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01.
arXiv (CS.CL) 2026-06-12

MiniPIC: Flexible Position-Independent Caching in <100LOC

Retrieval-augmented and agentic workloads repeatedly prefill recurring predictable structured inputs (which we call "spans") such as documents and code files. Yet, prefix caching in engines such as vLLM cannot reuse their KV entries unless they share identical prefixes with another request, while Position-Independent Caching (PIC) implementations within production-grade inference servers typically either require substantial server code changes or keep KV state outside the server, incurring host-to-device transfer overhead. We present Minimalistic PIC (MiniPIC): a minimal, flexible and fast vLLM design built from two ingredients: positional-encoding-free KV cache and user-controlled cache-reuse primitives. MiniPIC stores unrotated K vectors in the KV cache, applies RoPE to K tiles inside attention using per-request logical positions, and exposes three user-facing and token-level primitives: block-aligned padding, span separator (SSep), and prompt depend (PDep), that modify hashing behavior and effective block-level causal attention structure. With fewer than 100 lines of core-engine changes plus a custom attention backend, these primitives are sufficient to realize multiple PIC methods, including Block-Attention, EPIC, and Prompt Cache, within the same running vLLM instance, while natively integrating with KV cache CPU offload implementations. On 2WikiMultihopQA, MiniPIC with interleaved scheduling improves prefill throughput by 49% over baseline vLLM, reduces cached-span time-to-first-token by up to two orders of magnitude, preserves the linear prefill scaling of uncached spans, and incurs only 5.7% worst-case overhead.

02.
arXiv (CS.LG) 2026-06-16

Near-Optimal Stochastic Linear Bandits with Delay

arXiv:2606.16656v1 Announce Type: new Abstract: We study stochastic linear bandits with delayed feedback under several delay models and establish near-optimal regret guarantees. Our results identify when delayed linear bandits exhibit the same qualitative behavior as multi-armed bandits (MAB), and when the linear structure creates fundamentally new challenges. Specifically, (1) for loss-independent delays, where the delay does not depend on the realized loss (but potentially depends on the arm), we show that delays incur only an additive regret penalty. Under stochastic delays, this penalty scales with the expected delay, while under adversarial delays, it scales with the maximum number of outstanding observations. Notably, both delay penalties are dimension-free, improving upon the state-of-the-art results; (2) for loss-dependent delays, we show that linear bandits are substantially harder than MAB: unlike in MAB, we prove matching (up to log factors) upper and lower bounds in linear bandits, whose delay penalty depends on the square root of the dimension. (3) for the delay-as-payoff model, a special case of loss-dependent delay, we show that the optimal MAB guarantee, which depends only on the delay of the optimal arm, is also unattainable in linear bandits. Together, these results provide a sharp characterization of how delayed feedback interacts with linear generalization.

03.
arXiv (CS.LG) 2026-06-16

Latent space mapping of interpretable structural coordinates from stochastic single-molecule signals

arXiv:2606.16950v1 Announce Type: cross Abstract: Nanopores are versatile single-molecular sensors, but their utility is fundamentally constrained by stochastic translocation dynamics warping any encoded information. We resolve it by shifting from time-domain analysis to a learned latent-space mapping via a contrastive encoder trained exclusively on simulated signals from a physics-informed model. This encoder maps solid-state nanopore signals of engineered DNA barcodes into an interpretable molecular coordinate system. The learned representation is responsive to structural barcode parameters while remaining invariant to acquisition conditions and translocation conformation, allowing data pooling across devices. Molecule identification requires a single pass through the encoder, reducing computational cost by three orders of magnitude relative to alignment-based methods. We experimentally validate through mixture quantification, rare-variant detection, consensus barcode reconstruction, and real-time signal acquisition. This shift from temporal analysis to mapping structural coordinates into a latent space changes the paradigm behind analyzing stochastic sensor signals by linking classification to interpretable encoded molecular information.

