arXiv subjects

Shashanka Ubaru

Publications and source records attributed to Shashanka Ubaru.

At least 19 recordsLinked to original sources

arXiv2026

Closing the Consistency Gap: Self-Evolving Agents That Learn to Stay on Course

Large language model (LLM)-powered agents can be accurate on average yet unreliable in production, a discrepancy that has been observed but remains largely unaddressed. When given the same task five times, a ReAct agent on the AppWorld benchmark using GPT-4.1 succeeds in all five runs only 53% of the time, even though its per-run pass rate averages 77%. We call this 24-point shortfall the consistency gap, and we argue that addressing it is a precondition for trustworthy AI agent deployment. We present a self-evolving agent framework that reduces this gap by identifying unstable, low-consistency steps in agent trajectories and converting them into episodic memory the agent can draw on in future runs. At its core is a Consistency Analyzer that pinpoints where and why a trajectory is likely to flip across executions, and a Guideline Generator that converts the diagnosis into targeted guidelines, committed to memory and injected into future agent executions on similar tasks. On AppWorld with ReAct/GPT-4.1, our framework raises the fraction of tasks that succeed in all five runs by +16 points on same-task evaluation and +13 points on similar-task generalization.

cs.AI↗

arXiv2026

Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules

Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error $\varepsilon$ that compounds with depth $M$ as $M\varepsilon$, whereas exact equivariance holds at unbounded depth; we demonstrate this divergence at fourteen orders of magnitude. We show that a symmetry can be made exact by construction, as the multiplication rule of a tensor algebra. In the resulting $\starG$ algebra, defined by any finite group $G$, the group-Fourier transform block-diagonalizes every tensor into irreducible-representation blocks, making equivariance intrinsic; requiring equivariance conversely \emph{forces} this suitably normalized transform, so the algebra is determined by $G$ rather than chosen. The standard matrix toolbox, including a Frobenius-optimal low-rank factorization, transfers blockwise, machine-checked in Lean~4 under an explicit axiom budget, and extends unchanged to band-limited compact groups and, under periodic boundary conditions, to all 230 crystallographic space groups and the compact little-group fibers of Euclidean and Poincaré symmetry. This exactness is an applied capability: on inorganic-crystal elastic tensors the algebra enforces point-group selection rules exactly on the output of \emph{any} predictor, driving a trained graph network's forbidden-channel leakage from $10^{-2}$ to machine zero, eliminating mechanically unstable predictions, and recovering viable materials that an unconstrained screen discards; on molecular data, with no quantum-mechanical input, it exposes octahedral selection-rule signatures consistent with the Wigner--Eckart theorem. Matched networks lead on pooled molecular accuracy, which we report plainly: the contribution is a complementary algebraic calculus, structural and diagnostic, exact at any depth.

cs.LG↗

arXiv2026

Counting Triangles of Graphs via Randomized Trace Estimation with Incomplete Matrix-Vector Products

Counting triangles in graphs is a fundamental operation in network analysis, underpinning metrics such as clustering coefficients and serving as a signal for community detection, link prediction, and anomaly detection. The standard approach computes the trace of the cube of the adjacency matrix, but explicitly forming $\mathbf{A}^3$ is infeasible for large graphs. Hutchinson randomized trace estimator offers an efficient alternative by approximating the trace through stochastic averaging of quadratic forms, requiring only matrix vector products with $\mathbf{A}$. However, in distributed and heterogeneous computing environments, observing all entries of these products can be costly due to communication overhead and straggler effects. To address this, we propose a new variant of Hutchinson estimator that operates under partial observation constraints, where both the number and identities of observed entries are random. We provide theoretical guarantees on unbiasedness, variance bounds, and sample complexity, and demonstrate through experiments on synthetic and real world graphs that our method achieves accurate triangle count estimates while reducing synchronization costs. This work highlights the adaptability of randomized algorithms to modern computational architectures and opens avenues for efficient motif counting in large scale network analytics.

