arXiv subjects

Kamil Ciosek

Publications and source records attributed to Kamil Ciosek.

At least 19 recordsLinked to original sources

arXiv2026

Gradient Prediction with Control Variates in the Cheap-Forward Regime

We study whether otherwise-idle inference resources could reduce the scarce-GPU cost of training. Our analysis uses a simulated compute ledger in which fleet work is billed at a fraction of a scarce-GPU forward; all experiments run on a regular GPU. Our algorithm predicts gradients with a reduced-precision, inference-style reverse-mode program and combines many predictions with a few exact gradients through a control variate, so approximation error becomes variance rather than bias. On a 124M-parameter language model and selected short training windows, the method can lower simulated ledger cost relative to the tested baselines when fleet work is sufficiently cheap. Experiments spanning 10M-774M parameters show both transfers and failures. We do not test inference-only hardware, end-to-end distributed latency, or a full optimizer-by-batch-size baseline sweep.

cs.LG↗

arXiv2026

Impatient Bandits: Optimizing for the Long-Term Without Delay

Increasingly, recommender systems are tasked with improving users' long-term satisfaction. In this context, we study a content exploration task, which we formalize as a bandit problem with delayed rewards. There is an apparent trade-off in choosing the learning signal: waiting for the full reward to become available might take several weeks, slowing the rate of learning, whereas using short-term proxy rewards reflects the actual long-term goal only imperfectly. First, we develop a predictive model of delayed rewards that incorporates all information obtained to date. Rewards as well as shorter-term surrogate outcomes are combined through a Bayesian filter to obtain a probabilistic belief. Second, we devise a bandit algorithm that quickly learns to identify content aligned with long-term success using this new predictive model. We prove a regret bound for our algorithm that depends on the Value of Progressive Feedback, an information-theoretic metric that captures the quality of short-term leading indicators that are observed prior to the long-term reward. We apply our approach to a podcast recommendation problem, where we seek to recommend shows that users engage with repeatedly over two months. We empirically validate that our approach significantly outperforms methods that optimize for short-term proxies or rely solely on delayed rewards, as demonstrated by an A/B test in a recommendation system that serves hundreds of millions of users.

cs.LG↗

arXiv2026

The Neural Tangent Kernel for Classification

In wide neural networks, the Neural Tangent Kernel (NTK) remains approximately constant during training, providing a powerful theoretical tool for studying training dynamics, generalization, and connections to kernel methods. However, this theory is largely restricted to regression losses. It was previously thought that training on a classification loss, or more generally losses involving nonlinear output transformations, breaks this property, leading to divergent logits and a breakdown of the linearization. In this paper, we extend NTK theory to classification by identifying conditions under which wide neural networks remain in the lazy training regime. We show that parameter-space regularization ensures a constant NTK during training for cross-entropy loss, while in the absence of regularization the regime is recovered when targets are non-degenerate, i.e. when all classes have strictly positive probability. Under these conditions, training is well-approximated by the linearized model, yielding an explicit characterization of the solution in terms of the NTK. We further analyze the distribution of trained predictors induced by random initialization and relate this notion of model uncertainty to Bayesian methods.

cs.LG↗

arXiv2026

Richer Bayesian Last Layers with Subsampled NTK Features

Bayesian Last Layers (BLLs) provide a convenient and computationally efficient way to estimate uncertainty in neural networks. However, they underestimate epistemic uncertainty because they apply a Bayesian treatment only to the final layer, ignoring uncertainty induced by earlier layers. We propose a method that improves BLLs by leveraging a projection of Neural Tangent Kernel (NTK) features onto the space spanned by the last-layer features. This enables posterior inference that accounts for variability of the full network while retaining the low computational cost of inference of a standard BLL. We show that our method yields posterior variances that are provably greater or equal to those of a standard BLL, correcting its tendency to underestimate epistemic uncertainty. To further reduce computational cost, we introduce a uniform subsampling scheme for estimating the projection matrix and for posterior inference. We derive approximation bounds for both types of subsampling. Empirical evaluations on UCI regression, contextual bandits, image classification, and out-of-distribution detection tasks in image and tabular datasets, demonstrate improved calibration and uncertainty estimates compared to standard BLLs and competitive baselines, while reducing computational cost.