04.
arXiv (CS.CL) 2026-06-18

ScholaWrite: A Dataset of End-to-End Scholarly Writing Process

Writing is a cognitively demanding activity that requires constant decision-making, heavy reliance on working memory, and frequent shifts between tasks of different goals. To build writing assistants that truly align with writers' cognition, we must capture and decode the complete thought process behind how writers transform ideas into final texts. We present ScholaWrite, the first dataset of end-to-end scholarly writing, tracing the multi-month journey from initial drafts to final manuscripts. We contribute three key advances: (1) a Chrome extension that unobtrusively records keystrokes on Overleaf, enabling the collection of realistic, in-situ writing data; (2) a novel corpus of full scholarly manuscripts, enriched with fine-grained annotations of cognitive writing intentions. The dataset includes \LaTeX-based edits from five computer science preprints, capturing nearly 62K text changes over four months; and (3) analyses and insights into the micro-dynamics of scholarly writing, highlighting gaps between human writing processes and the current capabilities of large language models (LLMs) in providing meaningful assistance. ScholaWrite underscores the value of capturing end-to-end writing data to develop future writing assistants that support, not replace, the cognitive work of scientists.

05.
arXiv (CS.LG) 2026-06-17

AIMER: Calibration-Free Task-Agnostic MoE Expert Pruning

arXiv:2603.18492v3 Announce Type: replace Abstract: Mixture-of-Experts (MoE) language models increase parameter capacity without proportional per-token computation, yet deployment still requires storing the full expert pool, making expert pruning important for reducing memory and serving overhead. Existing task-agnostic expert-pruning methods are typically calibration-dependent: they estimate expert importance from routing or activation statistics on a calibration set, making pruning decisions sensitive to calibration-data variation while introducing substantial preprocessing cost. We propose AIMER (Absolute mean over root mean square IMportance for Expert Ranking), a simple calibration-free criterion that identifies more distinct experts by capturing the concentration pattern of expert weights, making it well suited for task-agnostic expert pruning. Across 7B to 47B MoE language models with distinct architectures and 16 diverse benchmarks, AIMER consistently delivers stronger capability balance across diverse tasks than existing calibration-free methods. Surprisingly, AIMER also achieves better balance than strong calibration-based expert-pruning baselines calibrated on the widely used task-agnostic C4 corpus, while requiring only 0.22–2.06 seconds to score all experts.

06.
arXiv (CS.AI) 2026-06-17

Quantum Cinema: An Interactive Cinematic Exploration of Quantum Computing Hardware via Generative World Models

arXiv:2606.17102v1 Announce Type: cross Abstract: Quantum computing promises transformative advances across science and industry, yet the physical hardware that enables these computations remains invisible to the public: quantum processors operate inside sealed dilution refrigerators at temperatures near absolute zero, making direct observation impossible. This "imagination gap" between quantum computing's growing societal impact and the public's ability to visualize it represents a significant barrier to quantum literacy and workforce development. We present Quantum Cinema, an open-source, browser-based interactive application that closes this gap by transforming invisible quantum hardware into explorable, cinematic experiences using generative world models. Quantum Cinema guides users through a four-act narrative – from the foundational Nobel Prize-winning science of quantum entanglement, through curated video introductions to three major quantum computing architectures (trapped-ion, neutral-atom, and superconducting systems), into immersive three-dimensional generative worlds that make invisible quantum phenomena observable, and finally to interactive radar-chart comparisons grounded in real quantum device specifications. All three-dimensional environments are generated using WorldLabs' generative world model platform and are scientifically grounded in curated metrics from Amazon Web Services (AWS) Braket quantum hardware. Quantum Cinema requires no installation, no specialized hardware, and no quantum computing background. It is designed to serve two distinct communities: scholars and developers seeking to replicate or extend the platform, and educators, researchers, and science communicators seeking an intuitive tool for explaining quantum hardware to diverse audiences. This paper describes the system architecture, the generative world model pipeline, use cases for both communities, and directions for future work.

07.
arXiv (CS.AI) 2026-06-18

The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior

arXiv:2604.13082v2 Announce Type: replace-cross Abstract: Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we argue that this delay reflects limited access to already learned structure rather than failure to acquire that structure in the first place. We study one-step Collatz prediction and find that the encoder organizes parity and residue structure within the first few thousand training steps, while output accuracy remains near chance for tens of thousands more. Causal interventions support the decoder bottleneck hypothesis. Transplanting a trained encoder into a fresh model accelerates grokking by 2.75 times, while transplanting a trained decoder actively hurts. Freezing a converged encoder and retraining only the decoder eliminates the plateau entirely and yields 97.6% accuracy, compared to 86.1% for joint training. What makes the decoder's job harder or easier depends on numeral representation. Across 15 bases, those whose factorization aligns with the Collatz map's arithmetic (e.g., base 24) reach 99.8% accuracy, while binary fails completely because its representations collapse and never recover. The choice of base acts as an inductive bias that controls how much local digit structure the decoder can exploit, producing large differences in learnability from the same underlying task.