math.NA↗

arXiv2026

Analysis of Power Iteration Algorithm with Partially Observed Matrix-vector Products

We consider the problem of computing the dominant eigenvector of a symmetric matrix via the power iteration algorithm subject to constraints in the computation of matrix-vector pr ucts. In particular, we focus on scenarios where the entries of matrix-vector products with the input matrix are only partially observed. Such constraints frequently arise on cloud architectures implemented via the controller-worker model where the matrix-vector products are distributed across workers on remote servers. Instead of a prolonged delay incurred by waiting for the slowest workers to return their output to the controller, a phenomenon known as straggling, a set of pre-determined values can replace the values of the delayed workers and allow the power iteration to proceed to the next iteration. In this paper, we develop two algorithms whose expected approximation converges to the true dominant eigenvector. The first algorithm relies on a probabilistic switch between two different approaches to set the omitted entries: either set them to zero or to their previous recorded value. The second algorithm relies on averaging previously generated partial power iteration approximations obtained by ignoring a set of columns of the iteration matrix. several theoretical details are discussed while numerical experiments verify the effectiveness of the two proposed schemes and demonstrate their comparative performance advantage over current state-of-the-art.

math.NA↗

arXiv2026

Interpretable epistemic uncertainty decomposition in sequential generative models via polynomial chaos surrogates

Sequential generative models conditioned on uncertain rewards are central to AI-driven scientific discovery, yet the epistemic uncertainty they inherit from imperfect reward estimates remains unquantified. We propagate this uncertainty through generative flow networks (GFlowNets) by fitting polynomial chaos expansions (PCEs) to small ensembles of trained models. The PCE coefficients yield analytical Sobol sensitivity indices, providing the first interpretable decomposition of which reward components drive which generative decisions, a capability unavailable from deep ensembles, Bayesian neural networks, or Monte Carlo dropout. Convergence guarantees are established theoretically and four of five are formally verified in the Lean 4 proof assistant. Across three real-world tasks the framework reveals actionable structure invisible to ensembles alone. On the Doyle-Dreher Buchwald-Hartwig dataset catalyst selection is robust ($D_{\mathrm{catalyst}}\approx 71$) while additive selection is fragile ($D_{\mathrm{additive}}\approx 179$, $2.5\times$ higher). In fragment-based molecular design the linker position is the most sensitive ($D_{\mathrm{linker}}\approx 28$) while decoration positions are the most robust ($D\approx 14$-$18$), reversing the conventional scaffold-robust / decoration-fragile assumption. On the Sachs protein signalling network, MAPK-cascade edges and PKA/PKC hub edges separate into distinct sensitivity regimes, providing a targeted map for perturbation experiments. Calibration coverage at the 95% level reaches 0.97-1.00 across the dominant steps, and the surrogate evaluates 10{,}000 policy samples in milliseconds - $10^{3}$-$10^{4}\times$ faster than exhaustive retraining.

cs.LG↗

arXiv2025

Comparing quantum and classical Monte Carlo algorithms for estimating Betti numbers of clique complexes

Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their common Monte Carlo structure within a new modular framework. We derive upper bounds for the number of samples needed to reach a given level of precision, and use them to compare these algorithms. By recombining the different modules, we create a new quantum algorithm with an exponentially-improved dependence in the sample complexity. We run classical simulations to verify convergence within the theoretical bounds and observe the predicted exponential separation, even though empirical convergence occurs substantially earlier than the conservative theoretical bounds.

