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Neel Patel

Publications and source records attributed to Neel Patel.

At least 19 recordsLinked to original sources
arXiv2026

Fully Dynamic All-Pairs Min Cuts on Planar Graphs via Planar Pattern Emulators

We study the fully-dynamic all-pairs minimum cut problem on planar graphs. Given an $n$-vertex undirected planar graph $G=(V,E)$ undergoing edge insertions and deletions, the goal is to efficiently process these updates while supporting $s$-$t$ minimum cut queries for any pair of vertices $s$ and $t$. We give a $(1+\varepsilon)$-approximate dynamic algorithm that supports edge updates and minimum cut queries in $n^{o(1)}$ time, for any $1/\text{poly}(\log n) < \varepsilon < 1$. For general graphs, previous results either are limited to partially dynamic settings or achieve only logarithmic-factor approximations. The main conceptual and technical contribution is to show that a suitable adaptation of the planar emulator of Chang, Krauthgamer, and Tan~[STOC'22] satisfies the stronger pattern emulator introduced by Chen and Tan~[ICALP'25]. This leads almost immediately to a nearly linear-time construction of pattern emulators, which, when combined with the recent fully dynamic $(1+\varepsilon)$-approximate all-pairs shortest paths algorithm of Filtser, Goranci, Patel, and Probst Gutenberg~[FOCS'24], yields our result.

cs.DS↗
arXiv2026

Nonlinear Stability of 3D Muskat Bubbles

This paper studies the three-dimensional Muskat problem for two immiscible fluids in a porous medium subject to gravity and surface tension. We consider the setting in which one fluid forms a bounded bubble surrounded by the other. For any value of the physical parameters, we prove the global-in-time nonlinear asymptotic stability of a translating spherical bubble for small initial perturbations in the critical Lipschitz class. This enlarges the class of critical spaces considered in previous two-dimensional bubble results. The proof combines spectral analysis of the linearized operator on $\mathbb{S}^2$ with multilinear singular integral estimates that exploit a crucial null structure in the nonlinear terms.

math.AP↗
arXiv2026

Graphic Matroid Secretary without the Graph

The matroid secretary problem (MSP) is one of the cleanest, and most captivating open problems in online algorithms. The famous MSP conjecture stipulates that there exists a constant-competitive algorithm, yet to date the best known algorithms are $O(\log \log (\text{rank}))$ competitive. It is widely believed that all information that an algorithm for the MSP should use is information that is available through an independence oracle on the already arrived elements. Despite this, there are natural classes of matroids where a constant-competitive algorithm is known if we are given additional upfront information about the matroid; while no such algorithm is known if all the algorithm can use is an independence oracle on the arrived elements. In this work, we tackle the perhaps most appealing such class of matroids, graphic matroids. We develop an algorithm for the MSP that has access to the independence oracle only. Our algorithm runs in polynomial time, and if the underlying matroid is graphic, it produces an independent set whose weight is at least $1/36$ of the maximum-weight independent set. Ours is the first constant-competitive algorithm for MSP on unknown graphic matroids.

cs.DS↗
arXiv2026

Memanto: Typed Semantic Memory with Information-Theoretic Retrieval for Long-Horizon Agents

The transition from stateless language model inference to persistent, multi session autonomous agents has revealed memory to be a primary architectural bottleneck in the deployment of production grade agentic systems. Existing methodologies largely depend on hybrid semantic graph architectures, which impose substantial computational overhead during both ingestion and retrieval. These systems typically require large language model mediated entity extraction, explicit graph schema maintenance, and multi query retrieval pipelines. This paper introduces Memanto, a universal memory layer for agentic artificial intelligence that challenges the prevailing assumption that knowledge graph complexity is necessary to achieve high fidelity agent memory. Memanto integrates a typed semantic memory schema comprising thirteen predefined memory categories, an automated conflict resolution mechanism, and temporal versioning. These components are enabled by Moorcheh's Information Theoretic Search engine, a no indexing semantic database that provides deterministic retrieval within sub ninety millisecond latency while eliminating ingestion delay. Through systematic benchmarking on the LongMemEval and LoCoMo evaluation suites, Memanto achieves state of the art accuracy scores of 89.8 percent and 87.1 percent respectively. These results surpass all evaluated hybrid graph and vector based systems while requiring only a single retrieval query, incurring no ingestion cost, and maintaining substantially lower operational complexity. A five stage progressive ablation study is presented to quantify the contribution of each architectural component, followed by a discussion of the implications for scalable deployment of agentic memory systems.

