humancompatible.interconnect: Testing Properties of Repeated Uses of Interconnections of AI Systems

Anthony Quinn; Jakub Marecek; Robert Shorten; Rodion Nazarov

REVIEW 2 major objections 5 minor 40 references

humancompatible.interconnect: Testing Properties of Repeated Uses of Interconnections of AI Systems

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Repeated uses of interconnected AI systems can be certified for fairness and robustness by checking a single contraction-on-average condition, and the paper packages that check in a PyTorch toolkit called interconnect.

desk verdict A useful PyTorch toolkit for estimating contraction-on-average in closed-loop AI models, but the paper overstates the guarantees by calling a finite-sample heuristic an 'a priori' certificate. read the letter →

arxiv 2507.09626 v1 pith:BFMEHEBD submitted 2025-07-13 cs.AI cs.SYeess.SY

Rodion Nazarov , Anthony Quinn , Robert Shorten , Jakub Marecek This is my paper · ORCID

classification cs.AIcs.SYeess.SY MSC 60J0593E1568T01

keywords fairnessguaranteesrobustnessergodicitycontractiononaverageiteratedfunctionsystemsmulti-agentclosed-loopAIPyTorchtoolkit

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to make fairness and robustness guarantees for repeated uses of AI systems computable in practice. Its move is to model the AI system and the agents it interacts with as one closed stochastic loop, then certify the loop with a single number: the contraction-on-average factor C of the joint state transition. If C is below 1, the loop is ergodic, meaning long-run averages of agent outcomes exist regardless of initial conditions; those averages are exactly what equal-impact fairness is about. The paper packages this in an open-source PyTorch toolkit that builds the loop as a computational graph and estimates C with a few function calls, which removes the burden of proving ergodicity by hand.

What carries the argument

The central object is the stochastic difference inclusion x(k+1) in {F_m(x(k)): m in M}, with maps F_m sampled according to probabilities p_m, where each F_m describes one joint transition of agents, controller, filter, and delay. The load-bearing test is condition (12): the sum over m of p_m times the ratio of state separation after one transition to separation before the transition must be less than a constant C strictly below 1, for every pair of states. The toolkit's get_factor_from_list() function estimates this factor from a user-supplied list of reference signals and agent probabilities by simulation, and if the estimated C is below 1, ergodicity—and hence existence of the long-run averages behind equal impact—follows from the theory of iterated function systems.

What would settle it

Take a deliberately non-ergodic loop, such as two disconnected dynamics with alternating probabilities that violate condition (12), and run get_factor_from_list() on a coarse grid of reference signals; if it reports C below 1 even though the true supremum is at least 1, the finite-sample check has produced a false certificate. A reader could also search for two states x and xhat on the grid whose empirical ratio sum is at least 1 while the reported C is below 1, which would expose an inconsistency in the estimator.

Watch

Extended reading notes

Core claim

The paper's central claim is that a stochastic closed-loop model of AI systems with agents—where each agent's state evolves through finitely many maps chosen with probabilities conditioned on the AI system's output—can be tested for robustness and fairness by checking whether the stochastic difference inclusion satisfies contraction on average: the expected ratio of state separation after one transition to separation before the transition must be bounded by a constant C below 1 uniformly over all state pairs. If this holds, the Markov chain has a unique invariant measure and the long-run averages in Definition 2 exist; those averages are what equal-impact fairness is defined on. The paper contributes a PyTorch toolkit, interconnect, that lets a user assemble such loops as computational graphs and calls get_factor_from_list() to estimate C and kernel density estimates of output distributions, turning a regulator's a priori fairness requirement into a concrete numerical check.

Load-bearing premise

The certificate is only as good as the finite simulation grid: get_factor_from_list() estimates the maximum over all state pairs from a finite set of reference signals and agent probabilities, and the paper gives no bound on how far that estimate can fall below the true worst case.

