasets.
method Preprocess SyGuS PBE problems with a neural network to reduce search space, then use automated reasoning for faster solution.
result System outperforms all competing tools in the 2019 SyGuS Competition for the PBE Strings track by 47.65%.
Transformers mimic Bayesian reasoning in controlled settings, revealing geometric mechanisms.
problem Verifying if transformers perform Bayesian reasoning rigorously in natural data.
method Constructing Bayesian wind tunnels with known posteriors and proving memorization impossibility.
result Transformers achieve 10−3-10−4 bit accuracy in Bayesian posteriors, while MLPs fail. The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is non-negative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical solution for European options.…
The paper uses regression models to predict COVID-19 spread and its stock market impact.
problem Predicting and understanding the impact of COVID-19 on stock markets.
method Logistic curve model with Bayesian regression for predictive analytics.
result Different crises have different impacts on the same stocks.
Defines complex structure for families of Hilbert spaces with reasonable curvature.
problem Curvature of families of Hilbert spaces not forming a holomorphic bundle.
method Defines a new complex analytic structure and curvature for families of Hilbert spaces.
result New proof of Berndtsson's theorem on curvature of direct images of semi-positively twisted relative canonical bundles.
We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bi…
SATNet integrates logical reasoning into deep learning with a differentiable MAXSAT solver.
problem Integrating logical reasoning into deep learning architectures.
method Differentiable MAXSAT solver based on fast coordinate descent for SDP.
result Minimally supervised learning of logical structures in deep learning systems.
New language model shows context length impacts generation quality and reasoning ability.
problem Analyzing the impact of context length and reasoning on autoregressive generation.
method Introduced synthetic hierarchical languages, used an exact k-gram ansatz, derived asymptotic predictions, and validated empirically.
result Reasoning models with limited context can generate sequences from the true language, improving exponentially over standard models.
The relationship between minimal algebraic Kac-Moody groups and twin buildings is well known as is the relationship between formal completions in one direction and affine buildings. Nevertheless, as the completion of a Kac-Moody group in one direction destroys the opposite BN-pair, there exists no longer a twin buildin…
This paper explores how to interpret machine learning models in business process analytics.
problem The lack of interpretability in machine learning models used for predictive process analytics.
method Derives explanations using interpretable machine learning techniques to compare and contrast predictive models.
result Highlights scenarios where accuracy alone may not be sufficient in assessing the suitability of techniques used to encode event log data.
In this paper, we compare static and dynamic (reduced form) approaches for modeling wrong-way risk in the context of CVA. Although all these approaches potentially suffer from arbitrage problems, they are popular (respectively) in industry and academia, mainly due to analytical tractability reasons. We complete the sto…
Erdős introduced the noncommuting graph, in order to study the number of commuting elements in a finite group. Despite the use of combinatorial ideas, his methods involved several techniques of classical analysis. The interest for this graph is becoming relevant in the last years for various reasons. Here we deal with …
Machine learning aids in clinical prediction tasks.
problem Improving accuracy in clinical predictions.
method Introduction to machine learning concepts and algorithms, followed by practical application to clinical datasets.
result Demonstrated the application of machine learning models to clinical prediction problems.
New insights into how to inspect and learn from multi-stage processes and AI reasoning.
problem Understanding how to attribute outcomes to early stages in multi-stage operations and AI reasoning.
method Information-theoretic analysis and mathematical proofs of four key results.
result Uniform checkpoint spacing is minimax-optimal for inspection design under homogeneous signal attenuation.
This paper proposes a web-based visual graph analytics platform for interactive graph mining, visualization, and real-time exploration of networks. GraphVis is fast, intuitive, and flexible, combining interactive visualizations with analytic techniques to reveal important patterns and insights for sense making, reasoni…
The paper offers a checklist for comparing human and machine visual perception.
problem Comparing human and machine visual perception.
method Designing, conducting, and interpreting experiments to investigate mechanisms.
result Feedback mechanisms may not be necessary for visual reasoning tasks.
Paper develops a new similarity metric for predicting stock market returns.
problem Predicting stock returns is challenging due to market stochasticity and various influencing factors.
method Case-based reasoning approach using historical pricing data and a novel similarity metric.
result Demonstrates the benefits of the novel similarity metric in predicting stock market returns.
The paper finds infinitely many cuspidal edges along a knot with the same first fundamental form.
problem Finding cuspidal edges with the same first fundamental form along a knot.
method Analyzes Cω-cuspidal edges along a knot C. result Infinitely many non-congruent cuspidal edges have the same first fundamental form.
Paper calibrates GARCH diffusion model for option pricing using PDE methods.
problem Lack of fast, semi-analytic solution for GARCH diffusion model option pricing.
method PDE-based finite difference solver for accurate calibrations.
result PDE calibration of GARCH diffusion model to SPX options.
Dropout has recently emerged as a powerful and simple method for training neural networks preventing co-adaptation by stochastically omitting neurons. Dropout is currently not grounded in explicit modelling assumptions which so far has precluded its adoption in Bayesian modelling. Using Bayesian entropic reasoning we s…
The paper introduces sanity tests to detect spurious correlations in AI-guided radiology systems.
problem Detecting when AI systems perform well on development data for the wrong reasons.
method Design and implementation of sanity tests to identify spurious correlations.
result Sanity tests can identify spurious correlations in AI-guided radiology systems.
