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Researcher profile

Ashutosh Trivedi

Ashutosh Trivedi contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceComputer Science and Game Theoryeess.SYFormal Languages and Automata TheoryLogic in Computer ScienceSoftware EngineeringSystems and ControlCryptography and SecurityComputation and LanguageComputational Complexitycs.CYData Structures and AlgorithmsPerformance

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Published work

17 published item(s)

preprint2026arXiv

KV-Fold: One-Step KV-Cache Recurrence for Long-Context Inference

We introduce KV-Fold, a simple, training-free long-context inference protocol that treats the key-value (KV) cache as the accumulator in a left fold over sequence chunks. At each step, the model processes the next chunk conditioned on the accumulated cache, appends the newly produced keys and values, and passes the enlarged cache forward; the same one-step update is applied repeatedly, analogous to foldl in functional programming. Building on the KV cache concatenation primitive introduced for latent multi-agent communication, we repurpose it as a chunk-to-chunk recurrence for long-context inference. When processing chunk t, the model attends to the KV cache carried from earlier chunks as a prefix, reusing its internal state across segments without modifying or retraining the model. Despite its simplicity, the induced recurrence is stable: per-step drift rises briefly and then saturates into a flat plateau that persists across deep chains. This plateau is insensitive to a 10,000x change in numerical precision, robust across chunk sizes, and consistent across model families. At the task level, KV-Fold preserves exact information over long distances. On a needle-in-a-haystack benchmark, it achieves 100% exact-match retrieval across 152 trials spanning contexts from 16K to 128K tokens and chain depths up to 511 on Llama-3.1-8B, while remaining within the memory limits of a single 40GB GPU. Compared to streaming methods, which trade fidelity for bounded memory, KV-Fold maintains long-range retrieval while operating as a sequence of tractable forward passes. Overall, our results show that frozen pretrained transformers already support a stable form of KV-cache recurrence, providing a practical route to long-context inference without architectural changes or training.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

On the Robustness of Fairness Practices: A Causal Framework for Systematic Evaluation

Machine learning (ML) algorithms are increasingly deployed to make critical decisions in socioeconomic applications such as finance, criminal justice, and autonomous driving. However, due to their data-driven and pattern-seeking nature, ML algorithms may develop decision logic that disproportionately distributes opportunities, benefits, resources, or information among different population groups, potentially harming marginalized communities. In response to such fairness concerns, the software engineering and ML communities have made significant efforts to establish the best practices for creating fair ML software. These include fairness interventions for training ML models, such as including sensitive features, selecting non-sensitive attributes, and applying bias mitigators. But how reliably can software professionals tasked with developing data-driven systems depend on these recommendations? And how well do these practices generalize in the presence of faulty labels, missing data, or distribution shifts? These questions form the core theme of this paper.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Alternating Good-for-MDP Automata

When omega-regular objectives were first proposed in model-free reinforcement learning (RL) for controlling MDPs, deterministic Rabin automata were used in an attempt to provide a direct translation from their transitions to scalar values. While these translations failed, it has turned out that it is possible to repair them by using good-for-MDPs (GFM) Büchi automata instead. These are nondeterministic Büchi automata with a restricted type of nondeterminism, albeit not as restricted as in good-for-games automata. Indeed, deterministic Rabin automata have a pretty straightforward translation to such GFM automata, which is bi-linear in the number of states and pairs. Interestingly, the same cannot be said for deterministic Streett automata: a translation to nondeterministic Rabin or Büchi automata comes at an exponential cost, even without requiring the target automaton to be good-for-MDPs. Do we have to pay more than that to obtain a good-for-MDP automaton? The surprising answer is that we have to pay significantly less when we instead expand the good-for-MDP property to alternating automata: like the nondeterministic GFM automata obtained from deterministic Rabin automata, the alternating good-for-MDP automata we produce from deterministic Streett automata are bi-linear in the the size of the deterministic automaton and its index, and can therefore be exponentially more succinct than minimal nondeterministic Büchi automata.