Editorial extensions

If this is right

If contraction on average holds for a specified loop, the Markov chain has a unique invariant measure, so the long-run averages in Definition 2 exist and are independent of initial conditions.
Regulators can demand such a check before deployment: the loop's designer supplies the PyTorch graph and a reported C below 1 as an a priori guarantee of equal impact.
The finite-state stochastic-pointer model covers discrete agent actions such as credit approved or denied, so non-Lipschitz classification maps do not block the ergodicity check.
For cascaded interconnections such as two-sided markets, the user assembles the components and the same get_factor_from_list() call certifies the composite loop, not just its parts.
The toolkit also estimates output-signal distributions by kernel density estimation, so the a priori guarantee is accompanied by a view of what the long-run behaviour looks like.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial extension: because condition (12) is sufficient for ergodicity but not necessary, a loop that fails the C below 1 test is not proven unfair; the tool is an a priori certifier for loops that pass, not a verdict on loops that fail.
Editorial extension: the same contraction-on-average estimate could be used as a gradient signal, since the loop is a PyTorch graph; one could in principle differentiate through the simulated factor and tune controller or agent parameters toward smaller C, turning certification into design.
Editorial extension: the guarantee concerns existence of long-run averages, not their rate of convergence, so two certified loops with the same C can still differ greatly in how many interactions regulators must observe before equal-impact averages are approached.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is the interconnect toolkit itself: a PyTorch implementation that lets you specify an interconnection of AI systems and agents as a computational graph and estimate the contraction-on-average factor C from Eq. (12). The underlying theory—Hairer's ergodic results and contraction-on-average conditions—is prior work by this group and others, so this is an engineering contribution, not a theoretical breakthrough. That is fine, and the toolkit does something useful: it gives practitioners a way to check a nontrivial ergodicity condition that is a real prerequisite for long-run fairness arguments. The closed-loop framing of equal treatment versus equal impact is also a helpful way to think about fairness in repeated interactions.

What the paper does well is package a somewhat exotic piece of stochastic control into a working tool, with code snippets and a worked example that suggest the authors actually built it. The text is honest about some limitations in Section 5, noting that bounded-error scalability is not available. That candor makes the overclaim in the abstract and Section 4 more frustrating: the paper consistently says "a priori guarantees," but what get_factor_from_list() actually returns is a stochastic approximation of C from a finite set of reference signals and trials (it=200, trials=500). No confidence interval, no PAC bound, no worst-case error is provided, even for the convex hull of the sampled points. Equation (12) is a universal condition over all state pairs; a finite simulation cannot rule out an unsampled pair where the ratio exceeds 1. So the output is a heuristic indicator, not a certificate, and the existence of long-run averages in Definition 2 does not follow from the tool's output.

A second soft spot is reproducibility: there is no repository URL, commit hash, or direct link to the code. The paper says "accessible via humancompatible.org," which is not verifiable from the text. For an engineering paper whose main contribution is an artifact, that is a significant omission.

These issues are real but fixable. The theory is credible, the toolkit is plausibly useful, and the limitations section shows the authors know where the edges are. The paper just needs to align its language with what the tool actually does: finite-sample estimates, not a priori certificates.

Recommendation: worth a serious referee, but the authors should be asked to soften the guarantee language, add error bars or a clear disclaimer, and provide a working link to the code. I would bring this to a reading group for the toolkit's practical angle, but I would not cite it in my own work as it stands.

Referee Report

2 major / 5 minor

Summary. The paper presents interconnect, an open-source PyTorch toolkit for modeling interconnections of AI systems and agents as closed-loop stochastic systems, and for testing properties of their repeated uses. The main theoretical premise is that fairness notions such as equal impact (Definition 2) require existence of long-run averages, which follows from ergodicity of the closed-loop system. The toolkit claims to provide a priori guarantees of robustness and fairness by checking a contraction-on-average condition (Eq. (12)) via the function get_factor_from_list(), which estimates the contraction factor C from finite simulations, and by approximating output distributions via kernel density estimation. The paper includes an example closed-loop system with ReLU controllers and two agent populations, together with code snippets and generated plots.

