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Kyle Lee

Publications and source records attributed to Kyle Lee.

At least 19 recordsLinked to original sources
arXiv2026

Precision Studies of Boosted Polarized Vector Bosons with Energy Correlators

Boosted, hadronically decaying $W$ and $Z$ bosons are among the most abundant heavy objects at colliders, and their vector nature makes their substructure qualitatively richer than that of a scalar. We initiate precision studies of the hadronic decays of boosted polarized vector bosons with energy correlators. In the narrow-width limit, the laboratory-frame two-point energy correlator is a sum of longitudinal and transverse decay spectra, each weighted by its polarized production rate and obtained by a closed-form boost kernel acting on rest-frame correlators. Combining polarized production density matrices, computed at NNLO in QCD for $pp\to V+X$ and at leading order for $e^+e^-\to W^+W^-$, with decay correlators that combine NNLO fixed order with NNLL collinear and N$^4$LL back-to-back resummation, we find for high-$p_T$ $W/Z$ production that polarization shifts the spectrum by $\mathcal{O}(10\%)$ relative to a naive unpolarized treatment. Even without any reconstruction, hadronic $W/Z$ decays stand out over the realistic QCD background of untagged jet samples as a localized angular bump. Our results open the door to using energy correlators for polarimetry of electroweak bosons through their hadronic decays, for standard-candle measurements of electroweak bosons inside jets, and in sharper searches for new resonances.

hep-ph↗
arXiv2026

Probabilistic Algorithms for Ising Machines from Optimization to Generative AI

Ising machines have emerged as promising hardware accelerators for intractable optimization and sampling problems, yet their practical impact increasingly hinges on the co-design of algorithms and hardware, where algorithmic demands shape new architectures and new hardware capabilities inspire entirely new algorithms. In this Review, we survey probabilistic algorithms designed for portability across diverse Ising platforms, advocating a top-down perspective that prioritizes principled methods with provable guarantees. We cover foundational methods such as simulated annealing and parallel tempering, including two-dimensional extensions that natively encode hard constraints, and examine approaches that expand the scale of solvable problems from cluster mean-field methods to variational samplers. We highlight the Probabilistic Approximate Optimization Algorithm (PAOA), a classical analog of QAOA that emerged directly from probabilistic hardware development, and explore how generative AI and Ising machines might reinforce each other: learned models propose global moves to accelerate optimization, while probabilistic techniques improve inference in large language models. Much as quantum computing has seen algorithms co-evolve with hardware, probabilistic and Ising computing stand at a similar inflection point. We outline a co-design framework for accelerating the capabilities and adoption of next-generation Ising machines.

cs.LG↗
arXiv2026

First measurement of the one-point charge correlator in $e^+e^-$ collisions at $\sqrt{s} = 91.2$ GeV with DELPHI Open Data

The chiral structure of the $Z$ couplings imprints a parity-odd flow of electric charge on hadronic $Z$ decays. The related forward-backward asymmetries, a key set of observables in the electroweak precision program, were measured at LEP and SLC using the jet charge. The one-point charge correlator offers a complementary route, measuring the hadronic charge flow directly as a function of polar angle relative to the incoming electron-beam axis, without reference to jets or a reconstructed quark direction, following the formalism developed in a companion paper. We report its first measurement, using $61~\mathrm{pb}^{-1}$ of archival DELPHI Open Data recorded at $\sqrt{s} = 91.2$~GeV in 1994 and 1995. Detector effects are corrected in two stages. The first is derived from fully simulated samples, and the second bounds the residual charge-misreconstruction difference between data and simulation using a measurement in $e^+e^-\toτ^+τ^-$ events. The measured charge correlator exhibits the characteristic parity-odd $\sin(2θ)$ modulation and agrees with the \textsc{PYTHIA}~8.3 prediction. The measurement demonstrates that the parity-odd charge flow of hadronic $Z$ decays is directly accessible in data, differentially in polar angle, and the paper discusses strategies for controlling the associated detector effects, paving the way for a new program of charge-flux measurements, both in archival $e^+e^-$ data and at future colliders.