cs.AI↗
arXiv2026

Less is More: Convergence Benefits of Fewer Data Weight Updates over Longer Horizon

Data mixing--the strategic reweighting of training domains--is a critical component in training robust machine learning models. This problem is naturally formulated as a bilevel optimization task, where the outer loop optimizes domain weights to minimize validation loss, and the inner loop optimizes model parameters to minimize the weighted training loss. Classical bilevel optimization relies on hypergradients, which theoretically require the inner optimization to reach convergence. However, due to computational constraints, state-of-the-art methods use a finite, often small, number of inner update steps before updating the weights. The theoretical implications of this approximation are not well understood. In this work, we rigorously analyze the convergence behavior of data mixing with a finite number of inner steps $T$. We prove that the "greedy" practical approach of using $T=1$ can fail even in a simple quadratic example. Under a fixed parameter update budget $N$ and assuming the per-domain losses are strongly convex, we show that the optimal $T$ scales as $Θ(\log N)$ (resp., $Θ({(N \log N)}^{1/2})$) for the data mixing problem with access to full (resp., stochastic) gradients. We complement our theoretical results with proof-of-concept experiments.

cs.LG↗
arXiv2025

An Explainable Hybrid AI Framework for Enhanced Tuberculosis and Symptom Detection

Tuberculosis remains a critical global health issue, particularly in resource-limited and remote areas. Early detection is vital for treatment, yet the lack of skilled radiologists underscores the need for artificial intelligence (AI)-driven screening tools. Developing reliable AI models is challenging due to the necessity for large, high-quality datasets, which are costly to obtain. To tackle this, we propose a teacher--student framework which enhances both disease and symptom detection on chest X-rays by integrating two supervised heads and a self-supervised head. Our model achieves an accuracy of 98.85% for distinguishing between COVID-19, tuberculosis, and normal cases, and a macro-F1 score of 90.09% for multilabel symptom detection, significantly outperforming baselines. The explainability assessments also show the model bases its predictions on relevant anatomical features, demonstrating promise for deployment in clinical screening and triage settings.

cs.CV↗
arXiv2025

Online Matroid Embeddings

We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. We establish the existence of such an embedding for binary matroids, and use it to relate variants of the binary matroid secretary problem to each other, showing that seemingly simpler problems are in fact equivalent to seemingly harder ones (up to constant-factors). Specifically, we show this to be the case for the version of the matroid secretary problem in which the matroid is not known in advance, and where it is known in advance. We also show that the version with known matroid structure, is equivalent to the problem where weights are not fully adversarial but drawn from a known pairwise-independent distribution.

cs.DS↗
arXiv2025

Fully Dynamic Euclidean Bi-Chromatic Matching in Sublinear Update Time

We consider the Euclidean bi-chromatic matching problem in the dynamic setting, where the goal is to efficiently process point insertions and deletions while maintaining a high-quality solution. Computing the minimum cost bi-chromatic matching is one of the core problems in geometric optimization that has found many applications, most notably in estimating Wasserstein distance between two distributions. In this work, we present the first fully dynamic algorithm for Euclidean bi-chromatic matching with sub-linear update time. For any fixed $\varepsilon > 0$, our algorithm achieves $O(1/\varepsilon)$-approximation and handles updates in $O(n^{\varepsilon})$ time. Our experiments show that our algorithm enables effective monitoring of the distributional drift in the Wasserstein distance on real and synthetic data sets, while outperforming the runtime of baseline approximations by orders of magnitudes.

cs.DS↗
arXiv2025

Equilibria and Learning in Modular Marketplaces

We envision a marketplace where diverse entities offer specialized "modules" through APIs, allowing users to compose the outputs of these modules for complex tasks within a given budget. This paper studies the market design problem in such an ecosystem, where module owners strategically set prices for their APIs (to maximize their profit) and a central platform orchestrates the aggregation of module outputs at query-time. One can also think about this as a first-price procurement auction with budgets. The first observation is that if the platform's algorithm is to find the optimal set of modules then this could result in a poor outcome, in the sense that there are price equilibria which provide arbitrarily low value for the user. We show that under a suitable version of the "bang-per-buck" algorithm for the knapsack problem, an $\varepsilon$-approximate equilibrium always exists, for any arbitrary $\varepsilon > 0$. Further, our first main result shows that with this algorithm any such equilibrium provides a constant approximation to the optimal value that the buyer could get under various constraints including (i) a budget constraint and (ii) a budget and a matroid constraint. Finally, we demonstrate that these efficient equilibria can be learned through decentralized price adjustments by module owners using no-regret learning algorithms.