08.
arXiv (CS.LG) 2026-06-15

Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operators

arXiv:2606.14195v1 Announce Type: new Abstract: Kalman filters based on the Embedded Latent Transfer Operators (ELTO) emerge as novel statistical tools for sequential state estimation. However, a critical limitation stems from their use of simplified noise models, which fail to dynamically adapt to non-stationary processes. To address this limitation, we introduce an ELTO-based Bayesian filtering approach with a new structured parameterization for the filter's noise model. This parameterization enables structured noise adaptation, which couples the data-driven learning of an optimal time-invariant noise model with dynamic parameter adaptation that responds to changes in dynamics within non-stationary processes. Empirical results show that our structured noise adaptation improves the filter's dynamic state estimation performance in noisy, time-varying environments.

09.
arXiv (CS.LG) 2026-06-12

Self-Guidance: Enhancing Neural Codecs via Decoder Manifold Alignment

arXiv:2606.12940v1 Announce Type: cross Abstract: Neural speech codecs based on Vector-Quantized VAEs (VQ-VAEs) are core audio tokenizers for speech LLMs, yet their reconstruction fidelity is bottlenecked by quantization error. Modifying the quantizer or increasing model capacity are common fixes, but they complicate downstream language modeling. Our core idea is to align the decoder's internal feature manifolds when processing both the quantized tokens and their original continuous embeddings, using a lightweight feature-mapping loss. This requires minimal training overhead and no inference-time changes. Applied to XCodec2, self-guidance improves all reconstruction metrics, achieving state-of-the-art low-bitrate performance. Notably, it enables a 4x codebook reduction without fidelity loss, which downstream TTS experiments show significantly improves LLM-based synthesis by simplifying the token modeling space. Multiple statistical observations and visualizations corroborate the enhanced internal manifold alignment in the decoder. Extensive experiments confirm its generality across various inductive biases. Self-guidance thus establishes an efficient, broadly applicable method for high-fidelity neural audio coding.

10.
arXiv (CS.AI) 2026-06-19

Interpretable and Verifiable Hardware Generation with LLM-Driven Stepwise Refinement

arXiv:2606.19387v1 Announce Type: cross Abstract: Large language models (LLMs) have achieved remarkable success in software development. However, they are susceptible to hallucinations, meaning that they can introduce subtle semantic and logical errors. Due to the high stakes in chip design and manufacturing, hardware engineers are still reluctant to rely on LLMs for register-transfer level (RTL) generation. In this paper, we propose a hardware generation framework that combines the creativity and broad knowledge of LLMs with the explainability and mathematical rigor of formal methods. Specifically, we devise a set of transformation rules that cover various design decisions and hardware features. By iteratively applying these rules, an LLM agent can convert a design specification into an RTL program with guaranteed correctness. Experimental results demonstrate the effectiveness and efficiency of the framework.

11.
arXiv (CS.CV) 2026-06-18

RUB: Evaluating Residual Knowledge in Unlearned Models

Machine Unlearning (MUL) has emerged as a key mechanism for privacy protection and content regulation, yet current techniques often fail to guarantee the complete removal of sensitive information. While most existing works focus on verifying the execution of unlearning, they overlook the critical question of whether models remain robust against adversarial attempts to recover forgotten knowledge. In this work, we advocate for the principle of Robust Unlearning, which requires models to be both indistinguishable from retrained counterparts and resilient against diverse adversarial threats. To instantiate this principle, we propose a unified benchmark, RUB (Robust Unlearning Benchmark), that systematically evaluates the robustness of unlearning algorithms across classification, image-to-image reconstruction, and text-to-image synthesis. Within this framework, we introduce the Unlearning Mapping Attack (UMA) as a generalizable method to detect residual information, and demonstrate how existing attack strategies can be adapted into this framework as long as they conform to the generic UMA framework. Our experiments across discriminative and generative tasks reveal that state-of-the-art unlearning methods remain vulnerable under these evaluations, even when passing standard verification metrics. By positioning robustness as the central criterion and providing a benchmark for adversarial evaluation, we hope RUB paves the way toward more reliable and secure unlearning practices. The codebase and model checkpoints in RUB will be published.