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preprint2022arXiv

Compositional Reinforcement Learning for Discrete-Time Stochastic Control Systems

We propose a compositional approach to synthesize policies for networks of continuous-space stochastic control systems with unknown dynamics using model-free reinforcement learning (RL). The approach is based on implicitly abstracting each subsystem in the network with a finite Markov decision process with unknown transition probabilities, synthesizing a strategy for each abstract model in an assume-guarantee fashion using RL, and then mapping the results back over the original network with approximate optimality guarantees. We provide lower bounds on the satisfaction probability of the overall network based on those over individual subsystems. A key contribution is to leverage the convergence results for adversarial RL (minimax Q-learning) on finite stochastic arenas to provide control strategies maximizing the probability of satisfaction over the network of continuous-space systems. We consider finite-horizon properties expressed in the syntactically co-safe fragment of linear temporal logic. These properties can readily be converted into automata-based reward functions, providing scalar reward signals suitable for RL. Since such reward functions are often sparse, we supply a potential-based reward shaping technique to accelerate learning by producing dense rewards. The effectiveness of the proposed approaches is demonstrated via two physical benchmarks including regulation of a room temperature network and control of a road traffic network.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Controller Synthesis for Omega-Regular and Steady-State Specifications

Given a Markov decision process (MDP) and a linear-time ($ω$-regular or LTL) specification, the controller synthesis problem aims to compute the optimal policy that satisfies the specification. More recently, problems that reason over the asymptotic behavior of systems have been proposed through the lens of steady-state planning. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior. We present an algorithm to find a deterministic policy satisfying $ω$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Fairness-aware Configuration of Machine Learning Libraries

This paper investigates the parameter space of machine learning (ML) algorithms in aggravating or mitigating fairness bugs. Data-driven software is increasingly applied in social-critical applications where ensuring fairness is of paramount importance. The existing approaches focus on addressing fairness bugs by either modifying the input dataset or modifying the learning algorithms. On the other hand, the selection of hyperparameters, which provide finer controls of ML algorithms, may enable a less intrusive approach to influence the fairness. Can hyperparameters amplify or suppress discrimination present in the input dataset? How can we help programmers in detecting, understanding, and exploiting the role of hyperparameters to improve the fairness? We design three search-based software testing algorithms to uncover the precision-fairness frontier of the hyperparameter space. We complement these algorithms with statistical debugging to explain the role of these parameters in improving fairness. We implement the proposed approaches in the tool Parfait-ML (PARameter FAIrness Testing for ML Libraries) and show its effectiveness and utility over five mature ML algorithms as used in six social-critical applications. In these applications, our approach successfully identified hyperparameters that significantly improve (vis-a-vis the state-of-the-art techniques) the fairness without sacrificing precision. Surprisingly, for some algorithms (e.g., random forest), our approach showed that certain configuration of hyperparameters (e.g., restricting the search space of attributes) can amplify biases across applications. Upon further investigation, we found intuitive explanations of these phenomena, and the results corroborate similar observations from the literature.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Inferring Probabilistic Reward Machines from Non-Markovian Reward Processes for Reinforcement Learning

The success of reinforcement learning in typical settings is predicated on Markovian assumptions on the reward signal by which an agent learns optimal policies. In recent years, the use of reward machines has relaxed this assumption by enabling a structured representation of non-Markovian rewards. In particular, such representations can be used to augment the state space of the underlying decision process, thereby facilitating non-Markovian reinforcement learning. However, these reward machines cannot capture the semantics of stochastic reward signals. In this paper, we make progress on this front by introducing probabilistic reward machines (PRMs) as a representation of non-Markovian stochastic rewards. We present an algorithm to learn PRMs from the underlying decision process and prove results around its correctness and convergence.

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preprint2022arXiv

Optimal Repair For Omega-regular Properties

This paper presents an optimization based framework to automate system repair against omega-regular properties. In the proposed formalization of optimal repair, the systems are represented as Kripke structures, the properties as $ω$-regular languages, and the repair space as repair machines -- weighted omega-regular transducers equipped with Büchi conditions -- that rewrite strings and associate a cost sequence to these rewritings. To translate the resulting cost-sequences to easily interpretable payoffs, we consider several aggregator functions to map cost sequences to numbers -- including limit superior, supremum, discounted-sum, and average-sum -- to define quantitative cost semantics. The problem of optimal repair, then, is to determine whether traces from a given system can be rewritten to satisfy an $ω$-regular property when the allowed cost is bounded by a given threshold. We also consider the dual challenge of impair verification that assumes that the rewritings are resolved adversarially under some given cost restriction, and asks to decide if all traces of the system satisfy the specification irrespective of the rewritings. With a negative result to the impair verification problem, we study the problem of designing a minimal mask of the Kripke structure such that the resulting traces satisfy the specifications despite the threshold-bounded impairment. We dub this problem as the mask synthesis problem. This paper presents automata-theoretic solutions to repair synthesis, impair verification, and mask synthesis problem for limit superior, supremum, discounted-sum, and average-sum cost semantics.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Recursive Reinforcement Learning

