arXiv subjects

Daniel Csillag

Publications and source records attributed to Daniel Csillag.

10 recordsLinked to original sources

arXiv2026

Functional Gradient Descent with Adaptive Representations

Functional optimization problems are typically solved by optimizing the parameters of a fixed representation, such as a neural network, resulting in highly nonconvex losses that complicate both training and theoretical analysis. An interesting alternative is functional gradient descent (FGD), that is, gradient descent directly in function space, which benefits from strong convergence results and admits a clean theory. However, FGD is difficult to implement in practice because functional gradients are infinite-dimensional, and thus cannot be fully computed nor stored in memory. Existing implementations therefore rely on fixed approximations, which introduce approximation error. We propose a new, theoretically-grounded FGD algorithm that adapts the representation of the functional gradients over the course of optimization. By explicitly incorporating this approximation into the analysis, we establish convergence to a stationary point (for smooth losses) and to a global minimizer (under smoothness + a Polyak-Lojasiewicz-type condition) regardless of our approximations. To the best of our knowledge, this is the first implementable FGD method with such guarantees in a general setting. We demonstrate the effectiveness of our method on regression, numerical solution of PDEs, and modern computer vision. Across settings, our method consistently outperforms both FGD with fixed approximations and neural network baselines in efficiency and accuracy.

math.OC↗

arXiv2026

Avoid What You Know: Divergent Trajectory Balance for GFlowNets

Generative Flow Networks (GFlowNets) are a flexible family of amortized samplers trained to generate discrete and compositional objects with probability proportional to a reward function. However, learning efficiency is constrained by the model's ability to rapidly explore diverse high-probability regions during training. To mitigate this issue, recent works have focused on incentivizing the exploration of unvisited and valuable states via curiosity-driven search and self-supervised random network distillation, which tend to waste samples on already well-approximated regions of the state space. In this context, we propose Adaptive Complementary Exploration (ACE), a principled algorithm for the effective exploration of novel and high-probability regions when learning GFlowNets. To achieve this, ACE introduces an exploration GFlowNet explicitly trained to search for high-reward states in regions underexplored by the canonical GFlowNet, which learns to sample from the target distribution. Through extensive experiments, we show that ACE significantly improves upon prior work in terms of approximation accuracy to the target distribution and discovery rate of diverse high-reward states.

cs.LG↗

arXiv2025

Random Gradient-Free Optimization in Infinite Dimensional Spaces

We propose a new gradient-free method for infinite-dimensional optimization in Hilbert spaces that requires only the computation of directional derivatives. Though functional optimization is often solved through finite-dimensional gradient descent over a parametrization, such as neural networks, we instead propose to leverage the functional nature of the optimization problem to enable provable guarantees. However, infinite-dimensional gradients are often hard to compute in practice, rendering na\"ive functional gradient descent intractable. To overcome this limitation, our framework leverages only directional derivatives and a pre-basis for the Hilbert space, i.e., a linearly independent set whose span is dense. This resolves the tractability issue, as pre-bases are much more accessible than full orthonormal bases or reproducing kernels -- which may not even exist -- and individual directional derivatives can be computed using automatic differentiation. We showcase the use of our method to solve partial differential equations \`a la physics-informed neural networks (PINNs), where it effectively enables provable convergence.

math.OC↗

arXiv2025

Adaptive Training of INRs via Pruning and Densification

Encoding input coordinates with sinusoidal functions into multilayer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of low-dimensional signals, enabling the modeling of high-frequency details. However, selecting appropriate input frequencies and architectures while managing parameter redundancy remains an open challenge, often addressed through heuristics and heavy hyperparameter optimization schemes. In this paper, we introduce AIRe ($\textbf{A}$daptive $\textbf{I}$mplicit neural $\textbf{Re}$presentation), an adaptive training scheme that refines the INR architecture over the course of optimization. Our method uses a neuron pruning mechanism to avoid redundancy and input frequency densification to improve representation capacity, leading to an improved trade-off between network size and reconstruction quality. For pruning, we first identify less-contributory neurons and apply a targeted weight decay to transfer their information to the remaining neurons, followed by structured pruning. Next, the densification stage adds input frequencies to spectrum regions where the signal underfits, expanding the representational basis. Through experiments on images and SDFs, we show that AIRe reduces model size while preserving, or even improving, reconstruction quality. Code and pretrained models will be released for public use.

