A new method shrinks a complex structure without much change.
problem Understanding the geometry of Bing's wild involution.
method Producing a counterintuitive construction to shrink the Bing decomposition without much change.
result A method to shrink a complex structure (Bing's decomposition) without much change.
Gold and currency markets form a unique pair with specific interactions and dynamics. We focus on the efficiency ranking of gold markets with respect to the currency of purchase. By utilizing the Efficiency Index (EI) based on fractal dimension, approximate entropy and long-term memory on a wide portfolio of 142 gold p…
Our knowledge about the evolution of guarantee network in downturn period is limited due to the lack of comprehensive data of the whole credit system. Here we analyze the dynamic Chinese guarantee network constructed from a comprehensive bank loan dataset that accounts for nearly 80% total loans in China, during 01/200…
Convolutional networks struggle with repeating patterns in ECGs.
problem Modeling repeating patterns in electrocardiogram signals.
method Demonstrated through ECG examples, highlighting systemic issues in deep learning.
result Counterintuitive effects on generalization in deep networks.
Cryptos remained resilient after SVB's collapse, contrary to expectations.
problem Impact of SVB collapse on crypto markets.
method Factual summary, sentiment analysis, and market performance examination.
result Cryptocurrencies showed resilience after SVB's collapse.
Estimates time-varying parameters from two OLS estimates.
problem Time-varying linear regression with hidden dynamics.
method Combines two OLS estimates for stable linear dynamics.
result Finite sample guarantee on estimation error.
Simplified Khovanov-Rozansky operators for link invariants.
problem Complexity in Khovanov-Rozansky knot invariants.
method Substituted matrix factorization with simple operators and conjugations.
result Global reductions for simplifying link invariants.
ETFs with 2x and 3x leverage underperformed the S&P 500 index due to compounding and volatility.
problem ETFs with higher leverage failed to match the performance of the underlying index.
method Analyzed the performance of leveraged ETFs compared to the S&P 500 index, accounting for compounding and volatility.
result Two-thirds of the underperformance was due to compounding and volatility, with the rest due to covariance.
Prompted by a recent experiment by Victor Haghani and Richard Dewey, this note generalises the Kelly strategy (optimal for simple investment games with log utility) to a large class of practical utility functions and including the effect of extraneous wealth. A counterintuitive result is proved : for any continuous, co…
Braids can be represented geometrically as curve diagrams. The geometric complexity of a braid is the minimal complexity of a curve diagram representing it. We introduce and study the corresponding notion of geometric generating function. We compute explicitly the geometric generating function for the group of braids o…
This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial exchangeability to provide a framework with maximal representation power for graphs. RP …
Gradient span algorithms show consistent progress in high dimensions.
problem Understanding consistent training progress in large machine learning models.
method Proving deterministic behavior of gradient span algorithms on Gaussian random functions.
result Gradient span algorithms have asymptotically deterministic behavior in high dimensions.
Single global merging boosts decentralized learning performance.
problem Limited communication in decentralized learning hinders performance.
method Scheduled communication, focusing on final step with global merging.
result Single global merging improves global test performance.
Study models growth of unorganized retail in Indian pharma sector amid organized and e-retail competition.
problem Survival strategies of unorganized retailers challenged by organized and e-retailers.
method Field investigation, conjoint analysis, design of experiments, agent-based simulation.
result Unorganized retailers' performance influenced by their own attribute levels and price discounts.
Quantitative analysis of soccer players' passing ability focuses on descriptive statistics without considering the players' real contribution to the passing and ball possession strategy of their team. Which player is able to help the build-up of an attack, or to maintain the possession of the ball? We introduce a novel…
For the supervised least squares classifier, when the number of training objects is smaller than the dimensionality of the data, adding more data to the training set may first increase the error rate before decreasing it. This, possibly counterintuitive, phenomenon is known as peaking. In this work, we observe that a s…
A new decomposition explains over-parameterized models' counterintuitive behaviors.
problem Understanding predictive error in over-parameterized models.
method Introducing the Generalized Aliasing Decomposition (GAD) to explain predictive performance.
result The GAD decomposes predictive error into three parts: model insufficiency, data insufficiency, and generalized aliasing.