Significance. If the claimed a priori guarantees could be made rigorous, the toolkit would fill a useful gap: it connects stochastic control theory (iterated function systems, contraction-on-average) with practical verification of fairness and robustness in multi-agent AI systems, and it is implemented as an open-source PyTorch library with a non-trivial worked example. The theoretical foundations are drawn from published literature, and the paper is honest in Section 5 about scalability limitations. However, the central computational step—estimating C from finitely many simulations—currently produces only a heuristic indicator, not a formal certificate, and this undermines the paper's stated a priori-guarantee claim. The underlying theory is sound, and the gap is in principle addressable by either adding confidence intervals or PAC-style bounds, or by explicitly repositioning the toolkit as a heuristic screening tool. The paper is therefore of interest but requires substantial clarification or strengthening before its main claim can be accepted.

major comments (2)

[Section 4, Eq. (12) and Figure 3] The central claim is that get_factor_from_list() provides a check of the contraction-on-average condition (12), which must hold for all state pairs x and xhat in X. The function, however, computes a stochastic approximation of C from a finite set of reference signals and agent probabilities (it=200, trials=500 in Figure 3), with no confidence interval, worst-case bound, or PAC certificate. An output C<1 therefore does not rule out the existence of an unsampled pair (x,xhat) for which the left-hand side of (12) exceeds C or exceeds 1. The paper's own Section 5 acknowledges that the error of the envisioned estimation methods 'has not been bounded a priori.' As written, the tool does not deliver the a priori guarantees promised in the abstract and in Section 4; it delivers a heuristic estimate of the contraction factor. This is a load-bearing gap between the universal condition and the implemented finite-sample check.
[Section 4 and Definition 2] The paper asserts that satisfying the contraction-on-average condition guarantees the existence of the long-run averages in Definition 2 (equal impact), but the main text does not state the precise theorem or the additional regularity conditions (e.g., Lipschitz continuity, boundedness away from 0 and 1, strong connectivity, primitivity of the adjacency matrix) that are required for the theorem to apply. The connection is made only by citing prior work [9,36,37,30,38]. For a toolkit whose goal is to certify a priori guarantees, the user-facing claim should state these conditions explicitly so that a user can know whether the theorem applies to a given model. At minimum, the paper should state the theorem in a form directly applicable to Eq. (12) and Definition 3.

minor comments (5)

[Section 4] Immediately after Eq. (12), the phrase 'if there there exists a constant' contains a duplicated word; it should read 'if there exists a constant'.
[Section 3.2] The word 'hierachi-cally' in Section 3.2 appears to be a typo for 'hierarchically'.
[References] References [10] and [30] cite the same Automatica paper, and references [11] and [37] cite the same Automatica paper; duplicate entries should be consolidated or cross-referenced to avoid confusion.
[Figures 4 and 5] Figures 4 and 5 lack axis labels and captions explaining what is plotted; adding these would substantially improve reproducibility and interpretability.
[Introduction] The introduction mentions 'some appropriate degree of statistical certainty' and PAC variants of the definitions, but the toolkit does not expose any way for a user to specify or verify such a certainty level; a brief note on how (or whether) this is supported would help align the text with the available functionality.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the toolkit's ergodicity guarantees are inherited from external iterated-function-system theorems, not redefined by construction.

full rationale

The derivation chain runs from Definition 2 (equal impact) to Definition 3 (robustness in the ergodic sense) to the contraction-on-average condition (12), which is a standard sufficient condition from iterated function systems, cited to Elton, Barnsley et al., Diaconis and Freedman, and Hairer et al., as well as to earlier work by the same group. These are external theorems with stated assumptions; the paper does not define equal impact in terms of the toolkit's get_factor_from_list() output, nor does it fit a parameter on a subset of data and then relabel that fit as a prediction. The get_factor_from_list() function in Figure 3 is presented as a stochastic approximation of C, and Section 5 explicitly concedes that for some scalable methods 'error has not been bounded a priori'; that is an acknowledged verification gap between a finite-sample estimate and the universal condition (12), not a circular definitional loop. The self-citations to [9,10,11,30,37,38] are load-bearing in the sense that they supply the theorems used, but these are prior peer-reviewed results invoked as evidence, not unverified claims manufactured within this paper. No step in the paper reduces to its own inputs by construction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on previously established ergodic theory and a modeling assumption about agent behavior. No new entities are postulated. The only tuned numerical quantity in the reported workflow is the KDE bandwidth h. The main burden is not circularity but the gap between a stochastic estimate of C and an a priori guarantee.