Recursion is the fundamental paradigm to finitely describe potentially infinite objects. As state-of-the-art reinforcement learning (RL) algorithms cannot directly reason about recursion, they must rely on the practitioner's ingenuity in designing a suitable "flat" representation of the environment. The resulting manual feature constructions and approximations are cumbersome and error-prone; their lack of transparency hampers scalability. To overcome these challenges, we develop RL algorithms capable of computing optimal policies in environments described as a collection of Markov decision processes (MDPs) that can recursively invoke one another. Each constituent MDP is characterized by several entry and exit points that correspond to input and output values of these invocations. These recursive MDPs (or RMDPs) are expressively equivalent to probabilistic pushdown systems (with call-stack playing the role of the pushdown stack), and can model probabilistic programs with recursive procedural calls. We introduce Recursive Q-learning -- a model-free RL algorithm for RMDPs -- and prove that it converges for finite, single-exit and deterministic multi-exit RMDPs under mild assumptions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Secure-by-Construction Synthesis of Cyber-Physical Systems

Correct-by-construction synthesis is a cornerstone of the confluence of formal methods and control theory towards designing safety-critical systems. Instead of following the time-tested, albeit laborious (re)design-verify-validate loop, correct-by-construction methodology advocates the use of continual refinements of formal requirements -- connected by chains of formal proofs -- to build a system that assures the correctness by design. A remarkable progress has been made in scaling the scope of applicability of correct-by-construction synthesis -- with a focus on cyber-physical systems that tie discrete-event control with continuous environment -- to enlarge control systems by combining symbolic approaches with principled state-space reduction techniques. Unfortunately, in the security-critical control systems, the security properties are verified ex post facto the design process in a way that undermines the correct-by-construction paradigm. We posit that, to truly realize the dream of correct-by-construction synthesis for security-critical systems, security considerations must take center-stage with the safety considerations. Moreover, catalyzed by the recent progress on the opacity sub-classes of security properties and the notion of hyperproperties capable of combining security with safety properties, we believe that the time is ripe for the research community to holistically target the challenge of secure-by-construction synthesis. This paper details our vision by highlighting the recent progress and open challenges that may serve as bricks for providing a solid foundation for secure-by-construction synthesis of cyber-physical systems.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Adding Negative Prices to Priced Timed Games

Priced timed games (PTGs) are two-player zero-sum games played on the infinite graph of configurations of priced timed automata where two players take turns to choose transitions in order to optimize cost to reach target states. Bouyer et al. and Alur, Bernadsky, and Madhusudan independently proposed algorithms to solve PTGs with nonnegative prices under certain divergence restriction over prices. Brihaye, Bruyere, and Raskin later provided a justification for such a restriction by showing the undecidability of the optimal strategy synthesis problem in the absence of this divergence restriction. This problem for PTGs with one clock has long been conjectured to be in polynomial time, however the current best known algorithm, by Hansen, Ibsen-Jensen, and Miltersen, is exponential. We extend this picture by studying PTGs with both negative and positive prices. We refine the undecidability results for optimal strategy synthesis problem, and show undecidability for several variants of optimal reachability cost objectives including reachability cost, time-bounded reachability cost, and repeated reachability cost objectives. We also identify a subclass with bi-valued price-rates and give a pseudo-polynomial algorithm to partially answer the conjecture on the complexity of one-clock PTGs.

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preprint2020arXiv

Data-Driven Debugging for Functional Side Channels

Information leaks through side channels are a pervasive problem, even in security-critical applications. Functional side channels arise when an attacker knows that a secret value of a server stays fixed for a certain time. Then, the attacker can observe the server executions on a sequence of different public inputs, each paired with the same secret input. Thus for each secret, the attacker observes a function from public inputs to execution time, for instance, and she can compare these functions for different secrets. First, we introduce a notion of noninterference for functional side channels. We focus on the case of noisy observations, where we demonstrate with examples that there is a practical functional side channel in programs that would be deemed information-leak-free or be underestimated using the standard definition. Second, we develop a framework and techniques for debugging programs for functional side channels. We extend evolutionary fuzzing techniques to generate inputs that exploit functional dependencies of response times on public inputs. We adapt existing results and algorithms in functional data analysis to model the functions and discover the existence of side channels. We use a functional extension of standard decision tree learning to pinpoint the code fragments causing a side channel if there is one. We empirically evaluate the performance of our tool FUCHSIA on a series of micro-benchmarks and realistic Java programs. On the set of benchmarks, we show that FUCHSIA outperforms the state-of-the-art techniques in detecting side channel classes. On the realistic programs, we show the scalability of FUCHSIA in analyzing functional side channels in Java programs with thousands of methods. Also, we show the usefulness of FUCHSIA in finding side channels including a zero-day vulnerability in OpenJDK and another vulnerability in Jetty that was since fixed by the developers.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Detecting and Understanding Real-World Differential Performance Bugs in Machine Learning Libraries

