arXiv subjects

Lav R. Varshney

Publications and source records attributed to Lav R. Varshney.

At least 19 recordsLinked to original sources

arXiv2026

Frame-Coded Legged Locomotion over Noisy Terrain

Open-loop multilegged locomotion over rough terrain has been interpreted as matter transport over a noisy channel: leg-ground interactions are discrete basic active contacts, terrain deletes or perturbs those contacts, and spatial redundancy concentrates the resulting thrust and arrival time. That construction is repetition-like because every module carries the same scalar locomotion task. It consequently provides neither a positive task rate nor a decoder that changes with the surviving contact set. Here we formulate locomotion instead as a quantized finite-frame expansion with erasures. A d-dimensional body-level command is mapped into N>d heterogeneous local contact commands. Rough terrain erases or corrupts frame coefficients, while a contact-gated compliant morphology physically realizes the weighted active-subframe decoder. For a linear-Gaussian model, mechanical equilibrium is exactly the posterior mean, tangent stiffness is posterior precision, and mechanical compliance is posterior covariance. Equal-norm Parseval frames are shown to be minimax optimal against one missing contact, two-contact robustness is governed by frame coherence, and a harmonic frame gives a directly realizable gait family. For independently surviving contacts of probability q, random Gaussian gait frames admit exact reconstruction at every analog dimension rate R q. Residual contact noise yields an asymptotic per-mode amplification 1/(q-R) and a vanishing mechanical stiffness margin at the threshold. An information-locomotion inequality and an exact incremental-redundancy rule direct the next gait component toward the softest task-relevant unresolved mode. The resulting analog frame-coding theorem establishes a finite relative redundancy and converse as part of a fundamental limit theory of legged locomotion.

cs.IT↗

arXiv2026

House-monotone multi-level apportionment has logarithmic quota discrepancy

Multi-level apportionment allocates integer seats through a hierarchy of groups. Schmidt-Kraepelin, Suksompong, and Wijaya proved that, at every fixed house size, lower and upper quota can be satisfied simultaneously; they also constructed house-monotone rules satisfying either quota separately. They left open whether one rule can satisfy lower quota, upper quota, and house monotonicity together, even when quota is required only relative to the root. We give a negative answer. For a full binary comb with $D$ equally entitled leaves, every house-monotone allocation sequence induces a sequence of seat recipients. Quota for the nested comb groups would force every grid-aligned prefix discrepancy to be below one. A midpoint embedding then bounds the full interval discrepancy by this quantity plus $1/2$, contradicting Schmidt's logarithmic lower bound. Conversely, a binary van der Corput seat schedule has comb-prefix error at most $\log D/(3\log 2)+1$. Thus the optimal worst-case error on the comb is $\Theta(\log D)$, and for sufficiently large finite $D$ no house-monotone quota rule exists. The proof isolates a static--dynamic gap: each house size admits a quota-feasible allocation, but the feasible allocations cannot be embedded into one monotone path. In quantization language, the result characterizes the order of the embedded-quantization penalty for progressive one-hot rounding on the comb.

cs.GT↗

arXiv2026

Quota and population monotonicity across house sizes are incompatible for apportionment to four states

Apportionment converts fractional entitlements into integer seat allocations. Quota requires each state to receive the floor or ceiling of its standard quota, whereas population monotonicity prohibits a state whose population weakly increases from losing a seat to a state whose population weakly decreases. G\"olz, Peters, and Procaccia recently removed the order-preservation assumptions used in classical incompatibility results by giving a five-state construction; together with the three-state Webster possibility result, this left four states as the unresolved boundary. We prove that no deterministic four-state apportionment solution satisfies both axioms under their definition, which permits the compared house sizes to differ. The proof is a finite logical gadget. Conditional on one quota choice at a central profile, twelve auxiliary profiles encode three bits and force a frustrated cycle. The argument uses only transfers between states whose populations are unchanged and assumes neither anonymity, neutrality, order preservation, homogeneity, nor other regularity conditions. It also applies to relative population monotonicity. Geometrically, the result is a global compatibility obstruction for quota-constrained lattice rounding, rather than an average-distortion bound.

cs.GT↗

arXiv2026

Agentic AI Orchestration of Heterogeneous Economic Models for Rapid, Multi-scenario Analysis of Energy Crises

