arXiv subjects

Sagnik Mukherjee

Publications and source records attributed to Sagnik Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

Multiplicity One for Unitary Ginzburg--Rallis Models over Local Fields

We prove multiplicity at most one for the unitary similitude Ginzburg--Rallis model over local fields of characteristic zero, for both the quasi-split and non-quasi-split groups. The theorem holds for all irreducible smooth representations over non-Archimedean fields and all irreducible Casselman--Wallach representations over the real field. We first describe the decomposition into parabolic double cosets and compute the required stabilizers. Over a non-Archimedean field we use character obstructions, localization, and transpose symmetry. Over the real field we use a Casimir identity and explicit normal vectors to prove the corresponding statement for distributions with prescribed infinitesimal character. The Gelfand--Kazhdan criterion and a dualizing involution then give the multiplicity bound.

math.RT↗

arXiv2026

ISO: An RLVR-Native Optimization Stack

Reinforcement learning with verifiable rewards (RLVR) advances the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood. We study this layer and functionally validate spectral inheritance: RLVR can reuse the base model's weight spectra while acquiring new behavior by adapting both the associated input and output singular frames. We operationalize this finding as Isospectral Optimization (ISO), an RLVR-native optimization stack with complementary offline and online instantiations. Offline, ISO-Merger composes shared-base specialists in fixed-spectrum frame coordinates without post-merge data, rollouts, or distillation, and achieves the highest aggregate scores among the data-free merging methods. Online, ISO-Optimizer applies AdamW or Muon directly to the frame variables under fixed base spectra, improving aggregate accuracy in the reported math and coding experiments. On Qwen3-4B-Base, ISO-AdamW reaches AdamW's 400-update accuracy in 280 updates with 1.5 X fewer updates and 27% less wall-clock time, and exceeds AdamW by 2.2 points at update 400. These results support a reusable RLVR design principle: inherit the spectrum, optimize the frames.

cs.LG↗

arXiv2026

Plancherel Decompositions and Distinctions for $\mathrm{Sp}_{2n}\backslash \mathrm{Gl}_{2n+1}$ and $P(\mathrm{Sp}_{2n})\backslash \mathrm{Gl}_{2n}$

Let $F$ be a non-Archimedean local field of characteristic zero. We determine the Plancherel decompositions of $\mathrm{Sp}_{2n}(F)\backslash\mathrm{GL}_{2n+1}(F)$ and $P(\mathrm{Sp}_{2n})(F)\backslash\mathrm{GL}_{2n}(F)$, where $P(\mathrm{Sp}_{2n})$ denotes the mirabolic subgroup of $\mathrm{Sp}_{2n}$, and study smooth distinction for both spaces. We carry out the local unfolding procedure of arXiv:1203.0039, Section 9.5, constructing unitary isomorphisms with degenerate Whittaker models by successive Fourier transforms. The isomorphism for the even model is already stated there in Example 9.5.17. The resulting Plancherel formulas are direct integrals of normalized parabolic inductions from the tempered duals of $\mathrm{GL}_n(F)\times\mathrm{GL}_{n+1}(F)$ and $\mathrm{GL}_n(F)\times\mathrm{GL}_n(F)$, respectively, with product Whittaker-Plancherel measures. In the odd case, the parameter map agrees with the prediction of arXiv:2409.04677. Using closed parabolic orbits and local Rankin-Selberg integrals, we prove that all representations induced from these tempered data are distinguished for the corresponding model. We also prove that essentially square-integrable representations are not distinguished for the odd model, and that supercuspidal representations are not distinguished for the even model. For the even model with $n=1,2$, we construct distinguished square-integrable representations outside the Plancherel support. Thus, the smooth tempered distinguished spectrum can be strictly larger than the corresponding $L^2$-spectrum. For $\mathrm{GL}_5(F)$, however, we prove that an irreducible tempered representation is $\mathrm{Sp}_4(F)$-distinguished if and only if it is induced from tempered representations of $\mathrm{GL}_2(F)$ and $\mathrm{GL}_3(F)$.

math.RT↗

arXiv2026

Does the High Energy LUX-ZEPLIN Event Suggest Hyperfine Atomic Dark Matter?