Programming errors that degrade the performance of systems are widespread, yet there is little tool support for analyzing these bugs. We present a method based on differential performance analysis---we find inputs for which the performance varies widely, despite having the same size. To ensure that the differences in the performance are robust (i.e. hold also for large inputs), we compare the performance of not only single inputs, but of classes of inputs, where each class has similar inputs parameterized by their size. Thus, each class is represented by a performance function from the input size to performance. Importantly, we also provide an explanation for why the performance differs in a form that can be readily used to fix a performance bug. The two main phases in our method are discovery with fuzzing and explanation with decision tree classifiers, each of which is supported by clustering. First, we propose an evolutionary fuzzing algorithm to generate inputs. For this fuzzing task, the unique challenge is that we not only need the input class with the worst performance, but rather a set of classes exhibiting differential performance. We use clustering to merge similar input classes which significantly improves the efficiency of our fuzzer. Second, we explain the differential performance in terms of program inputs and internals. We adapt discriminant learning approaches with clustering and decision trees to localize suspicious code regions. We applied our techniques to a set of applications. On a set of micro-benchmarks, we show that our approach outperforms state-of-the-art fuzzers in finding inputs to characterize the differential performance. On a set of case-studies, we discover and explain multiple performance bugs in popular machine learning frameworks. Four of these bugs, reported first in this paper, have since been fixed by the developers.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Formal Controller Synthesis for Continuous-Space MDPs via Model-Free Reinforcement Learning

A novel reinforcement learning scheme to synthesize policies for continuous-space Markov decision processes (MDPs) is proposed. This scheme enables one to apply model-free, off-the-shelf reinforcement learning algorithms for finite MDPs to compute optimal strategies for the corresponding continuous-space MDPs without explicitly constructing the finite-state abstraction. The proposed approach is based on abstracting the system with a finite MDP (without constructing it explicitly) with unknown transition probabilities, synthesizing strategies over the abstract MDP, and then mapping the results back over the concrete continuous-space MDP with approximate optimality guarantees. The properties of interest for the system belong to a fragment of linear temporal logic, known as syntactically co-safe linear temporal logic (scLTL), and the synthesis requirement is to maximize the probability of satisfaction within a given bounded time horizon. A key contribution of the paper is to leverage the classical convergence results for reinforcement learning on finite MDPs and provide control strategies maximizing the probability of satisfaction over unknown, continuous-space MDPs while providing probabilistic closeness guarantees. Automata-based reward functions are often sparse; we present a novel potential-based reward shaping technique to produce dense rewards to speed up learning. The effectiveness of the proposed approach is demonstrated by applying it to three physical benchmarks concerning the regulation of a room's temperature, control of a road traffic cell, and of a 7-dimensional nonlinear model of a BMW 320i car.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Mean-Payoff Games on Timed Automata

Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players, Player Min and Player Max, by moving a token along the states of the graph to form an infinite run. The goal of Player Min is to minimize the limit average weight of the run, while the goal of the Player Max is the opposite. Brenguier, Cassez, and Raskin recently studied a variation of these games and showed that mean-payoff games are undecidable for timed automata with five or more clocks. We refine this result by proving the undecidability of mean-payoff games with three clocks. On a positive side, we show the decidability of mean-payoff games on one-clock timed automata with binary price-rates. A key contribution of this paper is the application of dynamic programming based proof techniques applied in the context of average reward optimization on an uncountable state and action space.

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preprint2009arXiv

Average-Time Games on Timed Automata

An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimise the average time per transition and player Max wants to maximise it. A solution of average-time games is presented using a reduction to average-price game on a finite graph. A direct consequence is an elementary proof of determinacy for average-time games. This complements our results for reachability-time games and partially solves a problem posed by Bouyer et al., to design an algorithm for solving average-price games on priced timed automata. The paper also establishes the exact computational complexity of solving average-time games: the problem is EXPTIME-complete for timed automata with at least two clocks.

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preprint2009arXiv

Reachability-time games on timed automata

In a reachability-time game, players Min and Max choose moves so that the time to reach a final state in a timed automaton is minimised or maximised, respectively. Asarin and Maler showed decidability of reachability-time games on strongly non-Zeno timed automata using a value iteration algorithm. This paper complements their work by providing a strategy improvement algorithm for the problem. It also generalizes their decidability result because the proposed strategy improvement algorithm solves reachability-time games on all timed automata. The exact computational complexity of solving reachability-time games is also established: the problem is EXPTIME-complete for timed automata with at least two clocks.

0 citations0 reviewsNo code linkedOpen access