free parameters (1)

KDE bandwidth h = not stated (manually set)
Equation (19) defines the KDE estimate and the text says h is manually set in the toolkit; it affects the approximated output distributions but not the contraction check.

assumptions (4)

standard math Contractivity on average (12) implies existence of a unique invariant measure for the closed-loop Markov chain.
Invoked throughout Section 4 and Section 3.2; the toolkit treats this as a sufficient condition for ergodicity, citing [5,12,28,29].
domain assumption Conditional stochastic independence of the agents' response probabilities given the AI output is a sufficient condition for fairness.
Adopted in Section 2, final bullet; used to connect fairness definitions to the ergodic analysis.
domain assumption The graph G=(X,E) built from finite state transition maps is strongly connected and its adjacency matrix primitive, ensuring an attractive invariant measure.
Section 3.2 states this and uses it to conclude unique ergodicity.
domain assumption The AI system observes only filtered aggregate actions, not individual agent states.
Section 2, third bullet; this restricts applicability to the closed-loop model treated.

how reviews work

0 comments

Cite this review

Pith. "Pith review of humancompatible.interconnect: Testing Properties of Repeated Uses of Interconnections of AI Systems." pith.science (2026). https://pith.science/paper/BFMEHEBD

@misc{pith2026250709626,
  author       = {Pith},
  title        = {Pith review of: humancompatible.interconnect: Testing Properties of Repeated Uses of Interconnections of AI Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BFMEHEBD}},
  note         = {Machine review of arXiv:2507.09626}
}

read the original abstract

Artificial intelligence (AI) systems often interact with multiple agents. The regulation of such AI systems often requires that {\em a priori\/} guarantees of fairness and robustness be satisfied. With stochastic models of agents' responses to the outputs of AI systems, such {\em a priori\/} guarantees require non-trivial reasoning about the corresponding stochastic systems. Here, we present an open-source PyTorch-based toolkit for the use of stochastic control techniques in modelling interconnections of AI systems and properties of their repeated uses. It models robustness and fairness desiderata in a closed-loop fashion, and provides {\em a priori\/} guarantees for these interconnections. The PyTorch-based toolkit removes much of the complexity associated with the provision of fairness guarantees for closed-loop models of multi-agent systems.

Figures

Figures reproduced from arXiv: 2507.09626 by the authors.

**Figure 2.** A closed-loop model of an interconnection of two AI systems in a [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** An example of computing the contraction-on-average factor, [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Plots generated during testing with different combinations of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Plots of the estimated distributions of the model state after 100 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Specifying one element of the closed loop. [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: Specifying a filter in our interconnect. [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

**Figure 8.** Figure 8: Response functions of the two types of agents. [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

**Figure 9.** Figure 9: An example specification of a closed loop corresponding to model of [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]

**Figure 10.** Figure 10: A visual representation of the interconnection captured in Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

**Figure 11.** Figure 11: A visual representation of the interconnection captured in Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references · 38 canonical work pages

[1]

1689, no

European Commission, “Regulation (EU) 2024/1689 of the European par- liament and of the Council of 13 June 2024 laying down harmonised rules on artificial intelligence and amending regulations (EC) no 300/2008, (EU) no 167/2013, (EU) no 168/2013, (EU) 2018/858, (EU) 2018/1139 and (EU) 2019/2144 and directives 2014/90/EU, (EU) 2016/797 and (EU) 2020/1828 (...

work page 2024
[2]

Closed-loop view of the regulation of ai: Equal impact across repeated interactions,

Q. Zhou, R. Ghosh, R. Shorten, and J. Mareček, “Closed-loop view of the regulation of ai: Equal impact across repeated interactions,” in2024 IEEE 40th International Conference on Data Engineering Workshops (ICDEW), pp. 176–181, 2024

work page 2024
[3]

H. 88th Congress (1963-1964), “To enforce the constitutional right to vote, to confer jurisdiction upon the district courts of the united states to provide injunctive relief against discrimination in public accommodations, to autho- rize the attorney general to institute suits to protect constitutional rights in public facilities and public education, to ...

work page 1963
[4]