hep-ex↗
arXiv2026

Analysis note: one-point charge correlator with DELPHI Open Data

We present the first measurement of the one-point charge correlator, the angular flux of electric charge in hadronic final states, using DELPHI Open Data collected at LEP-1 at $\sqrt{s} = 91.2$~GeV during 1994 and 1995. The data, corrected for detector effects, exhibit a clear $\sin(2θ)$ modulation, consistent with the parity-violating hadronic charge flow that the chiral structure of the $Z$ couplings imprints on the final state. The measurement demonstrates the experimental feasibility of the observable and establishes strategies for controlling associated detector effects, thereby motivating a new program to measure charge-flux observables. This note documents the experimental details supporting the companion experimental paper and the joint theory--experiment Letter.

hep-ex↗
arXiv2026

SANTA++: Sampling Attention through Representative Keys

Attention often concentrates on a small subset of tokens in the context, but which subset matters changes from one query to the next. To exploit this changing structure, we introduce SANTA++, a training-free stochastic attention method that uses representative keys for memory-efficient selection without scanning the entire key-value (KV) cache. Cached keys are organized into teams, and the query scores one representative from each team to decide which teams to sample. We compute exact attention scores within the sampled teams and reweight each team's contribution by the inverse of its inclusion probability. This importance sampling correction estimates attention over the full cache, with a sampling budget that lets us trade memory reads for accuracy. Remarkably, with 32 or 64 sampled teams, SANTA++ uses 16% to 22% of dense attention's KV reads and retains 94% to 99% of the dense-attention baseline's scores on LongBench v2 and HELMET's retrieval-augmented generation subset, and 85% to 91% on RULER, with Qwen2.5-7B-Instruct at 32K context. With 31 sampled teams, our GPU implementation delivers a $1.69\times$ attention speedup over the dense FlashAttention baseline at 32K context. By reducing the number of cache entries read, SANTA++ in principle complements architectures with compressed KV representations, such as multi-head latent attention. Our kernels are available at: https://github.com/OPUSLab/santapp-kernel-demo.git.

cs.LG↗
arXiv2026

Generalized Detectors at Colliders

Recent progress in collider physics has reformulated phenomenological questions in terms of detector correlation functions and advanced their theoretical understanding. These advances have primarily focused on correlators of the average null energy operator, $\mathcal{E}(\vec{n})$, known as energy correlators. However, colliders have access to a much broader class of detector operators, $\mathcal{E}^n_R(\vec{n})$, which measure powers of the energy on a subset of hadrons $R$, such as charged hadrons. These generalized detectors are generically not infrared and collinear safe, and their description requires nonperturbative matching between the hadronic detectors measured in the infrared and the partonic detectors used in ultraviolet calculations. We develop a framework for computing their multi-point correlation functions. We introduce universal nonperturbative matching coefficients, termed "detector functions", that implement this infrared-ultraviolet matching. For the $\mathcal{E}_R^n$ operators studied here, these coefficients are represented by energy-weighted moments of single- and multi-hadron fragmentation functions. We present their renormalization group structure, derive QCD factorization theorems for the projected correlators, and compute jet functions through next-to-leading order. In the fixed-coupling pure Yang-Mills limit, we derive the light-ray OPE of hadronic detectors and connect it to the QCD factorization framework. We also identify universal nonperturbative power corrections generated by soft radiation, which are enhanced in the collinear limit and can substantially modify the perturbative angular scaling. A parton shower study finds qualitative agreement with the predicted perturbative and nonperturbative scaling behaviors. Our work significantly broadens the space of detector operators under theoretical control, with potential phenomenological applications.

hep-ph↗
arXiv2026

IsingFormer: Augmenting Parallel Tempering With Learned Proposals

Generative models have been extensively used to accelerate MCMC mixing for sampling and optimization, but their effective integration with standard MCMC remains an open question. Here, we introduce a global proposal move in which finite-temperature configurations from an external generator are used as proposals within Parallel Tempering (PT). We examine a specific generator, IsingFormer, a Transformer trained on long-run MCMC configurations intended to approximate equilibrium distributions, and call the resulting framework Transformer-Augmented Parallel Tempering (TAPT). The IsingFormer exhibits two useful capabilities: interpolation to untrained $β$ values and conditional completion under clamped settings absent from training. On 3D spin-glass instances, TAPT reaches substantially lower residual energies than standard PT in fewer Monte Carlo sweeps. On integer factorization, we show how a structured problem encoding can amortize the training cost by training IsingFormer once and reusing the same model across target products that were not imposed during training. Finally, in a scaling study that uses long-run MCMC configurations as proposals, with proposal generation excluded from the timing, TAPT reduces the fitted time-to-solution exponent by approximately $33\%$ relative to PT over the tested problem sizes.