Rigorous economic models can take months to construct, yet energy crises demand decisions from policymakers within days or even hours. Any disruption in energy markets is not isolated but rapidly disseminates through interlinked global systems. Off-the-shelf models that already exist typically focus only on limited aspects of the system and are distributed across research groups, programming languages, software architectures not designed for model integration, and incompatible formats. Integrating these models manually can take longer than the crisis itself, forcing analysts to rely on whichever models are easiest to connect and leaving consequential scenarios unexplored. Policymakers must make rapid decisions with obstructed and limited information. We show that large language models can perform the critical integration directly. The system constructs internally consistent scenarios, translates assumptions into model-specific inputs, executes existing economic and physical models in dependency order, and synthesizes outputs tailored to policymakers. The language model generates no quantitative results: every reported value is reproduced directly from an underlying model run, remains traceable to its source and is subject to analyst approval at each stage. We develop a LLM framework that coordinates 16 models of oil, natural gas, shipping, water, helium, fertilizer and macroeconomic equilibrium. The framework is applied across five scenarios to assess the 2026 closure of the Strait of Hormuz and refreshed weekly for eight weeks as events on the ground continued to unfold. By linking models that already exist and reading them as a suite rather than in isolation, this architecture mobilizes distributed scientific models rapidly during energy and geopolitical disruptions while keeping any single model's assumptions from driving the conclusion.

econ.GN↗

arXiv2026

Regret-weighted Bayes Fusion for Distributed Experimental Design

We study distributed experimental design with multiple candidate experiments, where local sites possess only partial information and transmit design recommendations to a fusion center. Unlike centralized design, in which the experiment that maximizes expected information gain can be selected directly, distributed design requires combining heterogeneous and potentially conflicting local recommendations. Formulating as a multi-class Bayes fusion problem, centralized oracle design is treated as an unknown label and each site is characterized by a local recommendation mechanism. The proposed fusion rule minimizes posterior expected information regret, rather than merely maximizing the number of local votes or the posterior probability (MAP) of the oracle label. This distinction is essential because different incorrect experimental choices may incur different losses in information gain. We show that majority vote is optimal only under restrictive symmetry assumptions and can otherwise be strictly suboptimal. Regret-weighted multi-class Chernoff bounds are derived to identify the pairwise separations governing distributed design performance. Numerical studies identify two operational regimes: MAP is effective when oracle-label accuracy and information regret are aligned, while regret-weighted Bayes fusion reduces information loss when the most probable oracle label is not the lowest-regret decision.

math.ST↗

arXiv2026

Two-player Alternate Uses Test: A Controlled Testbed for Interactive Human-AI and Human-Human Co-Creation

Controlled research on AI ideation typically compares independent agents, while field studies of human-AI collaboration sacrifice experimental control. We introduce a controlled, two-player extension of the Alternate Uses Test (AUT) that enables comparison of human-human and human-AI co-creation under matched interactive conditions, alongside calibrated non-interactive baselines. The platform supports decomposition of performance into three typically confounded factors: participant traits, partner perceptions, and content dynamics. An in-person pilot (N = 62) demonstrates its utility. Under matched time limits, originality with a GPT-4 partner is statistically equivalent to that with a human partner. Approach motivation (BAS Drive) moderates whether interactive partnership benefits originality, and self-reported cognitive outsourcing predicts lower originality specifically in human-human dyads. Prior exposure to highly creative ideas improves later performance, suggesting a "seeding" intervention. We release the platform, code, and dataset as a shared testbed for controlled studies of human-AI co-creation.

cs.HC↗

arXiv2026

Collective Cognition in Hybrid Groups: A Network Science Synthesis

The growing integration of AI agents into human teams calls for a principled understanding of how collective intelligence emerges in hybrid systems. Recent frameworks clarify how attention, memory, and reasoning differences shape human-AI interaction at the individual and dyadic levels, but a formal account of how these differences scale to group-level dynamics is lacking. Most network science has examined either human-only or multi-agent AI-only systems, leaving open how its findings and parametrizations translate to hybrid groups. This chapter synthesizes network science, collective cognition, and multi-agent systems through the lens of attention, memory, and reasoning. We review how task environments, group topologies, agent-level processes, and incentive structures shape collective outcomes in human-only and AI-only networks, then examine how these results extend to hybrid settings, conceptualizing hybrid networks as heterogeneous human-AI nodes and links with distinct individual and transactive constraints. Our comparative analysis identifies which network effects are robust across agent types and which require revision, and highlights configurations that were peripheral in single-type traditions, such as human gatekeepers of AI sub-networks, but become structurally central in hybrid teams. Integrating a cognitive systems perspective with network science, we clarify how established exploration-exploitation and efficiency-redundancy trade-offs may operate differently in hybrid teams, and conclude with implications for organizational design, governance, and the responsible development of hybrid intelligence systems.

