arXiv subjects

Naman Agarwal

Publications and source records attributed to Naman Agarwal.

At least 19 recordsLinked to original sources

arXiv2026

Quadratic Axion Couplings in String Theory

Axions and axion-like particles are a compelling candidate for physics beyond the standard model. While many axion searches are focused on the linear coupling to photons $θF \tilde{F}$, the possibility of a quadratic coupling to the electromagnetic kinetic term, $θ^2 F^2$, leads to novel phenomenology and new opportunities for testing axion-like particles. In this work we propose mechanisms for generating this coupling in string theory, which can be broadly classified as classical, perturbative, and non-perturbative. In benchmark examples, we find that both perturbative and non-perturbative quantum contributions such as instantons lead to couplings that are suppressed, $g \ll 1$ in units of $1/f^2$ where $f$ is axion decay constant, though easily larger than analogous coupling of the QCD axion that is generated through loops of charged pions. These analyses suggest that quadratic axion couplings to gauge fields are ubiquitous in string theory, and should be taken seriously as a probe of the string theory axiverse, both of string theory candidates for dynamical axions, such as dark matter or dark energy, and for spectroscopy of the string theory axiverse.

hep-th↗

arXiv2026

The Bayesian Geometry of Transformer Attention

Transformers often appear to perform Bayesian reasoning in context, but verifying this rigorously has been impossible: natural data lack analytic posteriors, and large models conflate reasoning with memorization. We address this by constructing \emph{Bayesian wind tunnels} -- controlled environments where the true posterior is known in closed form and memorization is provably impossible. In these settings, small transformers reproduce Bayesian posteriors with $10^{-3}$-$10^{-4}$ bit accuracy, while capacity-matched MLPs fail by orders of magnitude, establishing a clear architectural separation. Across two tasks -- bijection elimination and Hidden Markov Model (HMM) state tracking -- we find that transformers implement Bayesian inference through a consistent geometric mechanism: residual streams serve as the belief substrate, feed-forward networks perform the posterior update, and attention provides content-addressable routing. Geometric diagnostics reveal orthogonal key bases, progressive query-key alignment, and a low-dimensional value manifold parameterized by posterior entropy. During training this manifold unfurls while attention patterns remain stable, a \emph{frame-precision dissociation} predicted by recent gradient analyses. Taken together, these results demonstrate that hierarchical attention realizes Bayesian inference by geometric design, explaining both the necessity of attention and the failure of flat architectures. Bayesian wind tunnels provide a foundation for mechanistically connecting small, verifiable systems to reasoning phenomena observed in large language models.

cs.LG↗

arXiv2026

Gradient Dynamics of Attention: How Cross-Entropy Sculpts Bayesian Manifolds

Transformers empirically perform precise probabilistic reasoning in carefully constructed ``Bayesian wind tunnels'' and in large-scale language models, yet the mechanisms by which gradient-based learning creates the required internal geometry remain opaque. We provide a complete first-order analysis of how cross-entropy training reshapes attention scores and value vectors in a transformer attention head. Our core result is an \emph{advantage-based routing law} for attention scores, \[ \frac{\partial L}{\partial s_{ij}} = α_{ij}\bigl(b_{ij}-\mathbb{E}_{α_i}[b]\bigr), \qquad b_{ij} := u_i^\top v_j, \] coupled with a \emph{responsibility-weighted update} for values, \[ Δv_j = -η\sum_i α_{ij} u_i, \] where $u_i$ is the upstream gradient at position $i$ and $α_{ij}$ are attention weights. These equations induce a positive feedback loop in which routing and content specialize together: queries route more strongly to values that are above-average for their error signal, and those values are pulled toward the queries that use them. We show that this coupled specialization behaves like a two-timescale EM procedure: attention weights implement an E-step (soft responsibilities), while values implement an M-step (responsibility-weighted prototype updates), with queries and keys adjusting the hypothesis frame. Through controlled simulations, including a sticky Markov-chain task where we compare a closed-form EM-style update to standard SGD, we demonstrate that the same gradient dynamics that minimize cross-entropy also sculpt the low-dimensional manifolds identified in our companion work as implementing Bayesian inference. This yields a unified picture in which optimization (gradient flow) gives rise to geometry (Bayesian manifolds), which in turn supports function (in-context probabilistic reasoning).