cs.GT↗
arXiv2024

Learning biologically relevant features in a pathology foundation model using sparse autoencoders

Pathology plays an important role in disease diagnosis, treatment decision-making and drug development. Previous works on interpretability for machine learning models on pathology images have revolved around methods such as attention value visualization and deriving human-interpretable features from model heatmaps. Mechanistic interpretability is an emerging area of model interpretability that focuses on reverse-engineering neural networks. Sparse Autoencoders (SAEs) have emerged as a promising direction in terms of extracting monosemantic features from polysemantic model activations. In this work, we trained a Sparse Autoencoder on the embeddings of a pathology pretrained foundation model. We found that Sparse Autoencoder features represent interpretable and monosemantic biological concepts. In particular, individual SAE dimensions showed strong correlations with cell type counts such as plasma cells and lymphocytes. These biological representations were unique to the pathology pretrained model and were not found in a self-supervised model pretrained on natural images. We demonstrated that such biologically-grounded monosemantic representations evolved across the model's depth, and the pathology foundation model eventually gained robustness to non-biological factors such as scanner type. The emergence of biologically relevant SAE features was generalizable to an out-of-domain dataset. Our work paves the way for further exploration around interpretable feature dimensions and their utility for medical and clinical applications.

eess.IV↗
arXiv2024

Accelerating Retrieval-Augmented Generation

An evolving solution to address hallucination and enhance accuracy in large language models (LLMs) is Retrieval-Augmented Generation (RAG), which involves augmenting LLMs with information retrieved from an external knowledge source, such as the web. This paper profiles several RAG execution pipelines and demystifies the complex interplay between their retrieval and generation phases. We demonstrate that while exact retrieval schemes are expensive, they can reduce inference time compared to approximate retrieval variants because an exact retrieval model can send a smaller but more accurate list of documents to the generative model while maintaining the same end-to-end accuracy. This observation motivates the acceleration of the exact nearest neighbor search for RAG. In this work, we design Intelligent Knowledge Store (IKS), a type-2 CXL device that implements a scale-out near-memory acceleration architecture with a novel cache-coherent interface between the host CPU and near-memory accelerators. IKS offers 13.4-27.9x faster exact nearest neighbor search over a 512GB vector database compared with executing the search on Intel Sapphire Rapids CPUs. This higher search performance translates to 1.7-26.3x lower end-to-end inference time for representative RAG applications. IKS is inherently a memory expander; its internal DRAM can be disaggregated and used for other applications running on the server to prevent DRAM, which is the most expensive component in today's servers, from being stranded.

cs.CL↗
arXiv2024

Bounds on the Aspect Ratio of the Momentum Support of a 2D Collisionless Plasma

The relativistic Vlasov-Maxwell system is a kinetic model for collisionless plasmas. For the two-dimensional model, global well-posedness of this model is known and was proven by deriving global bounds on the momentum support of the particle density function. In this paper, we prove bounds on the magnitude of the momentum support in one direction depending on the magnitude of the support in the corresponding orthogonal direction.

math.AP↗
arXiv2024

Empowering Tuberculosis Screening with Explainable Self-Supervised Deep Neural Networks

Tuberculosis persists as a global health crisis, especially in resource-limited populations and remote regions, with more than 10 million individuals newly infected annually. It stands as a stark symbol of inequity in public health. Tuberculosis impacts roughly a quarter of the global populace, with the majority of cases concentrated in eight countries, accounting for two-thirds of all tuberculosis infections. Although a severe ailment, tuberculosis is both curable and manageable. However, early detection and screening of at-risk populations are imperative. Chest x-ray stands as the predominant imaging technique utilized in tuberculosis screening efforts. However, x-ray screening necessitates skilled radiologists, a resource often scarce, particularly in remote regions with limited resources. Consequently, there is a pressing need for artificial intelligence (AI)-powered systems to support clinicians and healthcare providers in swift screening. However, training a reliable AI model necessitates large-scale high-quality data, which can be difficult and costly to acquire. Inspired by these challenges, in this work, we introduce an explainable self-supervised self-train learning network tailored for tuberculosis case screening. The network achieves an outstanding overall accuracy of 98.14% and demonstrates high recall and precision rates of 95.72% and 99.44%, respectively, in identifying tuberculosis cases, effectively capturing clinically significant features.