cs.HC↗

arXiv2026

CreativityNeuro: Steering Language Model Weights to Improve Divergent Thinking and Reduce Mode Collapse

Divergent thinking is a crucial aspect of creativity, yet large language models (LLMs) tend to consistently generate similar responses to open-ended questions, in what has been termed the artificial hivemind effect. Here, we introduce CreativityNeuro, a data-free method for enhancing divergent thinking in LLMs via contrastive weight steering. We evaluate our method across multiple creativity assessments and report several main findings. On the Divergent Association Task (DAT), a vocabulary-space creativity test, CreativityNeuro improves performance by up to 14 human percentile points. Next, in a large-scale human evaluation (N=720) on the Alternative Uses Test (AUT) and the Task Task, CreativityNeuro achieves significant improvements in originality, surprise, and creativity, transferring to longer-form and more open-ended tasks. Importantly, we find that across all three tasks, CreativityNeuro demonstrably reduces measures of mode collapse. Moreover, activation steering achieves comparable performance to CreativityNeuro on the DAT, but it does not transfer to the AUT and Task Task, demonstrating the effectiveness of weight-space steering in generalizing to unseen tasks. In conclusion, CreativityNeuro improves divergent thinking and reduces mode collapse without requiring behavioral data, re-training, or gradient-based fine-tuning, providing a straightforward way to enhance LLM performance in creative domains.

cs.AI↗

arXiv2026

A P\={a}ninian Foundation for Indic Language Processing

More than a billion people communicate in Indic languages, yet the natural language processing infrastructure serving them remains fragmented and underdeveloped. The cause is structural: the field organizes its tools and benchmarks around individual languages or small subsets of genealogical language families, building separate analyzers, parsers, and datasets for each language and starting over for the next. This overlooks a deep regularity. Through more than two millennia of convergence around Sanskrit, Indic languages came to share a morphosyntactic architecture formalized in P\={a}nini's grammar, the Ast\={a}dhy\={a}y\={i}. This cuts across genealogical lines, uniting languages through a common framework. We argue that this P\={a}ninian framework supplies a unifying computational architecture the field has lacked, and that benchmarks grounded explicitly in it would make Indic language systems more accurate, more data-efficient, and more transferable, effectively merging many apparently disparate and sparse Indic language resources into a single high-resource metalanguage bedrock. We propose a four-part benchmark suite to render this shared architecture explicit, measurable, and ready to be leveraged for practical applications. Moreover, we underscore the question it raises for interpretability research: whether neural models trained on these languages come to represent P\={a}nini's categories on their own.

cs.CL↗

arXiv2026

Distributed Experimental Design: Bayes-optimal Fusion of Local Designs

We develop a decision-theoretic framework for distributed Bayesian experimental design in which local agents evaluate candidate experiments using expected information gain and transmit their local design decisions to a fusion center. Unlike centralized Bayesian design, where all likelihood components and information-gain values are available to a single planner, the fusion center in the distributed setting chooses a global experiment from compressed local recommendations. We derive the Bayes-optimal fusion rule, which selects the experiment with largest conditional expected centralized information gain given the observed local design decisions. This rule is analogous in spirit to optimal fusion rules in distributed detection, but differs fundamentally because the underlying utility is expected information gain and the resulting loss is information-gain regret rather than classification error. We also establish information-loss bounds and identify conditions under which the decision-only fusion rule is asymptotically equivalent to the centralized design. Numerical experiments show that Bayes-optimal fusion closely approximates the centralized oracle, whereas majority voting can be highly suboptimal when a minority of sites carry disproportionate information.