Title vi legal manual (updated),

C. R. D. of U.S. Department of Justice, “Title vi legal manual (updated),” Federal Coordination and Compliance Section, 2021. Section VII- Proving Discrimination- Disparate Impact

work page 2021
[5]

Asymptotic coupling and a general form of harris’ theorem with applications to stochastic delay equations,

M. Hairer, J. C. Mattingly, and M. Scheutzow, “Asymptotic coupling and a general form of harris’ theorem with applications to stochastic delay equations,” Probability theory and related fields, vol. 149, no. 1-2, pp. 223– 259, 2011

work page 2011
[6]

The complexity of Markov decision processes,

C. H. Papadimitriou and J. N. Tsitsiklis, “The complexity of Markov decision processes,” Mathematics of operations research, vol. 12, no. 3, pp. 441–450, 1987

work page 1987
[7]

PSPACE-completeness of modular supervisory control problems,

K. Rohloff and S. Lafortune, “PSPACE-completeness of modular supervisory control problems,”Discrete Event Dynamic Systems, vol. 15, pp. 145–167, 2005

work page 2005
[8]

On the undecidability of proba- bilistic planning and related stochastic optimization problems,

O. Madani, S. Hanks, and A. Condon, “On the undecidability of proba- bilistic planning and related stochastic optimization problems,”Artificial Intelligence, vol. 147, no. 1-2, pp. 5–34, 2003

work page 2003

Show all 40 references

[9]

On the ergodic control of ensembles,

A. R. Fioravanti, J. Marecek, R. N. Shorten, M. Souza, and F. Wirth, “On the ergodic control of ensembles,”Automatica, vol. 108, p. 108483, 2019

2019
[12]

Iterated piecewise-stationary ran- dom functions,

R. Ghosh, J. Marecek, and R. Shorten, “Iterated piecewise-stationary ran- dom functions,” arXiv preprint arXiv:1909.10093, 2019

1909 arXiv
[13]

K. H. J. Anuradha M. Annaswamy and G. J. Pappas, eds.,Control for Societal-scale Challenges: Road Map 2030. IEEE Control Systems Society,
[14]

2413, no

European Commission, “Directive (EU) 2023/2413 of the European Par- liament and of the council of 18 October 2023 amending directive (EU) 2018/2001, regulation (EU) 2018/1999 and directive 98/70/EC as regards the promotion of energy from renewable sources, and repealing counci...

2023
[15]

E. Commission, “Regulation (EU) 2024/1747 of the European Parliament and of the Council of 13 June 2024 amending regulations (EU) 2019/942 and (EU) 2019/943 as regards improving the Union’s electricity market design (text with EEA relevance),”Official Journal, L series, vol. 1...

2024
[16]

Optimal transport for fairness: Archival data repair using small research data sets,

A. Langbridge, A. Quinn, and R. Shorten, “Optimal transport for fairness: Archival data repair using small research data sets,” in2024 IEEE 40th International Conference on Data Engineering Workshops (ICDEW), 2024

2024
[17]

Obtaining fairness using optimal transport theory,

E. Del Barrio, G. Fabrice, P. Gordaliza, and J.-M. Loubes, “Obtaining fairness using optimal transport theory,” inInternational conference on machine learning, pp. 2357–2365, PMLR, 2019

2019
[18]

V. I. Bogachev,Weak convergence of measures. American Mathematical Society Providence, 2018

2018
[19]

Agenttorch: Agent-based modeling with automatic differentiation,

A. Chopra, J. Subramanian, B. Krishnamurthy, and R. Raskar, “Agenttorch: Agent-based modeling with automatic differentiation,” inSecond Agent Learning in Open-Endedness Workshop
[20]

Flame: A framework for learning in agent-based models,

A. Chopra, J. Subramanian, B. Krishnamurthy, and R. Raskar, “Flame: A framework for learning in agent-based models,” inProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems, pp. 391–399, 2024

2024
[21]

Practices for governing agentic ai systems,

Y. Shavit, S. Agarwal, M. Brundage, S. Adler, C. O’Keefe, R. Campbell, T. Lee, P. Mishkin, T. Eloundou, A. Hickey,et al., “Practices for governing agentic ai systems,”Research Paper, OpenAI, December, 2023

