arXiv subjects

Sotirios Sabanis

Publications and source records attributed to Sotirios Sabanis.

At least 19 recordsLinked to original sources

arXiv2026

The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity

We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures. To handle the superlinear regime, taming techniques are employed to produce a stable, explicit scheme. We derive non-asymptotic convergence bounds in Wasserstein-2 distance, with all constants tracked explicitly in terms of dimension and inverse temperature, improving upon the currently known rates for subgradient-based Langevin algorithms. We further provide excess risk estimates for the associated optimisation problem. We verify the assumptions, with explicit constants, for the regularized pretraining potential of a LLM in the GPT-2 lineage and the boosted coordinate-wise variant of SG-TULA pretrains the former competitively against finetuned AdamW and Muon, for which no comparable non-asymptotic guarantees are presently available.

cs.LG↗

arXiv2026

When Summaries Distort Decisions: Information Fidelity in LLM-Compressed Financial Analysis

Financial decision-makers face more information than they can directly inspect, making context compression necessary. Yet when large language models (LLMs) compress financial source material, they can alter the investment judgment supported by the original source. We frame this problem as information fidelity: compression loses fidelity when it changes the decision induced by the source. In agentic systems, such losses may recur across intermediate steps and amplify throughout the decision process. Across financial filings and earnings-call transcripts, we find that LLM-based compression can produce fluent and factually plausible compressed contexts that nevertheless alter downstream decisions. We analyze two diagnostic patterns associated with fidelity loss: decontextualization, where salient evidence is retained but separated from the caveats and contextual qualifiers needed for correct interpretation, and model dependency, where different compressors expose different views of the same source. We then propose Agentic Context Compression, which generates multiple candidate compressions and audits their disagreements against the original source. Our results suggest that financial compression should be evaluated not only by efficiency or factuality, but also by its ability to preserve decision-relevant context.

cs.AI↗

arXiv2026

Flatness-Aware Stochastic Gradient Langevin Dynamics

Flatness of the loss landscape has been widely studied as an important perspective for understanding the behavior and generalization of deep learning algorithms. Motivated by this view, we propose Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD), a first-order optimization method that biases learning its dynamics toward flat basins while retaining the computational and memory efficiency of SGD and SGLD. We provide a non-asymptotic theoretical analysis showing that fSGLD targets a flatness-biased Gibbs distribution under a theoretically prescribed coupling between the noise scale $σ$ and the inverse temperature $β$, together with explicit excess risk guarantees. We empirically evaluate fSGLD across standard optimizer benchmarks, Bayesian image classification, uncertainty quantification, and out-of-distribution detection, demonstrating consistently strong performance and reliable uncertainty estimates. Additional experiments confirm the effectiveness of the theoretically prescribed $β$-$σ$ coupling compared to decoupled choices.

cs.LG↗

arXiv2025

The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions

In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging techniques, such as the Moreau-Yosida envelope or Gaussian smoothing, and show consequently that the performance of samplers like ULA does not necessarily degenerate arbitrarily with low regularity. In particular, we show that the Lipschitz or Hölder continuity assumption can be replaced by a geometric one-sided Lipschitz condition that allows even for discontinuous log-gradients. We derive non-asymptotic guarantees for the convergence of the algorithm to the target distribution in Wasserstein distances. Non-asymptotic bounds are also provided for the performance of the algorithm as an optimizer, specifically for the solution of associated excess risk optimization problems.

stat.ML↗

arXiv2025

One More Question is Enough, Expert Question Decomposition (EQD) Model for Domain Quantitative Reasoning

Domain-specific quantitative reasoning remains a major challenge for large language models (LLMs), especially in fields requiring expert knowledge and complex question answering (QA). In this work, we propose Expert Question Decomposition (EQD), an approach designed to balance the use of domain knowledge with computational efficiency. EQD is built on a two-step fine-tuning framework and guided by a reward function that measures the effectiveness of generated sub-questions in improving QA outcomes. It requires only a few thousand training examples and a single A100 GPU for fine-tuning, with inference time comparable to zero-shot prompting. Beyond its efficiency, EQD outperforms state-of-the-art domain-tuned models and advanced prompting strategies. We evaluate EQD in the financial domain, characterized by specialized knowledge and complex quantitative reasoning, across four benchmark datasets. Our method consistently improves QA performance by 0.6% to 10.5% across different LLMs. Our analysis reveals an important insight: in domain-specific QA, a single supporting question often provides greater benefit than detailed guidance steps.