The LUX-ZEPLIN (LZ) Collaboration has reported a nuclear-recoil candidate at $248\pm23~({\rm stat})\pm23~({\rm sys})~{\rm keV}$ in an extended high energy search window. We investigate whether this event can arise from the hyperfine excitation of hydrogen-like atomic dark matter. For a TeV-scale dark atom, a hyperfine splitting near $340~{\rm keV}$ places xenon scattering close to the observed value by naturally selecting the high-velocity tail of the Galactic halo while suppressing the leading low-energy elastic response. The resulting endothermic kinematics predict a pronounced target hierarchy: the benchmark transition is inaccessible on Ar and Ge, lies close to threshold on Xe, and remains open on heavier targets such as W, which is specific to our model parameters. Because xenon probes the extreme high-speed tail, the signal exhibits a large annual modulation and a strong dependence on the assumed halo distribution. We also examine how the infall of the Large Magellanic Cloud enhances the high-speed tail of the Milky Way's local dark matter distribution, extending the kinematic reach to larger hyperfine splittings.

hep-ph↗

arXiv2026

Understanding LLM Parameter Update Sparsity through the Lens of Fisher

Recent studies have observed that parameter changes during language-model post-training can be concentrated in a small subset of coordinates. This phenomenon has been reported in reinforcement learning, on-policy distillation, and supervised fine-tuning on near-policy data. Its recurrence across different post-training paradigms suggests shared structure in training dynamics. In this paper, we examine this pattern through the diagonal model Fisher, which measures the sensitivity of the model's output distribution to individual parameters and is independent of any particular reward or teacher signal. Theoretically, we show that small diagonal Fisher leads to small expected gradients across a range of training objectives, providing a common explanation for sparse gradient updates. Empirically, we test this connection in RL and OPD. We find that Fisher identifies where gradients are concentrated, and fixed sparse masks selected from the initial Fisher retain a large proportion of the improvement from full training. Finally, we investigate the mechanisms underlying low Fisher in on-policy training. Our results show that high-probability next tokens tend to have similar parameter sensitivities, contributing to low Fisher. Together, these results establish the diagonal model Fisher as a unifying perspective linking update sparsity to on-policy training dynamics in LLM post-training.

cs.LG↗

arXiv2026

Constraining the Coexistence of Primordial Black Holes and Particle Dark Matter with Neutrino Observations

Primordial black holes (PBH) with a uniform mass scale could contribute up to 1\% of the gravitationally inferred dark matter relic abundance and remain consistent with observational limits over a large range of masses. In this case, the vast majority of the dark matter relic abundance is comprised of dark matter particles, such as WIMPs or FIMPs. Particle dark matter gravitationally captured around primordial black holes can form dense minispikes in which the annihilation rate is strongly enhanced. In this work, we investigate the constraints on the coexistence of PBHs and particle dark matter from high-energy neutrino observations. Relative to earlier analyses, we refine the treatment of the dark matter halo profile and its redshift evolution. We consider models of freeze-out and freeze-in dark matter, as well as Boltzmann-suppressed freeze-in. We present idealized IceCube event-based sensitivities together with conservative limits obtained by requiring that the predicted extragalactic neutrino intensity not exceed the upper envelope of the measured diffuse flux. We explore the constraints in terms of an idealized model with 100\% branching to neutrinos, we also discuss these results within the context fo a motivated gauged U(1)${}_{L_μ-L_τ}$ mediator model, emphasizing that a consistent particle-physics completion generally predicts correlated charged-lepton and neutrino final states.

hep-ph↗

arXiv2026

Minimal Freeze-in Dark Matter: Reviving electroweak doublet dark matter with Boltzmann suppressed freeze-in

Dark matter communicating with the Standard Model solely via electroweak interactions provides a compelling picture. However, thermal freeze-out of electroweak doublet dark matter is generically strongly excluded by direct detection. We show that SU(2)${}_L$ doublet fermion dark matter evades direct detection if its mass exceeds $10^{10}$ GeV. If the neutral Dirac fermion is split into a pseudo-Dirac pair (via high dimension operator) this limit can be relaxed to 300 GeV. Provided the dark matter mass is above the reheat temperature of the Universe, the production rate never exceeds the Hubble rate in cases of interest, thus the dark matter never thermalizes. We apply constraints from direct detection (e.g. LZ) and consider the discovery potential of Darwin. This scenario presents the most minimal model of freeze-in dark matter, and is both elegant and highly predictive.

