A Finite Sample Analysis for Quantile Temporal Difference Learning in Distributional Reinforcement Learning

We establish a global finite-sample guarantee for synchronous quantile temporal-difference learning (QTD) in tabular distributional reinforcement learning. The proof separates two stability mechanisms. A global comparison argument, based on the order monotonicity of reward cumulative distribution functions and the W_contraction of the distributional Bellman operator, brings an arbitrarily initialized iterate into a local neighborhood. Inside that neighborhood, we linearize the QTD mean field. Its Jacobian is a nonsingular M-matrix, and the associated positive semigroup permits a variance-sensitive martingale analysis. For stepsizes α_t=c(t+1)^{-a} with a(1/2,1), the leading last-iterate fluctuation is of order O(T^{-a/2}/{1-γ}) and has no polynomial dependence on the number of quantiles. The deterministic transient and the required burn-in can still depend on the smallest Bellman-target density, which is of order m^{-1} in the worst case. The result therefore distinguishes sharply between the local stochastic fluctuation and the global sample complexity.

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Elucidating the Design Space of LM Data Attribution↗

Data attribution methods for Language Models (LMs) are typically evaluated using downstream tasks like fact retrieval. However, existing evaluations vary multiple dataset properties simultaneously, making it impossible to isolate exactly why an attribution algorithm fails. To diagnose these failures, we explore the design space of LLM data attribution, with a primary focus on evaluation. We introduce the Controlled Attribution Benchmark (CATT) for fact tracing, in which we fine-tune LLMs on entirely fictitious knowledge, providing unambiguous ground truth for attribution. This synthetic setup allows us to systematically alter one dataset configuration at a time, such as document redundancy and lexical distractors. With this configurable evaluation, we demonstrate that redundancy and distractors consistently degrade attribution performance. Rather than proposing a new estimator, we examine two design choices that are underexplored: the loss used to compute gradients and how per-token attribution scores are aggregated into a document score. We find that the true causal evidence within a training document is highly localized, but standard methods dilute this evidence into noise by averaging attribution scores across the entire document. We find that replacing standard cross-entropy loss gradients with the negative log-odds gradients surfaces the critical tokens from other uninformative ones. We can then aggregate only the top token scores to improve ground truth recall by 35 to 72 percentage points across multiple baselines on our diagnostic benchmark. The negative log-odds correction also generalizes to FTRACE-TREX, improving counterfactual retraining performance for every method we test, by up to 4.9x.

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arXiv AI Papers·anteontem☆

Propose-Filter-Release: Scaling Noise to Typical Sensitivity via Private Filtering↗

An estimator can be accurate and stable on typical data, yet sensitive to a few possible records. Differentially private mechanisms commonly scale their noise to the worst-case influence of a single record, which lets these records dictate the noise even when the remaining data would allow far less. Removing them first would restore the smaller scale, but the removal must itself be private. We introduce propose-filter-release (PFR), which, by privately filtering its input, turns a mechanism that protects the addition or removal of a typical record, one that fits the remaining data, into one that is differentially private in the standard sense, on every input. Using our novel filtering step, PFR requires only a concave friendliness score, which measures how well a record fits a dataset, and a release mechanism that is friendly-DP, that is, private when the changed record fits the remaining data. For every such score and release mechanism, it guarantees differential privacy under public conditions on the number of records, so it is a general privacy primitive, comparable to propose-test-release, and FriendlyCore can be viewed as one of its implementations. We illustrate the generality of PFR by instantiating it for scalar statistics, principal subspace estimation, the KL divergence of user histograms, the effective resistances of a graph, and treatment-rule selection.

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arXiv AI Papers·anteontem☆

Rethinking Neural Thickets Without Weight Perturbations↗

The Neural Thickets hypothesis posits that pretrained language models lie in dense neighborhoods of task-specific experts in weight space, which random Gaussian perturbations can uncover. We reproduce the reported gains, but show that they do not require this geometric explanation. Perturbing a single decoder block already recovers much of the improvement, while keeping the model entirely frozen and adding a random bias to its output logits matches or exceeds full-weight perturbations on most reasoning tasks. This suggests an alternative explanation based on output diversity, validation-based selection, and voting. We formalize this view as Perturb-Select-Vote (PSV), a general procedure that generates perturbed predictors, selects high-performing members on a small validation set, and aggregates their predictions. This interpretation connects Neural Thickets to established inference-time methods, including sampling, self-consistency, and verifier-guided selection. A first-order analysis further shows that small weight perturbations act primarily through their induced logit shifts. We extend this analysis to vision, where logit PSV substantially improves performance under domain shift, including on Earth observation, while full-weight perturbations provide little additional benefit. Together, these results suggest that the gains attributed to nearby weight-space experts can instead be obtained through output diversity, selection, and voting. Logit PSV realizes these benefits with a fully frozen model, providing a simple, training-free alternative to full-weight perturbation ensembles across language and vision.

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arXiv AI Papers·anteontem☆

Read, Allocate, Route: Role-Coupled Tokenization for Pixel-Space Generative Transformers↗

Pixel-space generative Transformers typically use one token per image patch, so capturing finer detail requires more tokens and makes global attention increasingly expensive. We observe that finer detail does not necessarily require more global communication: low-frequency structure benefits from global exchange, while high-frequency detail can be modeled locally. Based on this insight, we introduce SpecSlot, a pixel-space rectified-flow Transformer that decouples output detail from the length of the global attention sequence. SpecSlot expands each spatial anchor into multiple slots, each assigned a disjoint band of DCT coefficients; this separates anchor density from spectral subdivision. Only the lowest-frequency slot from each anchor participates in global attention, while all slots interact locally. This allows the model to increase spectral detail without enlarging the global sequence. A spatial head further adds a local correction to the spectral prediction, while the generative state, target, and loss remain in pixel space. On ImageNet-256, SpecSlot achieves a comparable final FID to a FLOPs-matched JiT control while converging faster. On ImageNet-512, it improves FID by 2.84 over the control with 3.9% fewer FLOPs, and comes within only 0.69 FID of JiT-B/16 at 38.2% lower cost. On text-to-image generation, SpecSlot surpasses JiT-B/8 on DPG-Bench by 1.06 at 40.6% lower forward cost.

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