cs.CL↗

arXiv2025

Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients

Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and generating diverse samples, achieving state-of-the-art performance across domains such as computer vision, audio generation, reinforcement learning, and computational biology. Despite their empirical success, existing Wasserstein-2 convergence analysis typically assume strong regularity conditions-such as smoothness or strict log-concavity of the data distribution-that are rarely satisfied in practice. In this work, we establish the first non-asymptotic Wasserstein-2 convergence guarantees for SGMs targeting semiconvex distributions with potentially discontinuous gradients. Our upper bounds are explicit and sharp in key parameters, achieving optimal dependence of $O(\sqrt{d})$ on the data dimension $d$ and convergence rate of order one. The framework accommodates a wide class of practically relevant distributions, including symmetric modified half-normal distributions, Gaussian mixtures, double-well potentials, and elastic net potentials. By leveraging semiconvexity without requiring smoothness assumptions on the potential such as differentiability, our results substantially broaden the theoretical foundations of SGMs, bridging the gap between empirical success and rigorous guarantees in non-smooth, complex data regimes.

cs.LG↗

arXiv2025

FinGEAR: Financial Mapping-Guided Enhanced Answer Retrieval

Financial disclosures such as 10-K filings present challenging retrieval problems due to their length, regulatory section hierarchy, and domain-specific language, which standard retrieval-augmented generation (RAG) models underuse. We introduce FinGEAR (Financial Mapping-Guided Enhanced Answer Retrieval), a retrieval framework tailored to financial documents. FinGEAR combines a finance lexicon for Item-level guidance (FLAM), dual hierarchical indices for within-Item search (Summary Tree and Question Tree), and a two-stage cross-encoder reranker. This design aligns retrieval with disclosure structure and terminology, enabling fine-grained, query-aware context selection. Evaluated on full 10-Ks with queries aligned to the FinQA dataset, FinGEAR delivers consistent gains in precision, recall, F1, and relevancy, improving F1 by up to 56.7% over flat RAG, 12.5% over graph-based RAGs, and 217.6% over prior tree-based systems, while also increasing downstream answer accuracy with a fixed reader. By jointly modeling section hierarchy and domain lexicon signals, FinGEAR improves retrieval fidelity and provides a practical foundation for high-stakes financial analysis.

cs.CE↗

arXiv2025

kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients

Motivated by applications in deep learning, where the global Lipschitz continuity condition is often not satisfied, we examine the problem of sampling from distributions with super-linearly growing log-gradients. We propose a novel tamed Langevin dynamics-based algorithm, called kTULA, to solve the aforementioned sampling problem, and provide a theoretical guarantee for its performance. More precisely, we establish a non-asymptotic convergence bound in Kullback-Leibler (KL) divergence with the best-known rate of convergence equal to $2-\overlineε$, $\overlineε>0$, which significantly improves relevant results in existing literature. This enables us to obtain an improved non-asymptotic error bound in Wasserstein-2 distance, which can be used to further derive a non-asymptotic guarantee for kTULA to solve the associated optimization problems. To illustrate the applicability of kTULA, we apply the proposed algorithm to the problem of sampling from a high-dimensional double-well potential distribution and to an optimization problem involving a neural network. We show that our main results can be used to provide theoretical guarantees for the performance of kTULA.

math.ST↗

arXiv2025

Taming the Interacting Particle Langevin Algorithm: The Superlinear case

Recent advances in stochastic optimization have yielded the interacting particle Langevin algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to efficiently sample from approximate posterior densities. This becomes particularly crucial in relation to the framework of Expectation-Maximization (EM), where the E-step is computationally challenging or even intractable. Although prior research has focused on scenarios involving convex cases with gradients of log densities that grow at most linearly, our work extends this framework to include polynomial growth. Taming techniques are employed to produce an explicit discretization scheme that yields a new class of stable, under such non-linearities, algorithms which are called tamed interacting particle Langevin algorithms (tIPLA). We obtain non-asymptotic convergence error estimates in Wasserstein-2 distance for the new class under the best known rate.