quant-ph↗

arXiv2025

Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-based Matrix Inversion

Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually require preconditioners. Markov chain Monte Carlo (MCMC)-based matrix inversion can generate such preconditioners and accelerate Krylov iterations, but its effectiveness depends on parameters whose optima vary across matrices; manual or grid search is costly. We present an AI-driven framework recommending MCMC parameters for a given linear system. A graph neural surrogate predicts preconditioning speed from $A$ and MCMC parameters. A Bayesian acquisition function then chooses the parameter sets most likely to minimise iterations. On a previously unseen ill-conditioned system, the framework achieves better preconditioning with 50\% of the search budget of conventional methods, yielding about a 10\% reduction in iterations to convergence. These results suggest a route for incorporating MCMC-based preconditioners into large-scale systems.

cs.LG↗

arXiv2025

PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty

Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become prohibitively expensive for high-dimensional data. In this study, we introduce a dimensionality reduction surrogate modeling (DRSM) approach for representation learning and uncertainty quantification that aims to deal with data of moderate to high dimensions. The approach involves a two-stage learning process: 1) employing a variational autoencoder to learn a low-dimensional representation of the input data distribution; and 2) harnessing polynomial chaos expansion (PCE) formulation to map the low dimensional distribution to the output target. The model enables us to (a) capture the system dynamics efficiently in the low-dimensional latent space, (b) learn under uncertainty, a representation of the data and a mapping between input and output distributions, (c) estimate this uncertainty in the high-dimensional data system, and (d) match high-order moments of the output distribution; without any prior statistical assumptions on the data. Numerical results are presented to illustrate the performance of the proposed method.

cs.LG↗

arXiv2025

Transformers Learn Faster with Semantic Focus

Various forms of sparse attention have been explored to mitigate the quadratic computational and memory cost of the attention mechanism in transformers. We study sparse transformers not through a lens of efficiency but rather in terms of learnability and generalization. Empirically studying a range of attention mechanisms, we find that input-dependent sparse attention models appear to converge faster and generalize better than standard attention models, while input-agnostic sparse attention models show no such benefits -- a phenomenon that is robust across architectural and optimization hyperparameter choices. This can be interpreted as demonstrating that concentrating a model's "semantic focus" with respect to the tokens currently being considered (in the form of input-dependent sparse attention) accelerates learning. We develop a theoretical characterization of the conditions that explain this behavior. We establish a connection between the stability of the standard softmax and the loss function's Lipschitz properties, then show how sparsity affects the stability of the softmax and the subsequent convergence and generalization guarantees resulting from the attention mechanism. This allows us to theoretically establish that input-agnostic sparse attention does not provide any benefits. We also characterize conditions when semantic focus (input-dependent sparse attention) can provide improved guarantees, and we validate that these conditions are in fact met in our empirical evaluations.

cs.LG↗

arXiv2025

On Efficient Solutions of General Structured Markov Processes in Quantum Computational Environments

We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental problem within the context of quantum computational environments from a mathematical perspective and devise the first quantum algorithms for computing the stationary distribution of general structured Markov processes. We derive a mathematical analysis of the computational properties of our quantum algorithms together with related theoretical results, establishing that our quantum algorithms provide the potential for significant computational improvements over that of the best-known and most-efficient classical algorithms in various settings of both theoretical and practical importance. Although motivated by general structured Markov processes, our quantum algorithms can be exploited to address a much larger class of numerical computation problems, as well as to potentially play the role of a subroutine as part of solving larger computational problems involving the stationary distribution on a quantum computer.

quant-ph↗

arXiv2024

Randomized matrix-free quadrature: unified and uniform bounds for stochastic Lanczos quadrature and the kernel polynomial method

We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanczos quadrature, two widely used methods for these tasks. Our analysis of spectrum approximation unifies and simplifies several one-off analyses for these algorithms which have appeared over the past decade. In addition, we derive bounds for spectral sum approximation which guarantee that, with high probability, the algorithms are simultaneously accurate on all bounded analytic functions. Finally, we provide comprehensive and complimentary numerical examples. These examples illustrate some of the qualitative similarities and differences between the algorithms, as well as relative drawbacks and benefits to their use on different types of problems.