cs.LG↗

arXiv2026

Fast Adversarial Attacks with Gradient Prediction

Generating adversarial examples at scale is a core primitive for robustness evaluation, adversarial training, and red-teaming, yet even "fast" attacks such as FGSM remain throughput-limited by the cost of a backward pass. We introduce a family of attacks that eliminates the backward pass by predicting the input gradient from forward-pass hidden states via a lightweight linear regression. The approach is motivated by a kernel view of neural networks and is exact in the Neural Tangent Kernel regime, while remaining effective for practical finite-width models. Empirically, our methods recover much of FGSM's attack performance while using only a small fraction of the time, corresponding to a $532\%$ increase in throughput. These results suggest gradient prediction as a simple and general route to significantly faster adversarial generation under realistic wall-clock constraints.

cs.LG↗

arXiv2026

The Minimax Rate of Second-Order Calibration

We characterize the minimax rate of estimating the second-order calibration error for binary classification, which quantifies whether a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label probability on its level sets. Our key observation is that the sech perturbation kernel, previously used only to enforce smoothness of calibration functions, in fact makes them analytic in a strip of half-width $hπ/2$. Polynomial regression then estimates the calibration error at rate $\tilde{O}(1/\sqrt{n})$, with explicit constants, a qualitative improvement over the $O(n^{-1/4})$ rate achievable by bucketing or kernel smoothing. A matching $Ω(1/\sqrt{n})$ lower bound establishes minimax optimality up to logarithmic factors. As a corollary, we give the first finite-sample guarantee for second-order Platt scaling, yielding a post-hoc procedure that recalibrates both the mean prediction and the epistemic-variance estimate of any higher-order predictor. Along the way, we provide a bucket-free definition of second-order calibration and relate it quantitatively to the bucketed formulation of Ahdritz et al. [2025]. Our experiments confirm the predicted rate and the quality of the recalibrated uncertainties.

cs.LG↗

arXiv2026

A Bayesian Information-Theoretic Approach to Data Attribution

Training Data Attribution (TDA) seeks to trace model predictions back to influential training examples, enhancing interpretability and safety. We formulate TDA as a Bayesian information-theoretic problem: subsets are scored by the information loss they induce - the entropy increase at a query when removed. This criterion credits examples for resolving predictive uncertainty rather than label noise. To scale to modern networks, we approximate information loss using a Gaussian Process surrogate built from tangent features. We show this aligns with classical influence scores for single-example attribution while promoting diversity for subsets. For even larger-scale retrieval, we relax to an information-gain objective and add a variance correction for scalable attribution in vector databases. Experiments show competitive performance on counterfactual sensitivity, ground-truth retrieval and coreset selection, showing that our method scales to modern architectures while bridging principled measures with practice.

cs.LG↗

arXiv2026

A Gaussian Process View on Observation Noise and Initialization in Wide Neural Networks

Performing gradient descent in a wide neural network is equivalent to computing the posterior mean of a Gaussian Process with the Neural Tangent Kernel (NTK-GP), for a specific prior mean and with zero observation noise. However, existing formulations have two limitations: (i) the NTK-GP assumes noiseless targets, leading to misspecification on noisy data; (ii) the equivalence does not extend to arbitrary prior means, which are essential for well-specified models. To address (i), we introduce a regularizer into the training objective, showing its correspondence to incorporating observation noise in the NTK-GP. To address (ii), we propose a \textit{shifted network} that enables arbitrary prior means and allows obtaining the posterior mean with gradient descent on a single network, without ensembling or kernel inversion. We validate our results with experiments across datasets and architectures, showing that this approach removes key obstacles to the practical use of NTK-GP equivalence in applied Gaussian process modeling.

cs.LG↗

arXiv2026

Measuring Uncertainty Calibration

We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation. Second, we provide a method of modifying any classifier so that its calibration error can be upper bounded efficiently without significantly impacting classifier performance and without any restrictive assumptions. All our results are non-asymptotic and distribution-free. We conclude by providing advice on how to measure calibration error in practice. Our methods yield practical procedures that can be run on real-world datasets with modest overhead.