stat.AP↗

arXiv2026

Information Lattice Learning as Probabilistic Graphical Model Structure Learning

Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain. When the signal is a probability mass function, we show the probabilistic rules learned by ILL admit a natural probabilistic graphical model (PGM) interpretation and develop this interpretation in detail. A partition in ILL induces a deterministic quotient variable, and a rule is the marginal law of that quotient variable. A rule set is therefore a collection of marginal constraints over interpretable abstractions. General lifting is the feasible family of all joint distributions satisfying those constraints, while special lifting chooses a maximum-ignorance reconstruction, implemented in ILL by an L2 uniformity principle closely related to maximum entropy. Under a Shannon-entropy lifting, the same constraints yield a log-linear factor graph whose factors are indexed by learned abstractions. The information lattice itself, however, is not a Bayesian network: its edges encode refinement and coarsening of abstractions, not conditional dependence. Thus ILL is best viewed as structure learning for interpretable constraint-based factor graphs over quotient variables. This view clarifies how ILL relates to graphical models and maximum entropy models, while suggesting new directions for inference, identifiability, and hybrid symbolic-probabilistic learning.

cs.LG↗

arXiv2026

Optimal Guarantees for Auditing Rényi Differentially Private Machine Learning

We study black-box auditing for machine learning algorithms that claim R \ 'enyi differential privacy (RDP) guarantees. We introduce an auditing framework, based on hypothesis testing, that directly estimates Rényi divergence between neighboring executions using the Donsker-Varadhan (DV) variational estimator. Our analysis yields explicit and non-asymptotic confidence intervals for RDP auditing via class-restricted DV estimators, separating statistical estimation error from algorithmic privacy leakage. We prove matching minimax lower bounds showing that, up to logarithmic factors, our sample-complexity guarantees are information-theoretically optimal, thereby establishing the first optimal guarantees for auditing RDP via DV estimators. Empirically, we instantiate our framework for auditing DP-SGD in a fully black-box setting. Across MNIST and CIFAR-10, and over a wide range of privacy regimes, our auditors produce a strong overall improvement on empirical RDP lower bounds compared to prior state-of-the-art black-box methods especially at small and moderate Rényi orders where accurate auditing is most challenging.

cs.LG↗

arXiv2026

Containment Verification: AI Safety Guarantees Independent of Alignment

Agentic frameworks are the software layer through which AI agents act in the world. Existing safety methods intervene on the model and therefore remain conditional on unverifiable properties of learned behavior. We introduce containment verification, which locates safety guarantees in the agentic framework itself. Under havoc oracle semantics, the AI is modeled as an unconstrained oracle over the framework's typed action space, and the verified containment layer must enforce the boundary policy for every typed action value the AI can emit. For boundary-enforceable properties, expressed over modeled boundary events, action arguments, and state, we prove a universal guarantee by forward-simulation refinement and mechanize it in Dafny. We instantiate the paradigm by verifying PocketFlow, a minimalist agentic LLM framework, and use an agentic synthesis pipeline to generate the specification, operational model, and refinement proof under an information barrier against tautological specifications. To our knowledge, this is the first deductive formal verification of an agentic framework. The guarantee is independent of alignment because it quantifies over the framework's typed action boundary rather than over model behavior.

cs.AI↗

arXiv2026

Hiding in Plain Sight: Detectability-Aware Antidistillation of Reasoning Models

Distillation via sampling reasoning traces exposes closed-source frontier models to adversarial third parties who can bypass their guardrails and misappropriate their capabilities. Antidistillation methods aim to address this by poisoning reasoning traces to hinder student model learning while preserving teacher performance. However, current methods overlook detectability, both semantic and syntactic, which erodes trust in the teacher's outputs and signals the defense's presence to adversaries. We address this gap by formulating antidistillation as a Stackelberg game whose constraint set explicitly encodes detectability, and show that perturbing sparingly offers an effective, less detectable alternative to poisoning the full trace. Drawing on mechanistic interpretability, we identify thought anchors, sentences with disproportionate counterfactual influence on model outputs, as a principled sparse target: critical to reasoning yet minimally detectable. We instantiate this in TraceGuard, a training-free, black-box proof-of-concept that locates thought anchors via branching-token detection and poisons them to degrade student distillation while preserving trace coherence.