math.PR↗

arXiv2025

Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation

We develop a class of interacting particle systems for implementing a maximum marginal likelihood estimation (MMLE) procedure to estimate the parameters of a latent variable model. We achieve this by formulating a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space of parameters and latent variables. In particular, we prove that the parameter marginal of the stationary measure of this diffusion has the form of a Gibbs measure where number of particles acts as the inverse temperature parameter in classical settings for global optimisation. Using a particular rescaling, we then prove geometric ergodicity of this system and bound the discretisation error in a manner that is uniform in time and does not increase with the number of particles. The discretisation results in an algorithm, termed Interacting Particle Langevin Algorithm (IPLA) which can be used for MMLE. We further prove nonasymptotic bounds for the optimisation error of our estimator in terms of key parameters of the problem, and also extend this result to the case of stochastic gradients covering practical scenarios. We provide numerical experiments to illustrate the empirical behaviour of our algorithm in the context of logistic regression with verifiable assumptions. Our setting provides a straightforward way to implement a diffusion-based optimisation routine compared to more classical approaches such as the Expectation Maximisation (EM) algorithm, and allows for especially explicit nonasymptotic bounds.

stat.CO↗

arXiv2025

On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates

We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation is made of Lipschitz continuous functions avoiding any Lipschitzness assumption on the score function. We demonstrate via a motivating example, sampling from a Gaussian distribution with unknown mean, the powerfulness of our approach. In this case, explicit estimates are provided for the associated optimization problem, i.e. score approximation, while these are combined with the corresponding sampling estimates. As a result, we obtain the best known upper bound estimates in terms of key quantities of interest, such as the dimension and rates of convergence, for the Wasserstein-2 distance between the data distribution (Gaussian with unknown mean) and our sampling algorithm. Beyond the motivating example and in order to allow for the use of a diverse range of stochastic optimizers, we present our results using an $L^2$-accurate score estimation assumption, which crucially is formed under an expectation with respect to the stochastic optimizer and our novel auxiliary process that uses only known information. This approach yields the best known convergence rate for our sampling algorithm.

cs.LG↗

arXiv2024

A Tamed Euler Scheme for SDEs with Non-Locally Integrable Drift Coefficient

In this article we show that for SDEs with a drift coefficient that is non-locally integrable, one may define a tamed Euler scheme that converges in $L^p$ at rate $1/2$ to the true solution. The taming is required in this case since one cannot expect the regular Euler scheme to have finite moments in $L^p$. We additionally show that our setting applies to the case of two scalar valued particles with singular interaction kernel. To the best of the author's knowledge, this is the first work we are aware of to prove strong convergence of an Euler-type scheme in the case of non-locally integrable drift.

math.PR↗

arXiv2024

Langevin dynamics based algorithm e-TH$\varepsilon$O POULA for stochastic optimization problems with discontinuous stochastic gradient

We introduce a new Langevin dynamics based algorithm, called e-TH$\varepsilon$O POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks. We demonstrate both theoretically and numerically the applicability of the e-TH$\varepsilon$O POULA algorithm. More precisely, under the conditions that the stochastic gradient is locally Lipschitz in average and satisfies a certain convexity at infinity condition, we establish non-asymptotic error bounds for e-TH$\varepsilon$O POULA in Wasserstein distances and provide a non-asymptotic estimate for the expected excess risk, which can be controlled to be arbitrarily small. Three key applications in finance and insurance are provided, namely, multi-period portfolio optimization, transfer learning in multi-period portfolio optimization, and insurance claim prediction, which involve neural networks with (Leaky)-ReLU activation functions. Numerical experiments conducted using real-world datasets illustrate the superior empirical performance of e-TH$\varepsilon$O POULA compared to SGLD, TUSLA, ADAM, and AMSGrad in terms of model accuracy.