Develops an adversarial clustering algorithm for detecting cyber attacks.
problem Dealing with active adversaries in cyber security data analytics.
method Grid-based adversarial clustering algorithm using game theoretic ideas.
result Identifies normal and attack objects, sub-clusters, overlapping areas, and outliers.
Formally proves machine learning for simple classifiers.
problem Proving PAC learnability for decision stumps.
method Formal proof in Lean, separating deterministic and probabilistic proofs.
result Formal proof of PAC learnability for decision stumps.
Physics-informed model predicts beam stiffness and monitors structural health.
problem Predicting and monitoring the stiffness of Euler-Bernoulli beams.
method Physics-informed Gaussian process model using the Euler-Bernoulli beam equation.
result Model accurately predicts bending stiffness and detects structural damage.
Hybrid model speeds up galaxy simulations by incorporating baryonic properties.
problem Inaccurate baryonic properties in dark matter-only simulations.
method Combining analytic models and machine learning for faster, more accurate simulations.
result Hybrid model outperforms machine learning alone for some baryonic properties.
Stochastic volatility models describe asset prices St as driven by an unobserved process capturing the random dynamics of volatility σt. Here, we quantify how much information about σt can be inferred from asset prices St in terms of Shannon's mutual information I(St:σt). This motivates a careful nume…
We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration t…
Physics-Informed Neural Network improves option pricing accuracy.
problem Improving option pricing accuracy using machine learning.
method Physics-Informed Neural Network (PINN) applied to Black-Scholes equation.
result PINN model accurately captures option pricing behavior on both simulated and real market data.
Machine learning guides clinicians in predictive modeling using big data.
problem Insufficient understanding of machine learning among clinicians hinders its adoption.
method Provides a series of guides on machine learning principles, resampling, model evaluation, and coding.
result Clinicians need methodological rigor and clarity to use machine learning effectively.
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and stacks) important in the study of moduli spaces of curves and abelian varieties thro…
Deriving the optimal safety stock quantity with which to meet customer satisfaction is one of the most important topics in stock management. However, it is difficult to control the stock management of correlated marketable merchandise when using an inventory control method that was developed under the assumption that t…
Study shows big winner stocks significantly impact passive and active investment strategies.
problem Impact of big winner stocks on passive and active investment strategies.
method Numerical and analytical techniques applied to historical stock price data.
result Concentrated portfolios underperform equally weighted indexes due to missing big winner stocks.
Bayesian PINNs optimize loss weights for PDEs and data.
problem Optimizing loss weights in physics-informed neural networks.
method Laplace approximation for efficient model evidence computation.
result Unified Bayesian setting for PDEs and noisy measurements.
Silas provides transparent, verifiable machine learning models.
problem Creating reliable and explainable machine learning models.
method Formal verification, correct training, and transparent reasoning modules.
result Silas models are formally verified and correct.
General-purpose model learns visual reasoning without strong priors.
problem Achieving visual reasoning in image-related questions.
method Conditional Batch Normalization approach.
result 2.4% error rate on CLEVR Visual Reasoning benchmark.
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the market stochastic dynamics, allowing us to write and formally solve the generaliz…
LaTRO optimizes latent reasoning in LLMs without external reward.
problem Training LLMs to perform complex reasoning tasks.
method Formulates reasoning as latent distribution sampling and optimizes via variational approaches.
result LLMs improve reasoning and evaluation quality through self-improvement.
New method learns disentangled discrete representations using categorical variational autoencoders.
problem Learning disentangled representations from discrete latent spaces.
method Replaced standard Gaussian VAE with a categorical VAE to mitigate rotational invariance.
result Categorical distributions improve learning of disentangled representations.
Auto-CEI improves LLM reasoning by balancing assertiveness and conservativeness.
problem Hallucinations and laziness in LLM reasoning tasks.
method Expert Iteration explores reasoning trajectories, guiding incorrect paths back on track and promoting appropriate 'I don't know' responses.
result Auto-CEI achieves superior alignment in logical reasoning, mathematics, and planning tasks.
A framework isolates VQA reasoning from perception for better model evaluation.
problem Improper separation of visual perception and reasoning in VQA models.
method Introducing a framework and a top-down calibration technique to decouple reasoning from perception.
result Improved evaluation of VQA models by separating reasoning from perception.
A new method for math reasoning that allows for iterative correction.
problem Standard reasoning models commit to each token and cannot recover from early errors.
method Generative framework with latent thought vectors for iterative self-correction.
result 30 rethinking iterations surpass baselines with 15 times more parameters.
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard operations like covariant contraction, covariant derivative, and constructions like th…
FinZero improves financial time series forecasting accuracy with multimodal modeling.
problem Lack of interpretability, uncertainty, and scalability in financial time series forecasting.
method Developed a multimodal pre-trained model FinZero using UARPO method for reasoning, prediction, and uncertainty analysis.
result FinZero achieves an approximate 13.48% improvement in prediction accuracy over GPT-4o in high-confidence group.