cs.CR↗

arXiv2026

Context-Gated Associative Retrieval: From Theory to Transformers

Hopfield networks and their generalizations have established deep connections among biological associative memories, statistical physics, and transformers. Yet most models treat retrieval as a fixed query-to-memory mapping, ignoring the role of external context in recall. In this work, we propose a two-stage associative memory architecture, wherein a context-gate subcircuit reshapes the retrieval energy landscape before and during recall. We show theoretically that context gating increases inter-memory separation while inducing sparsity, translating into exponential improvements in retrieval. Crucially, we prove that the system admits a unique self-consistent fixed point, revealing that the resulting retrieval state is driven by both a direct contextual bias and a second-order retrieval-gate feedback loop. We then bridge this theory to transformers; specifically, we evaluate a first-order approximation on Llama-3, confirming that in-context learning acts as context-gated retrieval. Native dynamics mirror our theory: context localizes a memory subspace, enabling the zero-shot query to cleanly discriminate. Ultimately, this framework provides a mechanistic link between associative memory theory and LLM phenomenology.

cond-mat.dis-nn↗

arXiv2026

Skip-It? Theoretical Conditions for Layer Skipping in Vision-Language Models

Vision-language models achieve incredible performance across a wide range of tasks, but their large size makes inference costly. Recent work has shown that multimodal processing contains significant redundancies, making it possible to skip certain layers with minimal performance loss. Yet current pruning techniques remain ad-hoc, relying on heuristics or hyperparameter sweeps rather than principled criteria for determining when layer skipping is beneficial. In this paper, we propose a unified framework that characterizes the redundancy conditions under which pruning can enhance efficiency without sacrificing performance. Central to our approach are experimentally verifiable and interpretable notions of redundancy that can be evaluated without requiring downstream task performance as a metric. Applying this framework, we corroborate prior findings that both early and late vision tokens are redundant across models, and we validate our conditions by showing they align with actual performance degradation. Beyond these empirical results, our framework provides a theoretically grounded understanding of redundancy in VLMs and unifies many of the ideas behind modern layer-skipping techniques.

cs.AI↗

arXiv2026

Foundation Models for Discovery and Exploration in Chemical Space

Accurate prediction of atomistic, thermodynamic, and kinetic properties from molecular structures underpins materials innovation. Existing computational and experimental approaches lack the scalability required to navigate chemical space efficiently. Scientific foundation models trained on large unlabelled datasets offer a path towards navigating chemical space across application domains. Here, we develop MIST, a family of molecular foundation models with up to an order of magnitude more parameters and data than prior works. Trained using a novel tokenizer, Smirk, which comprehensively captures nuclear, electronic, and geometric information, MIST learns a diverse range of molecules. MIST models have been fine-tuned to predict more than 400 structure-property relationships and have been shown to match or exceed state-of-the-art performance across diverse benchmarks, from physiology to electrochemistry. We demonstrate the ability of these models to solve real-world problems across chemical space from multiobjective electrolyte solvent screening to stereochemical reasoning for organometallics and mixture property prediction. The clearest demonstration of a foundation model is its ability to solve problems that were neither explicit targets of training nor central to the intentions of its developers. We identify olfactory perception mapping as such a problem, and show that MIST accurately predicted scent profiles and learned a hierarchical representation of olfactory space consistent with hyperbolic geometry. We formulated hyperparameter aware Bayesian neural scaling laws which eliminate the need for hyperparameter sweeps at every scale, making training large compute-optimal models feasible on a limited compute budget. The methods and findings presented here represent a significant step towards accelerating materials discovery, design, and optimization using foundation models.

physics.chem-ph↗

arXiv2026

A Theoretical Game of Attacks via Compositional Skills

As large language models grow increasingly capable, concerns about their safe deployment have intensified. While numerous alignment strategies aim to restrict harmful behavior, these defenses can still be circumvented through carefully designed adversarial prompts. In this work, we introduce a theoretical framework that formalizes a game between an attacker and a defender. Within this framework, we design a theoretical best-response attack strategy and show that it is closely related to many existing adversarial prompting methods. We further analyze the resulting game, characterize its equilibria, and reveal inherent advantages for the attacker. Drawing on our theoretical analysis, we also derive a provably optimal defense strategy. Empirically, we evaluate a practical instantiation of the theoretically optimal attack and observe stronger performance relative to existing adversarial prompting approaches in diverse settings encompassing different LLMs and benchmarks.

cs.CL↗