The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one.…
Cosine similarity can force points to grow in magnitude, causing convergence issues.
problem Cosine similarity loss can lead to convergence issues in deep learning.
method Analyzing under-explored settings and proposing cut-initialization.
result Cosine similarity optimization forces points to grow in magnitude, leading to convergence issues.
Study finds short-term wage increases due to COVID-19, contrary to expectations.
problem Impact of COVID-19 on wages over time.
method Empirical analysis controlling for GDP as a demand proxy.
result Short-term positive wage effect, contrary to expectations.
We present a financial market model, characterized by self-organized criticality, that is able to generate endogenously a realistic price dynamics and to reproduce well-known stylized facts. We consider a community of heterogeneous traders, composed by chartists and fundamentalists, and focus on the role of informative…
EGP uses expander graphs to improve GNN performance.
problem Challenges in deploying GNNs on graph tasks, including bottlenecks and oversquashing.
method Proposes EGP model based on expander graph propagation.
result EGP addresses challenges without bottlenecks or oversquashing, with linear complexity.
Maximal extractable value in CFMMs can degrade or improve routing quality, with reordering MEV showing logarithmic impact.
problem Maximal extractable value in constant function market makers (CFMMs) and its impact on routing quality.
method Game theoretic analysis of MEV in CFMMs, constructing price of anarchy and analyzing reordering MEV.
result Conditions under which reordering MEV shows logarithmic impact, and implications for MEV searchers and CFMM designers.
The study proves unique path lifting properties and their implications on quotient spaces and covering maps.
problem Understanding unique path lifting properties and their implications on quotient spaces and covering maps.
method The study uses group actions on R-trees and path lifting properties to prove the main results. result Every map of manifolds with the unique path lifting property is a covering map.
New approach uses 'forward-looking' counterfactuals for treatment choice.
problem Using traditional 'retrospective' counterfactuals in treatment choice leads to counterintuitive results.
method Introduces 'counterfactual treatment choice' for forward-looking counterfactuals.
result Mismatches between interventional and forward-looking counterfactuals can lead to counterintuitive results.
Overprocuring reserves can improve network efficiency by using excess reserves for congestion management.
problem Optimizing energy and reserve allocation between zones to minimize costs and ensure deliverability.
method Developed allocation models for co-allocating traded energy and reserve products, considering both deterministic and stochastic flows.
result Excess reserve supplies can be used for congestion management, leading to additional network benefits.
The paper examines how spike strengths and alignments affect overfitting in linear regression models.
problem The impact of spike strengths and alignments on overfitting in linear regression models.
method Characterization of generalization error through exact expressions and analysis of spike strengths, aspect ratio, and target alignment.
result Increasing spike strength can lead to catastrophic overfitting before benign overfitting, especially in well-specified aligned problems.
A mathematical analysis of the distribution of voting power in the Council of the European Union operating according to the Treaty of Lisbon is presented. We study the effects of Brexit on the voting power of the remaining members, measured by the Penrose--Banzhaf Index. We note that the effects in question are non-mon…
The standard asset pricing models (the CCAPM and the Epstein-Zin non-expected utility model) counterintuitively predict that equilibrium asset prices can rise if the representative agent's risk aversion increases. If the income effect, which implies enhanced saving as a result of an increase in risk aversion, dominates…
We describe an approach to understand the peculiar and counterintuitive generalization properties of deep neural networks. The approach involves going beyond worst-case theoretical capacity control frameworks that have been popular in machine learning in recent years to revisit old ideas in the statistical mechanics of…
New proof links initial class bias to DNN trainability, challenging traditional understanding.
problem Understanding the initial class bias in DNNs and its impact on trainability.
method Theoretical proof linking initial class bias to mean field theories of DNNs.
result Efficient learning is connected to a network's prejudice towards a specific class, contradicting traditional understanding.
Paper investigates monotonicity issues in AI preference learning.
problem AI models may violate monotonicity when learning preferences.
method Investigates root causes of non-monotonicity in comparison-based preference learning.
result Proves local pairwise monotonicity under mild assumptions.
Quantum models show improved performance in overparameterized regimes.
problem Overfitting in quantum machine learning models.
method Analytical demonstration and numerical experiments on quantum kernel methods.
result Quantum models can operate in the modern, overparameterized regime without overfitting.