eess.IV↗
arXiv2024

Limitations of Stochastic Selection with Pairwise Independent Priors

Motivated by the growing interest in correlation-robust stochastic optimization, we investigate stochastic selection problems beyond independence. Specifically, we consider the instructive case of pairwise-independent priors and matroid constraints. We obtain essentially-optimal bounds for contention resolution and prophet inequalities. The impetus for our work comes from the recent work of Caragiannis et al., who derived a constant-approximation for the single-choice prophet inequality with pairwise-independent priors. For general matroids, our results are tight and largely negative. For both contention resolution and prophet inequalities, our impossibility results hold for the full linear matroid over a finite field. We explicitly construct pairwise-independent distributions which rule out an omega(1/Rank)-balanced offline CRS and an omega(1/log Rank)-competitive prophet inequality against the (usual) oblivious adversary. For both results, we employ a generic approach for constructing pairwise-independent random vectors -- one which unifies and generalizes existing pairwise-independence constructions from the literature on universal hash functions and pseudorandomness. Specifically, our approach is based on our observation that random linear maps turn linear independence into stochastic independence. We then examine the class of matroids which satisfy the so-called partition property -- these include most common matroids encountered in optimization. We obtain positive results for both online contention resolution and prophet inequalities with pairwise-independent priors on such matroids, approximately matching the corresponding guarantees for fully independent priors. These algorithmic results hold against the almighty adversary for both problems.

cs.DS↗
arXiv2023

On Nonlinear Stability of Muskat Bubbles

In this paper we consider gravity-capillarity Muskat bubbles in 2D. We obtain a new approach to improve our result in [25]. Due to a new bubble-adapted formulation, the improvement is two fold. We significantly condense the proof and we now obtain the global well-posedness result for Muskat bubbles in critical regularity.

math.AP↗
arXiv2023

Combinatorial Stationary Prophet Inequalities

Numerous recent papers have studied the tension between thickening and clearing a market in (uncertain, online) long-time horizon Markovian settings. In particular, (Aouad and Sarita{ç} EC'20, Collina et al. WINE'20, Kessel et al. EC'22) studied what the latter referred to as the Stationary Prophet Inequality Problem, due to its similarity to the classic finite-time horizon prophet inequality problem. These works all consider unit-demand buyers. Mirroring the long line of work on the classic prophet inequality problem subject to combinatorial constraints, we initiate the study of the stationary prophet inequality problem subject to combinatorially-constrained buyers. Our results can be summarized succinctly as unearthing an algorithmic connection between contention resolution schemes (CRS) and stationary prophet inequalities. While the classic prophet inequality problem has a tight connection to online CRS (Feldman et al. SODA'16, Lee and Singla ESA'18), we show that for the stationary prophet inequality problem, offline CRS play a similarly central role. We show that, up to small constant factors, the best (ex-ante) competitive ratio achievable for the combinatorial prophet inequality equals the best possible balancedness achievable by offline CRS for the same combinatorial constraints.

cs.GT↗
arXiv2023

On Supermodular Contracts and Dense Subgraphs

We study the combinatorial contract design problem, introduced and studied by Dutting et. al. (2021, 2022), in both the single and multi-agent settings. Prior work has examined the problem when the principal's utility function is submodular in the actions chosen by the agent(s). We complement this emerging literature with an examination of the problem when the principal's utility is supermodular. In the single-agent setting, we obtain a strongly polynomial time algorithm for the optimal contract. This stands in contrast to the NP-hardness of the problem with submodular principal utility due to Dutting et. al. (2021). This result has two technical components, the first of which applies beyond supermodular or submodular utilities. This result strengthens and simplifies analogous enumeration algorithms from Dutting et. al. (2021), and applies to any nondecreasing valuation function for the principal. Second, we show that supermodular valuations lead to a polynomial number of breakpoints, analogous to a similar result by Dutting et. al. (2021) for gross substitutes valuations. In the multi-agent setting, we obtain a mixed bag of positive and negative results. First, we show that it is NP-hard to obtain any finite multiplicative approximation, or an additive FPTAS. This stands in contrast to the submodular case, where efficient computation of approximately optimal contracts was shown by Dutting et. al. (2022). Second, we derive an additive PTAS for the problem in the instructive special case of graph-based supermodular valuations, and equal costs. En-route to this result, we discover an intimate connection between the multi-agent contract problem and the notorious k-densest subgraph problem. We build on and combine techniques from the literature on dense subgraph problems to obtain our additive PTAS.

cs.GT↗