cs.LG↗
arXiv2026

Flavor Flux Correlators, Forward-Backward Asymmetries, and Anomalies

Flavor plays a crucial role in the structure of the Standard Model. As such, many important collider physics measurements incorporate the flavor information of detected hadrons. Recent progress in the study of energy correlators has enabled collider physics measurements of energy flux to be reformulated as operator statements. In this Letter, we introduce flavor flux correlators, which measure the angular distribution and correlations of flavor quantum numbers. We emphasize a unique feature of heavy flavor flux correlators as compared to correlators of other charges, namely the $b$ and $c$ flavor quantum numbers are gapped at the heavy quark mass scale, making them a particularly clean perturbative observables, with $\mathcal{O}(Λ_{\text{QCD}}/m_Q)$ suppressed non-perturbative power corrections. As an application, we reformulate the heavy quark forward-backward asymmetry as a macroscopic consequence of a mixed electroweak anomaly of the heavy-quark flavor current. Using the relation to the anomaly, we compute the flavor flux correlator analytically at next-to-next-to-next-to-leading order and verify using parton shower simulations that non-perturbative corrections are suppressed, as expected from the gapped nature of the heavy flavor quantum numbers. Flavor flux correlators can be measured using archival electron-positron collision data, as well as at Belle II and future colliders.

hep-ph↗
arXiv2026

Observing Macroscopic Consequences of Electroweak Anomalies with Archival DELPHI Data

In this Letter, we emphasize that asymmetries in charge flux produced in the decays of on-shell Z-bosons provide a macroscopic manifestation of electroweak anomalies in the Standard Model (SM). We propose that these can be cleanly observed using charge correlators, providing a new formulation of forward-backward asymmetry measurements that is particularly well suited for precision studies of hadronic decays. Using archival DELPHI data, we perform a first measurement of the one-point charge correlator of electromagnetic charge flux on hadrons, and cleanly observe the macroscopic imprint of the underlying anomaly. Our analysis illustrates the potential of charge correlators as precision electroweak observables, and motivates a renewed effort to resolve longstanding tensions in hadronic asymmetry measurements.

hep-ph↗
arXiv2026

Energy Correlators in $V + X$ as a Benchmark Observable for Precision QCD

We propose projected energy correlators measured on the recoiling QCD radiation of a $Z/γ$ as a benchmark observable for precision QCD at the LHC. Using the $Z/γ$ as a hard scale prevents the need for a jet algorithm, simplifying both the perturbative and non-perturbative corrections. We develop a framework to combine state-of-the-art fixed-order amplitudes, high order resummation, and universal non-perturbative matrix elements. Our approach is based on numerically computed inclusive hard functions, allowing flexibility in the process and the inclusion of realistic experimental cuts. We perform detailed numerical studies of the projected energy correlators at next-to-leading order + next-to-next-to-leading logarithm (NLO+NNLL) to verify the stability of our setup. We present numerical results at NLO+NNLL, which are the first complete matched predictions for energy correlators at the LHC at this order. We discuss the prospects for extensions to higher orders, outlining a path to NNLO calculations of energy correlators at the LHC.

hep-ph↗
arXiv2026

Restoring Sparsity in Potts Machines via Mean-Field Constraints

Ising machines and related probabilistic hardware have emerged as promising platforms for NP-hard optimization and sampling. However, many practical problems involve constraints that induce dense or all-to-all couplings, undermining scalability and hardware efficiency. We address this constraint-induced density through two complementary approaches. First, we introduce a hardware-aware native formulation for multi-state probabilistic digits (p-dits) that avoids the locally dense intra-variable couplings required by binary Ising encodings. We validate p-dit dynamics by reproducing known critical behavior of the 2D Potts model. Second, we propose mean-field constraints (MFC), a hybrid scheme that replaces dense pairwise constraint couplings with dynamically updated single-node biases. Applied to balanced graph partitioning, MFC achieves solution quality comparable to exact all-to-all constraint formulations while dramatically reducing graph density. Finally, we demonstrate the practical impact of restored sparsity through an FPGA implementation. In comparisons using FPGA kernel time and CPU solver-loop time, and excluding the current prototype's host-device schedule transfer overhead, the FPGA reaches the 50% success threshold more than an order of magnitude faster than the CPU probabilistic solvers and more than two orders of magnitude faster than the Tabu Ising baseline. Together, these results outline a pathway for scaling constrained optimization on probabilistic hardware.