cs.LG↗

arXiv2025

When Embedding Models Meet: Procrustes Bounds and Applications

Embedding models trained separately on similar data often produce representations that encode stable information but are not directly interchangeable. This lack of interoperability raises challenges in several practical applications, such as model retraining, partial model upgrades, and multimodal search. Driven by these challenges, we study when two sets of embeddings can be aligned by an orthogonal transformation. We show that if pairwise dot products are approximately preserved, then there exists an isometry that closely aligns the two sets, and we provide a tight bound on the alignment error. This insight yields a simple alignment recipe, Procrustes post-processing, that makes two embedding models interoperable while preserving the geometry of each embedding space. Empirically, we demonstrate its effectiveness in three applications: maintaining compatibility across retrainings, combining different models for text retrieval, and improving mixed-modality search, where it achieves state-of-the-art performance.

cs.LG↗

arXiv2025

Hallucination Detection on a Budget: Efficient Bayesian Estimation of Semantic Entropy

Detecting whether an LLM hallucinates is an important research challenge. One promising way of doing so is to estimate the semantic entropy (Farquhar et al., 2024) of the distribution of generated sequences. We propose a new algorithm for doing that, with two main advantages. First, due to us taking the Bayesian approach, we achieve a much better quality of semantic entropy estimates for a given budget of samples from the LLM. Second, we are able to tune the number of samples adaptively so that `harder' contexts receive more samples. We demonstrate empirically that our approach systematically beats the baselines, requiring only 53% of samples used by Farquhar et al. (2024) to achieve the same quality of hallucination detection as measured by AUROC. Moreover, quite counterintuitively, our estimator is useful even with just one sample from the LLM.

cs.LG↗

arXiv2024

Epistemic Uncertainty and Observation Noise with the Neural Tangent Kernel

Recent work has shown that training wide neural networks with gradient descent is formally equivalent to computing the mean of the posterior distribution in a Gaussian Process (GP) with the Neural Tangent Kernel (NTK) as the prior covariance and zero aleatoric noise \parencite{jacot2018neural}. In this paper, we extend this framework in two ways. First, we show how to deal with non-zero aleatoric noise. Second, we derive an estimator for the posterior covariance, giving us a handle on epistemic uncertainty. Our proposed approach integrates seamlessly with standard training pipelines, as it involves training a small number of additional predictors using gradient descent on a mean squared error loss. We demonstrate the proof-of-concept of our method through empirical evaluation on synthetic regression.

cs.LG↗

arXiv2024

On the Importance of Uncertainty in Decision-Making with Large Language Models

We investigate the role of uncertainty in decision-making problems with natural language as input. For such tasks, using Large Language Models as agents has become the norm. However, none of the recent approaches employ any additional phase for estimating the uncertainty the agent has about the world during the decision-making task. We focus on a fundamental decision-making framework with natural language as input, which is the one of contextual bandits, where the context information consists of text. As a representative of the approaches with no uncertainty estimation, we consider an LLM bandit with a greedy policy, which picks the action corresponding to the largest predicted reward. We compare this baseline to LLM bandits that make active use of uncertainty estimation by integrating the uncertainty in a Thompson Sampling policy. We employ different techniques for uncertainty estimation, such as Laplace Approximation, Dropout, and Epinets. We empirically show on real-world data that the greedy policy performs worse than the Thompson Sampling policies. These findings suggest that, while overlooked in the LLM literature, uncertainty plays a fundamental role in bandit tasks with LLMs.

cs.LG↗

arXiv2023

Automatic Music Playlist Generation via Simulation-based Reinforcement Learning

Personalization of playlists is a common feature in music streaming services, but conventional techniques, such as collaborative filtering, rely on explicit assumptions regarding content quality to learn how to make recommendations. Such assumptions often result in misalignment between offline model objectives and online user satisfaction metrics. In this paper, we present a reinforcement learning framework that solves for such limitations by directly optimizing for user satisfaction metrics via the use of a simulated playlist-generation environment. Using this simulator we develop and train a modified Deep Q-Network, the action head DQN (AH-DQN), in a manner that addresses the challenges imposed by the large state and action space of our RL formulation. The resulting policy is capable of making recommendations from large and dynamic sets of candidate items with the expectation of maximizing consumption metrics. We analyze and evaluate agents offline via simulations that use environment models trained on both public and proprietary streaming datasets. We show how these agents lead to better user-satisfaction metrics compared to baseline methods during online A/B tests. Finally, we demonstrate that performance assessments produced from our simulator are strongly correlated with observed online metric results.

