Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Private Continual Counting of Unbounded Streams
Authors: Ben Jacobsen, Kassem Fawaz
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirically, we find that our algorithm s performance is also comparable to theirs in absolute terms: our variance is less than 1.5 theirs for t as large as 224. In this section, we investigate various practical considerations in the implementation of Algorithm 1. We plot relative error as a function of t, δ and K in Figure 1. Our results are visualized in Figure 2. |
| Researcher Affiliation | Academia | Ben Jacobsen Department of Computer Sciences University of Wisconsin Madison EMAIL Kassem Fawaz Department of Electrical and Computer Engineering University of Wisconsin Madison EMAIL |
| Pseudocode | Yes | Algorithm 1 Logarithmic Matrix Method Require: Matrix parameters γ < 1/2 and δ, privacy parameter Cε,δ Compute LTToep(f(z; γ, δ) 1 2 See Bounded Sensitivity in section 4 for t = 1, . . . , n do Receive input xt [0, 1] Set St Pt i=1 xt if t = 2m for some integer m then Sample zs N(0, C2 ε,δ 2) for t s 2t 1 Compute next t coefficients of L = LTToep(f(z; γ, δ)) in O(t log t) time See Computability in section 4 Compute next t terms of the sequence Lz in O(t log t) time with an FFT Output St + (Lz)t |
| Open Source Code | Yes | We have released our code as open-source software, including scripts to reproduce all figures in the paper. It is available at https://github.com/ben-jacobsen/centraldpolo/ |
| Open Datasets | No | The paper does not mention the use of any specific publicly available datasets. The experiments conducted are theoretical comparisons of variance and error rates of algorithms. |
| Dataset Splits | No | The paper does not use specific datasets for experiments, focusing instead on theoretical comparisons of algorithm performance metrics like variance and error rates. Therefore, no dataset splits are mentioned. |
| Hardware Specification | Yes | There are no special computational resources required to reproduce our experiments. All of them were carried out in python using a single commercial CPU in a few seconds or minutes. |
| Software Dependencies | No | We use mpmath [31] for this purpose in our experiments, which supports arbitrary-precision floating point computations and numerical integration. [31] Fredrik Johansson, Vinzent Steinberg, Sergey B Kirpichev, Kristopher L Kuhlman, Aaron Meurer, Ondˇrej ˇCertík, Case Van Horsen, Paul Masson, Juan Arias De Reyna, Timo Hartmann, et al. mpmath: a python library for arbitrary-precision floating-point arithmetic. Zenodo, 2013. |
| Experiment Setup | Yes | Choosing the value of α. While it is in principle possible to set α arbitrarily small, this would be unwise. [...] We conclude that setting α = 0.01 is likely a safe and practical choice for most applications. Choosing the value of δ. There are three natural choices for setting the value of δ, representing different tradeoffs in speed and accuracy. Setting δ = 0 is the fastest option computationally, but leads to a sub-optimal rate of growth in error. Choosing δ = γ is roughly 1.5 slower, but substantially improves error when n is greater than 1,000 or so. Finally, the special value δ = 6γ/5 is notable because it causes the first two Taylor coefficients of both f L and f R to match the function (1 z) 1/2 exactly. |