12.
arXiv (CS.LG) 2026-06-12

Differentiable Thermodynamic Phase-Equilibria for Machine Learning

arXiv:2603.11249v3 Announce Type: replace Abstract: Accurate prediction of phase equilibria remains a central challenge in chemical engineering. Physics-consistent machine learning methods that incorporate thermodynamic structure into neural networks have recently shown strong performance for activity-coefficient modeling. However, extending such approaches to equilibrium data arising from an extremum principle, such as liquid-liquid equilibria, remains difficult. Here we present DISCOMAX, a differentiable algorithm for phase-equilibrium calculation that guarantees thermodynamic consistency at both training and inference, only subject to a user-specified discretization. The method combines discrete enumeration of feasible phase states with masked softmax aggregation in the backward pass, with the propagation of the true equilibrium state in the forward pass, using a straight-through gradient estimator to enable physics-consistent end-to-end learning of neural \gls{gE}-models. We show that this approach bears analogy to statistical thermodynamics, and we evaluate it on binary liquid-liquid equilibrium data where it outperforms existing surrogate-based methods, while offering a general framework for learning from different kinds of equilibrium data.

13.
arXiv (CS.LG) 2026-06-16

{\alpha}-Fair Insurance Pricing: A Fairness Continuum

arXiv:2606.14898v1 Announce Type: new Abstract: Fairness in insurance pricing remains a long-standing and deeply debated puzzle. On one hand, insurers, driven by profitability considerations, set premiums that differentiate across individual risks to achieve actuarial fairness. On the other hand, insurance serves a critical societal function by pooling risks across a population, motivating cross-subsidization among groups to promote solidarity fairness. The tension between these two competing notions of fairness makes insurance pricing inherently complex, particularly in modern settings where granular data allow for increasingly fine risk differentiation and regulators face growing pressure to protect vulnerable groups. To address this challenge, we propose an $\alpha$-Fair Individual Solvent Premium ($\alpha$-FISP) framework for insurance pricing that explicitly captures the trade-off between actuarial and solidarity fairness while guaranteeing solvency, a fundamental requirement in insurance operations. We formulate the pricing problem as a constrained optimization task, where actuarially fair premiums are adjusted subject to budget constraints on cross-subsidization within each risk class. This formulation naturally yields a family of solutions parameterized by $\alpha$, tracing a continuum between purely actuarial and purely solidarity-based pricing and enabling decision-makers to select an operating point along this fairness spectrum. We derive theoretical guarantees for the proposed framework. Numerical experiments show that $\alpha$-FISP is computationally tractable and aligns well with the U.S. regulatory regimes featuring heterogeneous state-level fairness requirements.

14.
arXiv (quant-ph) 2026-06-17

A Quantum Approach to Stochastic Optimization in Insurance Underwriting

arXiv:2605.01169v2 Announce Type: replace Abstract: The presence of stochastic elements in combinatorial optimization problems makes them particularly challenging, as such problems quickly become intractable for classical computers even at relatively small sizes. In this work, we propose a novel quantum-classical hybrid scheme for solving a class of stochastic optimization problems known as chance-constrained knapsack problems, in which item weights follow probability distributions and constraints may be violated within a specified risk tolerance. Our method employs knapsack-specific QAOA-based circuits to generate samples which, when combined with a new self-consistent classical recovery scheme introduced in this work, produce high-quality solutions. Experiments carried out on IBM Heron processors, using circuits with depths up to 177 and comprising 3443 gates acting on as many as 150 qubits, yield solutions that indicate performance comparable to classical optimization schemes. The proposed quantum-classical scheme paves the way to tackling such problems, with the potential to outperform approaches that rely solely on classical computation.

15.
PLOS Computational Biology 2026-06-09

Evolution of phenocopying in a dynamical model of developmental trajectories

by Yuuki Matsushita, Archishman Raju Developmental trajectories are known to be canalized, or robust to both environmental and genetic perturbations. However, even when these trajectories are decanalized by an environmental perturbation outside the range of conditions to which they are robust, they often produce phenotypes similar to known mutants, called phenocopies. This correspondence between the effects of environmental and genetic perturbations has received little theoretical attention. Here, we study an abstract regulatory model that is evolved to follow a specific trajectory. We then study the effects of small and large perturbations to the trajectory, both by changing parameters and by perturbing the state at specific times. We find that the phenomenon of phenocopying emerges in evolved trajectories and is not present in a null model of randomly sampled trajectories. Our results suggest that, in this class of dynamic models, evolution can allow high-dimensional phenotypic landscapes to simultaneously exhibit robustness and phenocopying.