Deep learning models price convertible bonds with complex reset and call features.
problem Pricing convertible bonds with path-dependent reset and call provisions.
method Formulated as a PPDE, deep learning approximates conditional expectations.
result Deep learning produces stable and accurate prices across various model specifications.
New solver avoids memory issues for long differential equations.
problem Memory constraints in adaptive probabilistic ODE solvers.
method Fixed memory demands adaptive probabilistic solver using robust state estimation.
result Eliminates memory issues for long time series simulations.
New insights into experience replay in RL algorithms.
problem Understanding the impact of replay capacity and replay ratio in Q-learning.
method Systematic and extensive analysis of experience replay in Q-learning methods, focusing on replay capacity and replay ratio.
result Greater replay capacity significantly improves performance for certain algorithms, while other techniques offer limited benefit.
Recommender systems are widely used to predict personalized preferences of goods or services using users' past activities, such as item ratings or purchase histories. If collections of such personal activities were made publicly available, they could be used to personalize a diverse range of services, including targete…
We examine the Foreign Exchange (FX) spot price spreads with and without Last Look on the transaction. We assume that brokers are risk-neutral and they quote spreads so that losses to latency arbitrageurs (LAs) are recovered from other traders in the FX market. These losses are reduced if the broker can reject, ex-post…
New insights into ML models' accuracy and generalization for scientific problems.
problem Quantifying accuracy and generalization of ML models in scientific applications.
method Rigorous numerical analysis and theoretical bounds for linear differential equations.
result Different ML models can have opposing generalization behaviors, contrary to intuition.
Overparameterized models can worsen minority group errors even when overall test error improves.
problem Overparameterization exacerbates spurious correlations, harming minority groups.
method Simulations and experiments on image datasets, theoretical analysis of linear models.
result Subsampling the majority group can achieve low minority error in overparameterized models.
Wide networks learn from adversarial perturbations effectively.
problem Understanding why adversarial examples deceive classifiers and transfer between models.
method Assumed wide two-layer networks, proved with theoretical analysis.
result Adversarial perturbations contain class-specific features for networks to generalize.
Spatial information is not always necessary for spatio-temporal models.
problem The necessity of including spatial information in spatio-temporal models.
method Comparison of spatial agnostic neural networks with state-of-the-art models on ten datasets.
result Spatial information is not always needed in most spatio-temporal models.
Sepsis is the leading cause of death in non-coronary intensive care units. Moreover, a delay of antibiotic treatment of patients with severe sepsis by only few hours is associated with increased mortality. This insight makes accurate models for early prediction of sepsis a key task in machine learning for healthcare. P…
Refundable income annuities offer a money-back guarantee, now the majority of sales.
problem The complexity and market neglect of refundable income annuities.
method Explained the pricing, duration, and money's-worth-ratio of refundable IAs, proving a counterintuitive price behavior.
result The market price of cash-refund IAs is not a declining function of age, and older buyers might pay more than younger ones.
This paper extends RMT for deep learning models beyond eigenvalues.
problem Challenges in high-dimensional, overparameterized ML models.
method Introduces High-dimensional Equivalent to analyze nonlinear models.
result Unified understanding of training and generalization in deep learning.
Stochastic gradient descent approximates Gaussian process posteriors efficiently.
problem Efficiently sampling from Gaussian process posteriors with limited computational resources.
method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.
result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.
Hyperfitting improves LLM generation quality by enhancing diversity, contrary to simple temperature scaling.
problem Improving open-ended generation quality of LLMs with minimal fine-tuning effort.
method Demonstrates that hyperfitting, a phenomenon where LLMs are fine-tuned to near-zero training loss, enhances generation quality and mitigates repetition.
result Hyperfitting is distinct from temperature scaling and involves a dynamic, context-dependent rank reordering mechanism in the final transformer block.
A new SBM for bipartite networks improves community detection in noisy data.
problem Community detection in bipartite networks with stochastic blockmodels.
method Bayesian nonparametric formulation of SBM for bipartite networks, algorithm to find communities efficiently.
result Improves community detection results over general SBMs, especially in noisy data.