cs.CV↗

arXiv2025

Differentially Private E-Values

E-values have gained prominence as flexible tools for statistical inference and risk control, enabling anytime- and post-hoc-valid procedures under minimal assumptions. However, many real-world applications fundamentally rely on sensitive data, which can be leaked through e-values. To ensure their safe release, we propose a general framework to transform non-private e-values into differentially private ones. Towards this end, we develop a novel biased multiplicative noise mechanism that ensures our e-values remain statistically valid. We show that our differentially private e-values attain strong statistical power, and are asymptotically as powerful as their non-private counterparts. Experiments across online risk monitoring, private healthcare, and conformal e-prediction demonstrate our approach's effectiveness and illustrate its broad applicability.

stat.ME↗

arXiv2025

Extending Prediction-Powered Inference through Conformal Prediction

Prediction-powered inference is a recent methodology for the safe use of black-box ML models to impute missing data, strengthening inference of statistical parameters. However, many applications require strong properties besides valid inference, such as privacy, robustness or validity under continuous distribution shifts; deriving prediction-powered methods with such guarantees is generally an arduous process, and has to be done case by case. In this paper, we resolve this issue by connecting prediction-powered inference with conformal prediction: by performing imputation through a calibrated conformal set-predictor, we attain validity while achieving additional guarantees in a natural manner. We instantiate our procedure for the inference of means, Z- and M-estimation, as well as e-values and e-value-based procedures. Furthermore, in the case of e-values, ours is the first general prediction-powered procedure that operates off-line. We demonstrate these advantages by applying our method on private and time-series data. Both tasks are nontrivial within the standard prediction-powered framework but become natural under our method.

stat.ME↗

arXiv2025

Image Super-Resolution with Guarantees via Conformalized Generative Models

The increasing use of generative ML foundation models for image restoration tasks such as super-resolution calls for robust and interpretable uncertainty quantification methods. We address this need by presenting a novel approach based on conformal prediction techniques to create a 'confidence mask' capable of reliably and intuitively communicating where the generated image can be trusted. Our method is adaptable to any black-box generative model, including those locked behind an opaque API, requires only easily attainable data for calibration, and is highly customizable via the choice of a local image similarity metric. We prove strong theoretical guarantees for our method that span fidelity error control (according to our local image similarity metric), reconstruction quality, and robustness in the face of data leakage. Finally, we empirically evaluate these results and establish our method's solid performance.

cs.CV↗

arXiv2025

Prediction-Powered E-Values

Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to Z-estimation problems such as inference of means and quantiles. In this paper, we apply ideas of prediction-powered inference to e-values. By doing so, we inherit all the usual benefits of e-values -- such as anytime-validity, post-hoc validity and versatile sequential inference -- as well as greatly expand the set of inferences achievable in a prediction-powered manner. In particular, we show that every inference procedure that can be framed in terms of e-values has a prediction-powered counterpart, given by our method. We showcase the effectiveness of our framework across a wide range of inference tasks, from simple hypothesis testing and confidence intervals to more involved procedures for change-point detection and causal discovery, which were out of reach of previous techniques. Our approach is modular and easily integrable into existing algorithms, making it a compelling choice for practical applications.

stat.ML↗

arXiv2024

Strategic Conformal Prediction

When a machine learning model is deployed, its predictions can alter its environment, as better informed agents strategize to suit their own interests. With such alterations in mind, existing approaches to uncertainty quantification break. In this work we propose a new framework, Strategic Conformal Prediction, which is capable of robust uncertainty quantification in such a setting. Strategic Conformal Prediction is backed by a series of theoretical guarantees spanning marginal coverage, training-conditional coverage, tightness and robustness to misspecification that hold in a distribution-free manner. Experimental analysis further validates our method, showing its remarkable effectiveness in face of arbitrary strategic alterations, whereas other methods break.

stat.ML↗

arXiv2024

Generalization Bounds for Causal Regression: Insights, Guarantees and Sensitivity Analysis

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that provides such guarantees. By introducing a novel change-of-measure inequality, we are able to tightly bound the model loss in terms of the deviation of the treatment propensities over the population, which we show can be empirically limited. Our theory is fully rigorous and holds even in the face of hidden confounding and violations of positivity. We demonstrate our bounds on semi-synthetic and real data, showcasing their remarkable tightness and practical utility.

stat.ML↗