stat.ML↗

arXiv2026

Geometric Scaling of Bayesian Inference in LLMs

Recent work has shown that small transformers trained in controlled "wind-tunnel'' settings can implement exact Bayesian inference, and that their training dynamics produce a geometric substrate -- low-dimensional value manifolds and progressively orthogonal keys -- that encodes posterior structure. We investigate whether this geometric signature persists in production-grade language models. Across Pythia, Phi-2, Llama-3, and Mistral families, we find that last-layer value representations organize along a single dominant axis whose position strongly correlates with predictive entropy, and that domain-restricted prompts collapse this structure into the same low-dimensional manifolds observed in synthetic settings. To probe the role of this geometry, we perform targeted interventions on the entropy-aligned axis of Pythia-410M during in-context learning. Removing or perturbing this axis selectively disrupts the local uncertainty geometry, whereas matched random-axis interventions leave it intact. However, these single-layer manipulations do not produce proportionally specific degradation in Bayesian-like behavior, indicating that the geometry is a privileged readout of uncertainty rather than a singular computational bottleneck. Taken together, our results show that modern language models preserve the geometric substrate that enables Bayesian inference in wind tunnels, and organize their approximate Bayesian updates along this substrate.

cs.LG↗

arXiv2026

Toward an Effective Theory of the Volume Modulus

We investigate the 4-dimensional effective theory of the warped volume modulus in the presence of stabilizing effects from gaugino condensation by analyzing the linearized 10-dimensional supergravity equations of motion. Warping is generally expected to scale down the masses of bulk modes to the IR scale at the tip of a throat. We find that the mass of the warped volume modulus evades expectations and is largely insensitive to the effects of warping, even in strongly warped backgrounds. Instead, the mass is parametrically tied to the 4-dimensional AdS curvature scale $m^2 \sim {\mathcal O}(1) |\hat R_{\rm AdS}|$, presenting a challenge for scale separation in these backgrounds. We trace this effect to a universal contribution arising from the 10-dimensional equations of motion, and comment on the importance of a 10-dimensional treatment of the warped volume modulus for effective field theories and model building.

hep-th↗

arXiv2026

LUMOS: Large User MOdels for User Behavior Prediction

User behavior prediction at scale remains a critical challenge for online B2C platforms. Traditional approaches rely heavily on task-specific models and domain-specific feature engineering. This is time-consuming, computationally expensive, and requires domain expertise and therefore, not scalable. We present LUMOS (Large User MOdel Series), a transformer-based architecture that eliminates task-specific models and manual feature engineering by learning multiple tasks jointly using only raw user activity data. LUMOS introduces a novel cross-attention mechanism that conditions predictions on future known events (e.g., holidays, sales, etc.), enabling the model to predict complex behavior patterns like "how will upcoming holidays affect user engagement?" The architecture also employs multi-modal tokenization, combining user activities, event context, and static user demographic attributes into rich representations processed through specialized embedding pathways. Through extensive experiments on a production dataset spanning 1.7 trillion user activity tokens from 250 million users, we demonstrate that LUMOS achieves superior performance compared to traditional task-specific models. Across 5 tasks with established baselines, we achieve an average improvement of 0.025 in ROC-AUC for binary classification tasks and 4.6\% reduction in MAPE for regression tasks. Online A/B testing validates these improvements translate to measurable business impact with a 3.15\% increase in Daily Active Users.

cs.LG↗

arXiv2026

The Percept-V Challenge: Can Multimodal LLMs Crack Simple Perception Problems?

Cognitive science research treats visual perception, the ability to understand and make sense of a visual input, as one of the early developmental signs of intelligence. Its TVPS-4 framework categorizes and tests human perception into seven skills such as visual discrimination, and form constancy. Do Multimodal Large Language Models (MLLMs) match up to humans in basic perception? Even though there are many benchmarks that evaluate MLLMs on advanced reasoning and knowledge skills, there is limited research that focuses evaluation on simple perception. In response, we introduce Percept-V, a dataset containing 6000 program-generated uncontaminated images divided into 30 domains, where each domain tests one or more TVPS-4 skills. Our focus is on perception, so we make our domains quite simple and the reasoning and knowledge required for solving them are minimal. Since modern-day MLLMs can solve much more complex tasks, our a-priori expectation is that they will solve these domains very easily. Contrary to our belief, our experiments show a weak performance of SoTA proprietary and open-source MLLMs compared to very high human performance on Percept-V. We find that as number of objects in the image increases, performance goes down rather fast. Our experiments also identify the perception skills that are considerably harder for all models.

cs.CL↗

arXiv2026

Energy density driven ultrafast electronic excitations in a cuprate superconductor