cond-mat.stat-mech↗
arXiv2026

Improving parton shower predictions via precision moments of energy flow polynomials

We study conceptual and practical aspects of using maximum-entropy reweighting to upgrade parton-shower event samples with higher-accuracy theoretical constraints. Our approach produces strictly positive per-event weights that improve parton-shower predictions while preserving full event-level exclusivity, allowing any observable to be computed without rebinning or regeneration. On the conceptual side, we explain how theoretical principles can help determine which constraints to use and which kinds of priors lead to efficient reweighting. On the practical side, we perform a proof-of-concept study with hemisphere observables in $e^+e^- \to$ hadrons, and show that even when the parton-shower prior is degraded by removing the non-singular parts of the QCD splitting functions, a small set of precision calculations can restore the correct behavior. We use energy flow polynomials (EFPs) as a systematic basis for infrared- and collinear-safe constraints, and study how information transfers from constrained to unconstrained observables. We find rapid information saturation, where a compact set of EFP moments achieves broad improvements across observable space, including for standard hemisphere observables never used in training. By construction, the imposed moments of the posterior are formally as accurate as the precision inputs, while the improvement of any other observable is an empirical statement about information transfer that we quantify numerically. Physics-motivated basis reductions from collinear power counting achieve comparable performance to complete bases, and mixed moments combining polynomial and logarithmic terms outperform pure alternatives. These results suggest a systematic approach to improving parton-shower event generators, where theoretical constraints of the highest accuracy translate into full phase-space predictions of experimental relevance.

hep-ph↗
arXiv2026

Factorization of elastic, single, and double diffractive $pp$ scattering

We use effective field theory techniques to factorize elastic, single, and double diffractive forward $pp$ scattering in the Regge limit $|t|\ll s$, where $t$ is the squared momentum transfer. These processes involve a large rapidity gap and comprise about half the total $pp$ cross section. We explain why the diffractive PDFs appearing in $ep$ diffraction do not appear as universal hadronic functions for $pp$ diffraction. For $|t|\sim Λ_{\rm QCD}^2$, we show that the hadronic functions in $ep$ and $pp$ diffraction differ, and hence are non-universal. In general, we prove that rapidity anomalous dimensions are universal between diffractive $ep$ and $pp$ processes, and that color-singlet (Pomeron) evolution equations can be determined at the amplitude level.

hep-ph↗
arXiv2026

Dissecting Parton Showers with Multi-Point Energy Correlators

The last several years have seen tremendous progress in the ability to both compute and measure multi-point correlations in energy flux. The highly differential nature of energy correlators makes them ideal probes of multi-collinear factorization and azimuthal structure within jets. In this paper, we explore the phenomenology of four-point correlators in jet substructure. We identify experimentally realizable projections that probe different factorization channels onto splitting tensors and splitting functions. We perform a detailed phenomenological study using both Herwig and Pythia. By comparing parton shower results with analytic calculations in kinematic limits, we are able to disentangle intrinsic spin correlations from kinematic azimuthal correlations. In experimentally accessible kinematic regions, we find the spin correlations are subdominant, strongly motivating a complete calculation of the four-point correlator in QCD to provide a test of the parton shower results. We also present parameterizations and analysis algorithms that can be used experimentally. Our work sets the stage for the experimental measurement of these observables at the LHC, and their use as probes of the next generation of parton showers.

hep-ph↗
arXiv2026

Putting Jet Substructure on Track(s)

One of the main advances in analysis strategies at the Large Hadron Collider (LHC) has been the ability to study the detailed structure of energy flow within high transverse momentum jets, a field referred to as jet substructure. Jet substructure has provided new ways to search for new physics, measure Standard Model parameters, and study the dynamics of the strong nuclear force. To push to the next level of precision, and to make measurements of increasingly subtle correlations, requires exquisite angular resolution achieved through the use of tracking information. In this paper we leverage recent progress in our understanding of factorization theorems and renormalization group techniques to present the first complete calculations of jet substructure observables at the LHC on tracks. We compute projected energy correlators up to four points at next-to-leading collinear logarithmic accuracy, matching the state of the art for jet substructure observables, but extending to tracks. This marks a significant step in enhancing the collider physics program, enabling precise and systematically improvable comparisons between experimental measurements and theoretical calculations, made possible by the exceptional angular resolution of tracking.