hep-ph↗

arXiv2026

VASR: Variance-Aware Systematic Resampling for Reward-Guided Diffusion

Sequential Monte Carlo (SMC) samplers for reward-guided diffusion models often suffer from rapid lineage collapse: a few high-reward particles dominate the population within a handful of resampling steps, destroying diversity and degrading sample quality. We propose a variance-decomposition framework for reward-guided diffusion SMC that separates continuation variance $V_t^{\mathrm{cont}}$ from residual variance $V_t^{\mathrm{res}}$, revealing that high offspring-count variance under the commonly used multinomial resampling drives this collapse. This motivates \textsc{VASR} (Variance-Aware Systematic Resampling), which addresses both variance terms via variance-optimal mass allocation $m_t \propto w_t e^{r_t}$ (minimizing $V_t^{\mathrm{cont}}$) and systematic resampling (controlling $V_t^{\mathrm{res}}$). For latent diffusion models where intermediate rewards are noisy due to stochastic continuations, we propose \textsc{VASR-Max}, a deliberately biased high-selection variant for variance-sensitive reward optimization. Both methods are training-free, fully parallelizable, and add only linear overhead. On MNIST and CIFAR-10, VASR achieves as high as $26\%$ better FID than prior SMC methods while remaining 66 times faster than MCTS-based value methods at matched compute. On text-to-image generation, \textsc{VASR-Max} consistently outperforms the strongest SMC baseline across compute budgets and matches MCTS-based methods within 2.5--3% reward at high budgets while being approximately times faster.

cs.AI↗

arXiv2026

Next-to-Minimal Freeze-in Dark Matter

If the dark matter mass exceeds the highest temperature of the thermal bath, then dark matter production is Boltzmann suppressed. This opens new possibilities for dark matter model building. In particular, WIMP models that are experimentally excluded can be revived in this setting; conversely, freeze-in models, which would typically be beyond experimental reach, are potentially discoverable in the Boltzmann suppressed regime. In a recent letter, we highlighted these aspects for the case of electroweak doublet fermion dark matter assuming instantaneous inflationary reheating. Due to its elegance and simplicity, we coin this {\em Minimal Freeze-in} (MFI) Dark Matter. Here we consider next-to-minimal extensions of MFI dark matter. We present the implications for non-instantaneous reheating, including scenarios beyond the standard picture in which the Universe is initially matter dominated prior to reheating. Furthermore, we explore model variations within the electroweak dark matter scenario. Specifically, we consider fermion dark matter in higher representations of SU(2)${}_L$, exploring the current limits and the near-future discovery potential.

hep-ph↗

arXiv2026

Do We Need Adam? Surprisingly Strong and Sparse Reinforcement Learning with SGD in LLMs

Reinforcement learning (RL), particularly RL from verifiable reward (RLVR), has become a crucial phase of training large language models (LLMs) and a key focus of current scaling efforts. However, optimization practices in RL largely follow those of next-token prediction stages (e.g., pretraining and supervised fine-tuning), despite fundamental differences between RL and these stages highlighted by recent work. One such practice is the use of the AdamW optimizer, which is widely adopted for training large-scale transformers despite its high memory overhead. Our analysis shows that both momentum and adaptive learning rates in AdamW are less influential in RL than in SFT, leading us to hypothesize that RL benefits less from Adam-style per-parameter adaptive learning rates and momentum. Confirming this hypothesis, our experiments demonstrate that the substantially more memory-efficient SGD, which is known to perform poorly in supervised learning of large-scale transformers, matches or even outperforms AdamW in RL for LLMs. Remarkably, full fine-tuning with SGD updates fewer than 0.02% of model parameters without any sparsity-promoting regularization, more than 1000 times fewer than AdamW. Our analysis offers potential reasons for this update sparsity. These findings provide new insights into the optimization dynamics of RL in LLMs and show that RL can be substantially more parameter-efficient than previously recognized.

cs.LG↗

arXiv2026

Graph Neural Network Assisted Genetic Algorithm for Structural Dynamic Response and Parameter Optimization

The optimization of structural parameters, such as mass(m), stiffness(k), and damping coefficient(c), is critical for designing efficient, resilient, and stable structures. Conventional numerical approaches, including Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) simulations, provide high-fidelity results but are computationally expensive for iterative optimization tasks, as each evaluation requires solving the governing equations for every parameter combination. This study proposes a hybrid data-driven framework that integrates a Graph Neural Network (GNN) surrogate model with a Genetic Algorithm (GA) optimizer to overcome these challenges. The GNN is trained to accurately learn the nonlinear mapping between structural parameters and dynamic displacement responses, enabling rapid predictions without repeatedly solving the system equations. A dataset of single-degree-of-freedom (SDOF) system responses is generated using the Newmark Beta method across diverse mass, stiffness, and damping configurations. The GA then searches for globally optimal parameter sets by minimizing predicted displacements and enhancing dynamic stability. Results demonstrate that the GNN and GA framework achieves strong convergence, robust generalization, and significantly reduced computational cost compared to conventional simulations. This approach highlights the effectiveness of combining machine learning surrogates with evolutionary optimization for automated and intelligent structural design.