math.NA↗

arXiv2024

Combinatorial Multi-armed Bandits: Arm Selection via Group Testing

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

cs.LG↗

arXiv2024

Multivariate trace estimation using quantum state space linear algebra

In this paper, we present a quantum algorithm for approximating multivariate traces, i.e. the traces of matrix products. Our research is motivated by the extensive utility of multivariate traces in elucidating spectral characteristics of matrices, as well as by recent advancements in leveraging quantum computing for faster numerical linear algebra. Central to our approach is a direct translation of a multivariate trace formula into a quantum circuit, achieved through a sequence of low-level circuit construction operations. To facilitate this translation, we introduce \emph{quantum Matrix States Linear Algebra} (qMSLA), a framework tailored for the efficient generation of state preparation circuits via primitive matrix algebra operations. Our algorithm relies on sets of state preparation circuits for input matrices as its primary inputs and yields two state preparation circuits encoding the multivariate trace as output. These circuits are constructed utilizing qMSLA operations, which enact the aforementioned multivariate trace formula. We emphasize that our algorithm's inputs consist solely of state preparation circuits, eschewing harder to synthesize constructs such as Block Encodings. Furthermore, our approach operates independently of the availability of specialized hardware like QRAM, underscoring its versatility and practicality.

quant-ph↗

arXiv2024

Topological data analysis on noisy quantum computers

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.

quant-ph↗

arXiv2024

Multi-Function Multi-Way Analog Technology for Sustainable Machine Intelligence Computation

Numerical computation is essential to many areas of artificial intelligence (AI), whose computing demands continue to grow dramatically, yet their continued scaling is jeopardized by the slowdown in Moore's law. Multi-function multi-way analog (MFMWA) technology, a computing architecture comprising arrays of memristors supporting in-memory computation of matrix operations, can offer tremendous improvements in computation and energy, but at the expense of inherent unpredictability and noise. We devise novel randomized algorithms tailored to MFMWA architectures that mitigate the detrimental impact of imperfect analog computations while realizing their potential benefits across various areas of AI, such as applications in computer vision. Through analysis, measurements from analog devices, and simulations of larger systems, we demonstrate orders of magnitude reduction in both computation and energy with accuracy similar to digital computers.

math.NA↗

arXiv2023

Capacity Analysis of Vector Symbolic Architectures

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership $i \in S$ and estimating set intersection sizes $|X \cap Y|$ for two sets of symbols $X$ and $Y$, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

cs.LG↗

arXiv2022

Representation of the Fermionic Boundary Operator

The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including differential equations, machine learning, computational geometry, machine vision and control systems. We consider the problem of representing the full boundary operator on a quantum computer. We first prove that the boundary operator has a special structure in the form of a complete sum of fermionic creation and annihilation operators. We then use the fact that these operators pairwise anticommute to produce an $O(n)$-depth circuit that exactly implements the boundary operator without any Trotterization or Taylor series approximation errors. Having fewer errors reduces the number of shots required to obtain desired accuracies.

quant-ph↗

arXiv2021

Efficient Scaling of Dynamic Graph Neural Networks

We present distributed algorithms for training dynamic Graph Neural Networks (GNN) on large scale graphs spanning multi-node, multi-GPU systems. To the best of our knowledge, this is the first scaling study on dynamic GNN. We devise mechanisms for reducing the GPU memory usage and identify two execution time bottlenecks: CPU-GPU data transfer; and communication volume. Exploiting properties of dynamic graphs, we design a graph difference-based strategy to significantly reduce the transfer time. We develop a simple, but effective data distribution technique under which the communication volume remains fixed and linear in the input size, for any number of GPUs. Our experiments using billion-size graphs on a system of 128 GPUs shows that: (i) the distribution scheme achieves up to 30x speedup on 128 GPUs; (ii) the graph-difference technique reduces the transfer time by a factor of up to 4.1x and the overall execution time by up to 40%

cs.DC↗