Deep temporal architectures such as TCNs achieve strong predictive performance on sequential data, yet theoretical understanding of their generalization remains limited. We address this gap through three contributions: introducing an evaluation methodology for temporal models, revealing surprising empirical phenomena about temporal dependence, and the first architecture-aware theoretical framework for dependent sequences. Fair-Comparison Methodology. We introduce evaluation protocols that fix effective sample size $N_{\text{eff}}$ to isolate temporal structure effects from information content. Empirical Findings. Applying this method reveals that under $N_{\text{eff}} = 2000$, strongly dependent sequences ($ρ= 0.8$) exhibit approx' $76\%$ smaller generalization gaps than weakly dependent ones ($ρ= 0.2$), challenging the conventional view that dependence universally impedes learning. However, observed convergence rates ($N_{\text{eff}}^{-1.21}$ to $N_{\text{eff}}^{-0.89}$) significantly exceed theoretical worst-case predictions ($N^{-0.5}$), revealing that temporal architectures exploit problem structure in ways current theory does not capture. Lastly, we develop the first architecture-aware generalization bounds for deep temporal models on exponentially $β$-mixing sequences. By embedding Golowich et al.'s i.i.d. class bound within a novel blocking scheme that partitions $N$ samples into approx' $B \approx N/\log N$ quasi-independent blocks, we establish polynomial sample complexity under convex Lipschitz losses. The framework achieves $\sqrt{D}$ depth scaling alongside the product of layer-wise norms $R = \prod_{\ell=1}^{D} M^{(\ell)}$, avoiding exponential dependence. While these bounds are conservative, they prove learnability and identify architectural scaling laws, providing worst-case baselines that highlight where future theory must improve.

Differential privacy is increasingly formalized through the lens of hypothesis testing via the robust and interpretable $f$-DP framework, where privacy guarantees are encoded by a baseline Blackwell trade-off function $f_{\infty} = T(P_{\infty}, Q_{\infty})$ involving a pair of distributions $(P_{\infty}, Q_{\infty})$. The problem of choosing the right privacy metric in practice leads to a central question: what is a statistically appropriate baseline $f_{\infty}$ given some prior modeling assumptions? The special case of Gaussian differential privacy (GDP) showed that, under compositions of nearly perfect mechanisms, these trade-off functions exhibit a central limit behavior with a Gaussian limit experiment. Inspired by Le Cam's theory of limits of statistical experiments, we answer this question in full generality in an infinitely divisible setting. We show that suitable composition experiments $(P_n^{\otimes n}, Q_n^{\otimes n})$ converge to a binary limit experiment $(P_{\infty}, Q_{\infty})$ whose log-likelihood ratio $L = \log(dQ_{\infty} / dP_{\infty})$ is infinitely divisible under $P_{\infty}$. Thus any limiting trade-off function $f_{\infty}$ is determined by an infinitely divisible law $P_{\infty}$, characterized by its Levy--Khintchine triplet, and its Esscher tilt defined by $dQ_{\infty}(x) = e^{x} dP_{\infty}(x)$. This characterizes all limiting baseline trade-off functions $f_{\infty}$ arising from compositions of nearly perfect differentially private mechanisms. Our framework recovers GDP as the purely Gaussian case and yields explicit non-Gaussian limits, including Poisson examples. It also positively resolves the empirical $s^2 = 2k$ phenomenon observed in the GDP paper and provides an optimal mechanism for count statistics achieving asymmetric Poisson differential privacy.

In particular: 1. both memory and computation overheads are only linear in the dimension 2.

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(See Figure 1).

Sampling and learning these symmetric DPP's is pretty well understood. In this work, we consider a new class of DPP's, which we call signed DPP's, where we break the symmetry and allow attractive behaviors.

Neural Information Processing Systems http://nips.cc/

Surprisingly we show that volume sampling can have poor behavior when we require a very accurate approximation - indeed worse than some i.i.d.

While the original algorithm was slow, efficient implementations have been provided since then (e.g., see

Matrix sketching is a powerful tool for reducing the size of large data matrices.