Controlling nonequilibrium dynamics in quantum materials requires ultrafast probes with spectral selectivity. We report femtosecond reflectivity measurements on the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ using free-electron laser extreme-ultraviolet (23.5--177~eV) and near-infrared (1.5~eV) pump pulses. EUV pulses access deep electronic states, while NIR light excites valence-band transitions. Despite these distinct channels, both schemes produce nearly identical dynamics: above $T_c$, excitations relax through fast (100--300~fs) and slower (1--5~ps) channels; below $T_c$, a delayed component signals quasiparticle recombination and condensate recovery. We find that when electronic excitations are involved, the ultrafast response is governed mainly by absorbed energy rather than by the microscopic nature of the excitation. In contrast, bosonic driving in the THz or mid-infrared produces qualitatively different dynamics. By demonstrating that EUV excitation of a correlated superconductor yields macroscopic dynamics converging with those from optical pumping, this work defines a new experimental paradigm: FEL pulses at core-level energies provide a powerful means to probe and control nonequilibrium electronic states in quantum materials on their intrinsic femtosecond timescales. This establishes FEL-based EUV pumping as a new capability for ultrafast materials science, opening routes toward soft X-ray and attosecond studies of correlated dynamics.

cond-mat.supr-con↗

arXiv2025

Ultrafast surface melting of orbital order in La0.5Sr1.5MnO4

Understanding how light modifies long-range order in quantum materials is key to improving our ability to control functionality. However, this is challenging if the response is heterogeneous. Here we address the most common form of light-induced heterogeneity, surface melting, and measure the dynamics of orbital order in the layered manganite, La0.5Sr1.5MnO4. We isolate the surface dynamics from the bulk by measuring the orbital truncation rod as well as orbital Bragg peak. After photoexcitation, the orbital Bragg peak shows an unusual narrowing, which suggests an increase in the correlation length in the probed volume. In contrast, the correlation length at the surface decreases. These differences can be reconciled if the material is heterogeneous, and light melts a less ordered surface. By isolating the surface response, we determine that the loss of long-range order is an incoherent process, which is likely accompanied by the formation of local polarons.

cond-mat.str-el↗

arXiv2025

FutureFill: Fast Generation from Convolutional Sequence Models

We address the challenge of efficient auto-regressive generation in sequence prediction models by introducing FutureFill, a general-purpose fast generation method for any sequence prediction algorithm based on convolutional operators. FutureFill reduces generation time from quadratic to quasilinear in the context length. Moreover, when generating from a prompt, it requires a prefill cache whose size grows only with the number of tokens to be generated, often much smaller than the caches required by standard convolutional or attention based models. We validate our theoretical claims with experiments on synthetic tasks and demonstrate substantial efficiency gains when generating from a deep convolutional sequence prediction model.

cs.LG↗

arXiv2025

Benchmarking Neural Network Training Algorithms

Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.

cs.LG↗

arXiv2025

How far away are truly hyperparameter-free learning algorithms?

Despite major advances in methodology, hyperparameter tuning remains a crucial (and expensive) part of the development of machine learning systems. Even ignoring architectural choices, deep neural networks have a large number of optimization and regularization hyperparameters that need to be tuned carefully per workload in order to obtain the best results. In a perfect world, training algorithms would not require workload-specific hyperparameter tuning, but would instead have default settings that performed well across many workloads. Recently, there has been a growing literature on optimization methods which attempt to reduce the number of hyperparameters -- particularly the learning rate and its accompanying schedule. Given these developments, how far away is the dream of neural network training algorithms that completely obviate the need for painful tuning? In this paper, we evaluate the potential of learning-rate-free methods as components of hyperparameter-free methods. We freeze their (non-learning rate) hyperparameters to default values, and score their performance using the recently-proposed AlgoPerf: Training Algorithms benchmark. We found that literature-supplied default settings performed poorly on the benchmark, so we performed a search for hyperparameter configurations that performed well across all workloads simultaneously. The best AlgoPerf-calibrated learning-rate-free methods had much improved performance but still lagged slightly behind a similarly calibrated NadamW baseline in overall benchmark score. Our results suggest that there is still much room for improvement for learning-rate-free methods, and that testing against a strong, workload-agnostic baseline is important to improve hyperparameter reduction techniques.

cs.LG↗

arXiv2025

Training neural networks faster with minimal tuning using pre-computed lists of hyperparameters for NAdamW