stat.ML↗

arXiv2023

Impatient Bandits: Optimizing Recommendations for the Long-Term Without Delay

Recommender systems are a ubiquitous feature of online platforms. Increasingly, they are explicitly tasked with increasing users' long-term satisfaction. In this context, we study a content exploration task, which we formalize as a multi-armed bandit problem with delayed rewards. We observe that there is an apparent trade-off in choosing the learning signal: Waiting for the full reward to become available might take several weeks, hurting the rate at which learning happens, whereas measuring short-term proxy rewards reflects the actual long-term goal only imperfectly. We address this challenge in two steps. First, we develop a predictive model of delayed rewards that incorporates all information obtained to date. Full observations as well as partial (short or medium-term) outcomes are combined through a Bayesian filter to obtain a probabilistic belief. Second, we devise a bandit algorithm that takes advantage of this new predictive model. The algorithm quickly learns to identify content aligned with long-term success by carefully balancing exploration and exploitation. We apply our approach to a podcast recommendation problem, where we seek to identify shows that users engage with repeatedly over two months. We empirically validate that our approach results in substantially better performance compared to approaches that either optimize for short-term proxies, or wait for the long-term outcome to be fully realized.

cs.LG↗

arXiv2023

A Strong Baseline for Batch Imitation Learning

Imitation of expert behaviour is a highly desirable and safe approach to the problem of sequential decision making. We provide an easy-to-implement, novel algorithm for imitation learning under a strict data paradigm, in which the agent must learn solely from data collected a priori. This paradigm allows our algorithm to be used for environments in which safety or cost are of critical concern. Our algorithm requires no additional hyper-parameter tuning beyond any standard batch reinforcement learning (RL) algorithm, making it an ideal baseline for such data-strict regimes. Furthermore, we provide formal sample complexity guarantees for the algorithm in finite Markov Decision Problems. In doing so, we formally demonstrate an unproven claim from Kearns & Singh (1998). On the empirical side, our contribution is twofold. First, we develop a practical, robust and principled evaluation protocol for offline RL methods, making use of only the dataset provided for model selection. This stands in contrast to the vast majority of previous works in offline RL, which tune hyperparameters on the evaluation environment, limiting the practical applicability when deployed in new, cost-critical environments. As such, we establish precedent for the development and fair evaluation of offline RL algorithms. Second, we evaluate our own algorithm on challenging continuous control benchmarks, demonstrating its practical applicability and competitiveness with state-of-the-art performance, despite being a simpler algorithm.

cs.LG↗

arXiv2022

Deep Interactive Bayesian Reinforcement Learning via Meta-Learning

Agents that interact with other agents often do not know a priori what the other agents' strategies are, but have to maximise their own online return while interacting with and learning about others. The optimal adaptive behaviour under uncertainty over the other agents' strategies w.r.t. some prior can in principle be computed using the Interactive Bayesian Reinforcement Learning framework. Unfortunately, doing so is intractable in most settings, and existing approximation methods are restricted to small tasks. To overcome this, we propose to meta-learn approximate belief inference and Bayes-optimal behaviour for a given prior. To model beliefs over other agents, we combine sequential and hierarchical Variational Auto-Encoders, and meta-train this inference model alongside the policy. We show empirically that our approach outperforms existing methods that use a model-free approach, sample from the approximate posterior, maintain memory-free models of others, or do not fully utilise the known structure of the environment.

cs.LG↗

arXiv2022

Imitation Learning by Reinforcement Learning

Imitation learning algorithms learn a policy from demonstrations of expert behavior. We show that, for deterministic experts, imitation learning can be done by reduction to reinforcement learning with a stationary reward. Our theoretical analysis both certifies the recovery of expert reward and bounds the total variation distance between the expert and the imitation learner, showing a link to adversarial imitation learning. We conduct experiments which confirm that our reduction works well in practice for continuous control tasks.

stat.ML↗