math.OC↗

arXiv2024

Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks

We present a new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of deep learning models. Its underpinning theory relies on recent advances of Euler's polygonal approximations for stochastic differential equations (SDEs) with monotone coefficients. As a result, it inherits the stability properties of tamed algorithms, while it addresses other known issues, e.g. vanishing gradients in neural networks. In particular, we provide a nonasymptotic analysis and full theoretical guarantees for the convergence properties of an algorithm of this novel class, which we named TH$\varepsilon$O POULA (or, simply, TheoPouLa). Finally, several experiments are presented with different types of deep learning models, which show the superior performance of TheoPouLa over many popular adaptive optimization algorithms.

cs.LG↗

arXiv2024

Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization

We provide a nonasymptotic analysis of the convergence of the stochastic gradient Hamiltonian Monte Carlo (SGHMC) to a target measure in Wasserstein-2 distance without assuming log-concavity. Our analysis quantifies key theoretical properties of the SGHMC as a sampler under local conditions which significantly improves the findings of previous results. In particular, we prove that the Wasserstein-2 distance between the target and the law of the SGHMC is uniformly controlled by the step-size of the algorithm, therefore demonstrate that the SGHMC can provide high-precision results uniformly in the number of iterations. The analysis also allows us to obtain nonasymptotic bounds for nonconvex optimization problems under local conditions and implies that the SGHMC, when viewed as a nonconvex optimizer, converges to a global minimum with the best known rates. We apply our results to obtain nonasymptotic bounds for scalable Bayesian inference and nonasymptotic generalization bounds.

math.OC↗

arXiv2023

Convergence Of The Unadjusted Langevin Algorithm For Discontinuous Gradients

We demonstrate that for strongly log-convex densities whose potentials are discontinuous on manifolds, the ULA algorithm converges with stepsize bias of order $1/2$ in Wasserstein-p distance. Our resulting bound is then of the same order as the convergence of ULA for gradient Lipschitz potential. Additionally, we show that so long as the gradient of the potential obeys a growth bound (therefore imposing no regularity condition), the algorithm has stepsize bias of order $1/4$. We therefore unite two active areas of research: i) the study of numerical methods for SDEs with discontinuous coefficients and ii) the study of the non-asymptotic bias of the ULA algorithm (and variants). In particular this is the first result of the former kind we are aware of on an unbounded time interval.

math.PR↗

arXiv2023

Taming under isoperimetry

In this article we propose a novel taming Langevin-based scheme called $\mathbf{sTULA}$ to sample from distributions with superlinearly growing log-gradient which also satisfy a Log-Sobolev inequality. We derive non-asymptotic convergence bounds in $KL$ and consequently total variation and Wasserstein-$2$ distance from the target measure. Non-asymptotic convergence guarantees are provided for the performance of the new algorithm as an optimizer. Finally, some theoretical results on isoperimertic inequalities for distributions with superlinearly growing gradients are provided. Key findings are a Log-Sobolev inequality with constant independent of the dimension, in the presence of a higher order regularization and a Poincare inequality with constant independent of temperature and dimension under a novel non-convex theoretical framework.

math.PR↗

arXiv2023

Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function

We consider non-convex stochastic optimization problems where the objective functions have super-linearly growing and discontinuous stochastic gradients. In such a setting, we provide a non-asymptotic analysis for the tamed unadjusted stochastic Langevin algorithm (TUSLA) introduced in Lovas et al. (2020). In particular, we establish non-asymptotic error bounds for the TUSLA algorithm in Wasserstein-1 and Wasserstein-2 distances. The latter result enables us to further derive non-asymptotic estimates for the expected excess risk. To illustrate the applicability of the main results, we consider an example from transfer learning with ReLU neural networks, which represents a key paradigm in machine learning. Numerical experiments are presented for the aforementioned example which support our theoretical findings. Hence, in this setting, we demonstrate both theoretically and numerically that the TUSLA algorithm can solve the optimization problem involving neural networks with ReLU activation function. Besides, we provide simulation results for synthetic examples where popular algorithms, e.g. ADAM, AMSGrad, RMSProp, and (vanilla) stochastic gradient descent (SGD) algorithm, may fail to find the minimizer of the objective functions due to the super-linear growth and the discontinuity of the corresponding stochastic gradient, while the TUSLA algorithm converges rapidly to the optimal solution. Moreover, we provide an empirical comparison of the performance of TUSLA with popular stochastic optimizers on real-world datasets, as well as investigate the effect of the key hyperparameters of TUSLA on its performance.

math.OC↗