hep-ph↗
arXiv2026

Programmable Probabilistic Computer with 1,000,000 p-bits

Probabilistic computers built from p-bits have been proposed as hardware accelerators for sampling and optimizing Ising models, but existing systems have been confined to a single chip, capped by its capacity and memory bandwidth. Here we break this limit by networking FPGAs into a single Ising machine far larger than any one device could hold, realizing a programmable probabilistic computer with one million p-bits. The machine performs Gibbs sampling at over a trillion flips per second while keeping every coupling weight in local on-chip memory. During execution, devices exchange nothing but 1-bit boundary states. This architecture exposes a question fundamental to any distributed sampler: how frequently boundary information must be refreshed for a partitioned machine to behave as an unpartitioned one. Using three-dimensional Edwards-Anderson spin glasses, we show that the answer is set by a single timing ratio, eta = f_comm/f_p-bit, of the boundary-exchange frequency to the local p-bit update frequency. Above a topology-dependent threshold, the distributed machine matches a monolithic GPU reference. Below it, residual energy still decays as a power law but with a reduced exponent, turning parallelism into a quantifiable throughput-accuracy tradeoff. A theoretical cluster mean-field model reproduces the same behavior, showing that this tradeoff is a universal property of partitioned stochastic dynamics. These results provide a programmable million-p-bit platform, demonstrated across spin glasses, Max-Cut, and Boolean satisfiability, together with a quantitative design rule for scaling probabilistic computers beyond the single-chip limit.

cs.DC↗
arXiv2026

Stochastic Sparse Attention for Memory-Bound Inference

Autoregressive decoding becomes bandwidth-limited at long contexts, as generating each token requires reading all $n_k$ key and value vectors from KV cache. We present Stochastic Additive No-mulT Attention (SANTA), a method that sparsifies value-cache access by sampling $S \ll n_k$ indices from the post-softmax distribution and aggregates only those value rows. This yields an unbiased estimator of the post-softmax value aggregation while replacing value-stage multiply-accumulates with gather-and-add. We introduce stratified and systematic sampling to design variance-reduced, GPU-friendly variants. Evaluated on Llama-3.1-8B-Instruct at 32k-token contexts, S$^2$ANTA matches baseline accuracy while achieving up to $1.5\times$ decode-step attention-kernel speedup over FlashInfer and FlashDecoding on an NVIDIA RTX 6000 Ada. In batched long-context generation, these kernel gains translate to up to $1.25\times$ end-to-end decode-latency speedup. Finally, we propose Bernoulli $qK^\mathsf{T}$ sampling as a complementary technique to sparsify the score stage, reducing key-feature access through stochastic ternary queries. Both methods are complementary to upstream quantization, low-rank projection, KV-cache compression, and KV-cache selection methods. Together, they point toward sparse, multiplier-free, and energy-efficient inference. We open-source our kernels at: https://github.com/OPUSLab/SANTA.git

cs.LG↗
arXiv2026

Projected Energy Correlators: Two-Loop Jet Functions and NNLL Resummation

We present the next-to-next-to-leading logarithmic (NNLL) collinear resummation of projected $N$-point energy correlators (ENCs) up to $N=6$, matched to fixed-order predictions at NLO, in both electron-positron annihilation and Higgs decay to gluons. The key new ingredient is the two-loop jet function for $N=4,5,6$, which we compute semi-analytically using Integration-by-Parts and differential equations. We further include the leading non-perturbative corrections for ENCs, described by two universal soft matrix elements $\overlineΩ_{1q},\overlineΩ_{1g}$ of order $Λ_{\rm QCD}$, whose evolution is governed by anomalous dimensions for $(N-1)$-point correlators. The matched distributions are compared with parton-shower simulations from Pythia8 and Herwig7, and we study the sensitivity of both the absolute spectra and their ratios to the two-point energy correlator under variations of $α_s$ and $\overlineΩ_{1q,1g}$. Our results show that higher-point projected energy correlators are now under quantitative control at NNLL accuracy, opening the door to future $α_s$ extractions with complementary systematics.

hep-ph↗