2023
[22]

Automated design of agentic systems,

S. Hu, C. Lu, and J. Clune, “Automated design of agentic systems,”arXiv preprint arXiv:2408.08435, 2024

2024 arXiv
[23]

Bayesian calibration of differentiable agent-based models,

A. Quera-Bofarull, A. Chopra, A. Calinescu, M. Wooldridge, and J. Dyer, “Bayesian calibration of differentiable agent-based models,”arXiv preprint arXiv:2305.15340, 2023

2023 arXiv
[24]

An ergodic theorem for iterated maps,

J. H. Elton, “An ergodic theorem for iterated maps,”Ergodic Theory and Dynamical Systems, vol. 7, no. 04, pp. 481–488, 1987

1987
[25]

Recurrent iterated function systems,

M. F. Barnsley, J. H. Elton, and D. P. Hardin, “Recurrent iterated function systems,” Constructive approximation, vol. 5, no. 1, pp. 3–31, 1989

1989
[26]

Iterated random functions,

P. Diaconis and D. Freedman, “Iterated random functions,”SIAM Review, vol. 41, no. 1, pp. 45–76, 1999

1999
[27]

Random ordinary differential equations,

J. Strand, “Random ordinary differential equations,”Journal of Differential Equations, vol. 7, no. 3, pp. 538–553, 1970

1970
[28]

Ergodic theorem for contractive Markov systems,

I. Werner, “Ergodic theorem for contractive Markov systems,”Nonlinearity, vol. 17, no. 6, pp. 2303–2313, 2004. 14

2004
[29]

Contractive Markov systems,

I. Werner, “Contractive Markov systems,”Journal of the London Mathe- matical Society, vol. 71, no. 1, pp. 236–258, 2005

2005
[30]

Predictability and fairness in load aggregation and operations of virtual power plants,

J. Mareček, M. Roubalik, R. Ghosh, R. N. Shorten, and F. R. Wirth, “Predictability and fairness in load aggregation and operations of virtual power plants,”Automatica, vol. 147, p. 110743, 2023

2023
[31]

On the scalability and memory efficiency of semidefinite programs for lipschitz constant estimation of neural networks,

Z.Wang, B.Hu, A.J.Havens, A.Araujo, Y.Zheng, Y.Chen, andS.Jha, “On the scalability and memory efficiency of semidefinite programs for lipschitz constant estimation of neural networks,” in The Twelfth International Conference on Learning Representations, 2024

2024
[32]

Evaluating the robustness of neural networks: An extreme value theory approach,

T.-W. Weng, H. Zhang, P.-Y. Chen, J. Yi, D. Su, Y. Gao, C.-J. Hsieh, and L. Daniel, “Evaluating the robustness of neural networks: An extreme value theory approach,” inInternational Conference on Learning Representations, 2018

2018
[33]

Gradient masking causes clever to overestimate adversarial perturbation size,

I. Goodfellow, “Gradient masking causes clever to overestimate adversarial perturbation size,” 2018

2018
[34]

On extensions of clever: A neural network robustness evaluation algorithm,

T.-W. Weng, H. Zhang, P.-Y. Chen, A. Lozano, C.-J. Hsieh, and L. Daniel, “On extensions of clever: A neural network robustness evaluation algorithm,” in 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), pp. 1159–1163, IEEE, 2018

2018
[35]

Formal specification for deep neural networks,

S. A. Seshia, A. Desai, T. Dreossi, D. J. Fremont, S. Ghosh, E. Kim, S. Shivakumar, M. Vazquez-Chanlatte, and X. Yue, “Formal specification for deep neural networks,” inAutomated Technology for Verification and Analysis: 16th International Symposium, ATVA 2018, Los Angeles, CA...