If we want to train a neural network using any of the most popular optimization algorithms, we are immediately faced with a dilemma: how to set the various optimization and regularization hyperparameters? When computational resources are abundant, there are a variety of methods for finding good hyperparameter settings, but when resources are limited the only realistic choices are using standard default values of uncertain quality and provenance, or tuning only a couple of the most important hyperparameters via extremely limited handdesigned sweeps. Extending the idea of default settings to a modest tuning budget, Metz et al. (2020) proposed using ordered lists of well-performing hyperparameter settings, derived from a broad hyperparameter search on a large library of training workloads. However, to date, no practical and performant hyperparameter lists that generalize to representative deep learning workloads have been demonstrated. In this paper, we present hyperparameter lists for NAdamW derived from extensive experiments on the realistic workloads in the AlgoPerf: Training Algorithms benchmark. Our hyperparameter lists also include values for basic regularization techniques (i.e. weight decay, label smoothing, and dropout). In particular, our best NAdamW hyperparameter list performs well on AlgoPerf held-out workloads not used to construct it, and represents a compelling turn-key approach to tuning when restricted to five or fewer trials. It also outperforms basic learning rate/weight decay sweeps and an off-the-shelf Bayesian optimization tool when restricted to the same budget.

cs.LG↗

arXiv2025

Stacking as Accelerated Gradient Descent

Stacking, a heuristic technique for training deep residual networks by progressively increasing the number of layers and initializing new layers by copying parameters from older layers, has proven quite successful in improving the efficiency of training deep neural networks. In this paper, we propose a theoretical explanation for the efficacy of stacking: viz., stacking implements a form of Nesterov's accelerated gradient descent. The theory also covers simpler models such as the additive ensembles constructed in boosting methods, and provides an explanation for a similar widely-used practical heuristic for initializing the new classifier in each round of boosting. We also prove that for certain deep linear residual networks, stacking does provide accelerated training, via a new potential function analysis of the Nesterov's accelerated gradient method which allows errors in updates. We conduct proof-of-concept experiments to validate our theory as well.

cs.LG↗

arXiv2024

Analysis of long-lived effects in high-repetition-rate stroboscopic transient X-ray absorption experiments on thin films

Time-resolved X-ray absorption spectroscopy (tr-XAS) has been shown to be a versatile measurement technique for investigating non-equilibrium dynamics. Novel X-ray free electron laser (XFEL) facilities like the European XFEL offer increased repetition rates for stroboscopic XAS experiments through a burst operation mode, which enables measurements with up to 4.5 MHz. These higher repetition rates lead to higher data acquisition rates but can also introduce long-lived excitations that persist and thus build up during each burst. Here, we report on such long-lived effects in Ni and NiO thin film samples that were measured at the European XFEL. We disentangle the long-lived excitations from the initial pump-induced change and perform a detailed modelling-based analysis of how they modify transient X-ray spectra. As a result, we link the long-lived effects in Ni to a local temperature increase, as well as the effects in NiO to excited charge carrier trapping through polaron formation. In addition, we present possible correction methods, as well as discuss ways in which the effects of these long-lived excitations could be minimized for future time-resolved X-ray absorption spectroscopy measurements.

cond-mat.mtrl-sci↗

arXiv2024

Provable Length Generalization in Sequence Prediction via Spectral Filtering

We consider the problem of length generalization in sequence prediction. We define a new metric of performance in this setting -- the Asymmetric-Regret -- which measures regret against a benchmark predictor with longer context length than available to the learner. We continue by studying this concept through the lens of the spectral filtering algorithm. We present a gradient-based learning algorithm that provably achieves length generalization for linear dynamical systems. We conclude with proof-of-concept experiments which are consistent with our theory.

cs.LG↗

arXiv2024

Spectral State Space Models

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model. Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

cs.LG↗

arXiv2024

Adaptive Gradient Methods at the Edge of Stability

Very little is known about the training dynamics of adaptive gradient methods like Adam in deep learning. In this paper, we shed light on the behavior of these algorithms in the full-batch and sufficiently large batch settings. Specifically, we empirically demonstrate that during full-batch training, the maximum eigenvalue of the preconditioned Hessian typically equilibrates at a certain numerical value -- the stability threshold of a gradient descent algorithm. For Adam with step size $η$ and $β_1 = 0.9$, this stability threshold is $38/η$. Similar effects occur during minibatch training, especially as the batch size grows. Yet, even though adaptive methods train at the ``Adaptive Edge of Stability'' (AEoS), their behavior in this regime differs in a significant way from that of non-adaptive methods at the EoS. Whereas non-adaptive algorithms at the EoS are blocked from entering high-curvature regions of the loss landscape, adaptive gradient methods at the AEoS can keep advancing into high-curvature regions, while adapting the preconditioner to compensate. Our findings can serve as a foundation for the community's future understanding of adaptive gradient methods in deep learning.

cs.LG↗