cs.NE↗

arXiv2025

Reinforcement Learning Finetunes Small Subnetworks in Large Language Models

Reinforcement learning (RL) yields substantial improvements in large language models (LLMs) downstream task performance and alignment with human values. Surprisingly, such large gains result from updating only a small subnetwork comprising just 5 percent to 30 percent of the parameters, with the rest effectively unchanged. We refer to this phenomenon as parameter update sparsity induced by RL. It is observed across all 7 widely used RL algorithms (e.g., PPO, GRPO, DPO) and all 10 LLMs from different families in our experiments. This sparsity is intrinsic and occurs without any explicit sparsity promoting regularizations or architectural constraints. Finetuning the subnetwork alone recovers the test accuracy, and, remarkably, produces a model nearly identical to the one obtained via full finetuning. The subnetworks from different random seeds, training data, and even RL algorithms show substantially greater overlap than expected by chance. Our analysis suggests that this sparsity is not due to updating only a subset of layers, instead, nearly all parameter matrices receive similarly sparse updates. Moreover, the updates to almost all parameter matrices are nearly full-rank, suggesting RL updates a small subset of parameters that nevertheless span almost the full subspaces that the parameter matrices can represent. We conjecture that the this update sparsity can be primarily attributed to training on data that is near the policy distribution, techniques that encourage the policy to remain close to the pretrained model, such as the KL regularization and gradient clipping, have limited impact.

cs.LG↗

arXiv2025

AURA: A Diagnostic Framework for Tracking User Satisfaction of Interactive Planning Agents

The growing capabilities of large language models (LLMs) in instruction-following and context-understanding lead to the era of agents with numerous applications. Among these, task planning agents have become especially prominent in realistic scenarios involving complex internal pipelines, such as context understanding, tool management, and response generation. However, existing benchmarks predominantly evaluate agent performance based on task completion as a proxy for overall effectiveness. We hypothesize that merely improving task completion is misaligned with maximizing user satisfaction, as users interact with the entire agentic process and not only the end result. To address this gap, we propose AURA, an Agent-User inteRaction Assessment framework that conceptualizes the behavioral stages of interactive task planning agents. AURA offers a comprehensive assessment of agent through a set of atomic LLM evaluation criteria, allowing researchers and practitioners to diagnose specific strengths and weaknesses within the agent's decision-making pipeline. Our analyses show that agents excel in different behavioral stages, with user satisfaction shaped by both outcomes and intermediate behaviors. We also highlight future directions, including systems that leverage multiple agents and the limitations of user simulators in task planning.

cs.CL↗

arXiv2025

Constraining the Coexistence of Freeze-in Dark Matter and Primordial Black Holes

Particle dark matter and primordial black holes (PBH) might coexist with appreciable cosmic abundances, with both contributing to the observed dark matter density $Ω_{\rm DM}$. Large populations of PBH (with $Ω_{\rm PBH}\sim Ω_{\rm DM}$) are tightly constrained for PBH heavier than $10^{-11} M_\odot$. However, large fractional abundances with $ f_{\rm PBH}\simeq Ω_{\rm PBH}/Ω_{\rm DM}\sim0.01$ are consistent with the limits on PBH for a wide range of PBH masses. Scenarios with significant populations of both particle dark matter and PBH are intriguing. Notably, if the particle dark matter has interactions with the Standard Model, new constraints arise due to pair-annihilations that are enhanced by the PBHs, resulting in dark matter indirect detection constraints on $f_{\rm PBH}$. Here we derive the bounds on mixed scenarios in which PBHs coexist with particle dark matter whose relic abundance is set via freeze-in (``FIMPs''). We show that while the restrictions on $f_{\rm PBH}$ are less constraining for FIMPs than WIMPs, modest bounds still arise for large classes of models. We examine both IR and UV freeze-in scenarios, including the case of ``superheavy'' particle dark matter with PeV scale mass.