2018
[36]

Pre- dictability and fairness in social sensing,

R. Ghosh, J. Mareček, W. M. Griggs, M. Souza, and R. N. Shorten, “Pre- dictability and fairness in social sensing,”IEEE Internet of Things Journal, 2021

2021
[37]

On the ergodic control of ensembles in the presence of non-linear filters,

V. Kungurtsev, J. Marecek, R. Ghosh, and R. Shorten, “On the ergodic control of ensembles in the presence of non-linear filters,” Automatica, vol. 152, p. 110946, 2023

2023
[38]

Stochastic model predictive control as an iterated function system,

V. Kungurtsev, J. Marecek, and R. Shorten, “Stochastic model predictive control as an iterated function system,”arXiv preprint arXiv:2112.08138, 2021

2021 arXiv
[39]

Metrics for ergodicity and design of ergodic dy- namics for multi-agent systems,

G. Mathew and I. Mezić, “Metrics for ergodicity and design of ergodic dy- namics for multi-agent systems,”Physica D: Nonlinear Phenomena, vol. 240, no. 4-5, pp. 432–442, 2011

2011
[40]

Iterated function systems: A comprehensive survey,

R. Ghosh and J. Marecek, “Iterated function systems: A comprehensive survey,” arXiv preprint arXiv:2211.14661, 2022. 15 Supplementary Material: Part A A PyTorch Implementation It is clear that a formal specification of the AI system and the environment

2022 arXiv
[42]

i n p u t 1

and their interactions is needed to verify the properties of the closed loop. Considering the complexity of many AI systems, it seems natural to use the specification of the AI system within a machine-learning library such as PyTorch and their computational graphs. We have imp...
[2023]

Sponsored by the IEEE Control Systems Society, International Federation of Automatic Control (IFAC), and National Science Foundation (NSF)

Based on the 2022 IEEE CSS Workshop on Control for Societal-Scale Challenges. Sponsored by the IEEE Control Systems Society, International Federation of Automatic Control (IFAC), and National Science Foundation (NSF)

2022

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

1689, no

European Commission, “Regulation (EU) 2024/1689 of the European par- liament and of the Council of 13 June 2024 laying down harmonised rules on artificial intelligence and amending regulations (EC) no 300/2008, (EU) no 167/2013, (EU) no 168/2013, (EU) 2018/858, (EU) 2018/1139 and (EU) 2019/2144 and directives 2014/90/EU, (EU) 2016/797 and (EU) 2020/1828 (...

work page 2024

[2] [2]

Closed-loop view of the regulation of ai: Equal impact across repeated interactions,

Q. Zhou, R. Ghosh, R. Shorten, and J. Mareček, “Closed-loop view of the regulation of ai: Equal impact across repeated interactions,” in2024 IEEE 40th International Conference on Data Engineering Workshops (ICDEW), pp. 176–181, 2024

work page 2024

[3] [3]

H. 88th Congress (1963-1964), “To enforce the constitutional right to vote, to confer jurisdiction upon the district courts of the united states to provide injunctive relief against discrimination in public accommodations, to autho- rize the attorney general to institute suits to protect constitutional rights in public facilities and public education, to ...

work page 1963

[4] [4]

Title vi legal manual (updated),

C. R. D. of U.S. Department of Justice, “Title vi legal manual (updated),” Federal Coordination and Compliance Section, 2021. Section VII- Proving Discrimination- Disparate Impact

work page 2021

[5] [5]

Asymptotic coupling and a general form of harris’ theorem with applications to stochastic delay equations,

M. Hairer, J. C. Mattingly, and M. Scheutzow, “Asymptotic coupling and a general form of harris’ theorem with applications to stochastic delay equations,” Probability theory and related fields, vol. 149, no. 1-2, pp. 223– 259, 2011

work page 2011

[6] [6]

The complexity of Markov decision processes,

C. H. Papadimitriou and J. N. Tsitsiklis, “The complexity of Markov decision processes,” Mathematics of operations research, vol. 12, no. 3, pp. 441–450, 1987

work page 1987

[7] [7]

PSPACE-completeness of modular supervisory control problems,

K. Rohloff and S. Lafortune, “PSPACE-completeness of modular supervisory control problems,”Discrete Event Dynamic Systems, vol. 15, pp. 145–167, 2005

work page 2005

[8] [8]

On the undecidability of proba- bilistic planning and related stochastic optimization problems,

O. Madani, S. Hanks, and A. Condon, “On the undecidability of proba- bilistic planning and related stochastic optimization problems,”Artificial Intelligence, vol. 147, no. 1-2, pp. 5–34, 2003

work page 2003