hep-ph↗

arXiv2025

Boltzmann Suppressed Ultraviolet Freeze-in

If the dark matter mass $m$ exceeds the maximum temperature of the Universe ($T_{\rm max} < m$), then its production rate will be Boltzmann suppressed. The important implications of this Boltzmann suppression have been explored for dark matter freeze-in via renormalizable operators. Here we extend these considerations to the case of ultraviolet (UV) freeze-in for which freeze-in proceeds via non-renormalizable operators. The UV freeze-in variant has a number of appealing features, not least that a given effective field theory can describe a multitude of UV completions, and thus such analyses are model agnostic for a given high dimension freeze-in operator. We undertake model independent analyses of UV freeze-in for portal operators of general mass dimensions. Subsequently, we explore a number of specific examples, namely, Higgs portals, bino dark matter, and gravitino dark matter. Finally, we discuss how significant differences arise if one departs from the standard assumptions regarding inflationary reheating (i.e. transitions from an early matter dominated era to radiation domination). As a motivated example we examine the implications of early kination domination. Boltzmann suppressed UV freeze-in is well motivated and permits a number of compelling scenarios. In particular, we highlight that for $T_{\rm max} \sim$ 1 TeV it is feasible that the freeze-in mechanism is entirely realized within a couple of orders of magnitude of the TeV scale, making it experimentally accessible in contrast to traditional freeze-in scenarios.

hep-ph↗

arXiv2025

Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs

Chain-of-Thought (CoT) prompting enhances mathematical reasoning in large language models (LLMs) by enabling detailed step-by-step solutions. However, due to the verbosity of LLMs, the resulting reasoning chains can be long, making it harder to verify the reasoning steps and trace issues resulting from dependencies between the steps that may be farther away in the sequence of steps. Importantly, mathematical reasoning allows each step to be derived from a small set of premises, which are a subset of the preceding steps in the reasoning chain. In this paper, we present a framework that identifies the premises for each step, to improve the evaluation of reasoning. We restructure conventional linear reasoning chains into Premise Augmented Reasoning Chains (PARC) by introducing premise links, resulting in a directed acyclic graph where the nodes are the steps and the edges are the premise links. Through experiments with a PARC-based dataset that we built, namely PERL (Premises and ERrors identification in LLMs), we demonstrate that LLMs can reliably identify premises within complex reasoning chains. In particular, even open-source LLMs achieve 90% recall in premise identification. We also show that PARC helps to identify errors in reasoning chains more reliably. The accuracy of error identification improves by 6% to 16% absolute when step-by-step verification is carried out in PARC under the premises. Our findings highlight the utility of premise-centric representations in addressing complex problem-solving tasks and open new avenues for improving the reliability of LLM-based reasoning evaluations.

cs.CL↗

arXiv2025

ReasoningFlow: Semantic Structure of Complex Reasoning Traces

Large reasoning models (LRMs) generate complex reasoning traces with planning, reflection, verification, and backtracking. In this work, we introduce ReasoningFlow, a unified schema for analyzing the semantic structures of these complex traces. ReasoningFlow parses traces into directed acyclic graphs, enabling the characterization of distinct reasoning patterns as subgraph structures. This human-interpretable representation offers promising applications in understanding, evaluating, and enhancing the reasoning processes of LRMs.

cs.CL↗

arXiv2024

Infogent: An Agent-Based Framework for Web Information Aggregation

Despite seemingly performant web agents on the task-completion benchmarks, most existing methods evaluate the agents based on a presupposition: the web navigation task consists of linear sequence of actions with an end state that marks task completion. In contrast, our work focuses on web navigation for information aggregation, wherein the agent must explore different websites to gather information for a complex query. We consider web information aggregation from two different perspectives: (i) Direct API-driven Access relies on a text-only view of the Web, leveraging external tools such as Google Search API to navigate the web and a scraper to extract website contents. (ii) Interactive Visual Access uses screenshots of the webpages and requires interaction with the browser to navigate and access information. Motivated by these diverse information access settings, we introduce Infogent, a novel modular framework for web information aggregation involving three distinct components: Navigator, Extractor and Aggregator. Experiments on different information access settings demonstrate Infogent beats an existing SOTA multi-agent search framework by 7% under Direct API-Driven Access on FRAMES, and improves over an existing information-seeking web agent by 4.3% under Interactive Visual Access on AssistantBench.

cs.AI↗