16.
arXiv (quant-ph) 2026-06-17

Coherent Dark State Formation of a Lead-Vacancy Spin Qubit in Diamond

arXiv:2605.27841v2 Announce Type: replace Abstract: A lead-vacancy (PbV) center in diamond exhibits coherent emission above the liquid helium temperature, making it highly attractive for quantum network applications. Here, we report the magneto-optical and spin properties of PbV centers in diamond. We record a spin lifetime of 12 ms at 7.5 K under large off-axis magnetic field. Furthermore, we observe formation of the coherent dark state by coherent population trapping and estimate a spin dephasing time of 177 ns at 6.5 K. This work demonstrates the outstanding thermal robustness of the PbV spin compared to other group-IV centers above 4 K.

17.
arXiv (CS.AI) 2026-06-19

PiDR: Physics-Informed Inertial Dead Reckoning for Autonomous Platforms

arXiv:2601.03040v2 Announce Type: replace-cross Abstract: A fundamental requirement for full autonomy is the ability to sustain accurate navigation in the absence of external data, such as GNSS signals or visual information. In these challenging environments, the platform must rely exclusively on inertial sensors, leading to pure inertial navigation. However, the inherent noise and other error terms of the inertial sensors in such real-world scenarios will cause the navigation solution to drift over time. Although conventional deep-learning models have emerged as a possible approach to inertial navigation, they are inherently black-box in nature. Furthermore, they struggle to learn effectively with limited supervised sensor data and often fail to preserve physical principles. To address these limitations, we propose PiDR, a physics-informed inertial dead-reckoning framework for autonomous platforms in situations of pure inertial navigation. PiDR offers transparency by explicitly integrating inertial navigation principles into the network training process through the physics-informed residual component. PiDR plays a crucial role in mitigating abrupt trajectory deviations even under limited or sparse supervision. We evaluated PiDR on real-world datasets collected by a mobile robot and an autonomous underwater vehicle. We obtained more than 29% positioning improvement in both datasets, demonstrating the ability of PiDR to generalize different platforms operating in various environments and dynamics. Thus, PiDR offers a robust, lightweight, yet effective architecture and can be deployed on resource-constrained platforms, enabling real-time pure inertial navigation in adverse scenarios.

18.
arXiv (quant-ph) 2026-06-16

QALM: Escaping Local Minima via Interleaved Exploration and Exploitation in Quantum Circuit Optimization

arXiv:2606.16221v1 Announce Type: new Abstract: Quantum circuit optimizers face a fundamental limitation in how they tolerate temporary cost increases. At one extreme, greedy rule-based optimizers immediately apply any cost-reducing transformation, achieving high efficiency but quickly becoming trapped in local minima. At the other extreme, search-based optimizers accept cost-increasing moves to explore the circuit space and escape such minima. However, because search-based optimizers cannot determine within a reasonable time budget whether a given point is promising, that is, whether its neighborhood contains a deeper local minimum, they must blindly explore higher-cost regions. As a result, escaping the current basin to reach a promising point takes exponentially many steps. In this work, we show that this limitation can be overcome with a hybrid framework that interleaves the exhaustive exploration capabilities of search algorithms with the efficiency of rule-based optimization. We implement this framework as QALM, a novel optimizer designed to escape local minima without incurring the runtime penalties of pure search. Crucially, our results demonstrate that QALM does not merely strike a balance; it outperforms existing rule-based and search-based optimizers in circuit reduction rates while operating with the computational efficiency of rule-based systems. In a comprehensive evaluation across 248 circuits, QALM matches or exceeds the fidelity of the strongest baseline on 83.9% of these circuits, given the same time budget.

19.
arXiv (quant-ph) 2026-06-15

Fourier analysis of quantum neural network with non-linear data embedding

arXiv:2606.14206v1 Announce Type: new Abstract: Fourier analysis has become a crucial tool for understanding the expressivity of Variational Quantum Circuit (VQC) models, as well as an important indicator of barren plateaus (BP). While existing literature has only studied angle-embedded VQCs in a noiseless environment, here we develop the Fourier analysis of VQCs with non-linear data embedding, with particular focus on amplitude embedding, which provides a naturally compact encoding scheme. We first investigate a subtle difference in the domain of input features within amplitude embedding that leads to a distinct expressivity of the zero-frequency Fourier coefficient. By assuming that the ensemble of unitaries generated from the parameter space forms at least a 2-design with respect to the unitary group, we derive, via Weingarten calculus, that the mean of the Fourier coefficients is concentrated at zero, and the variance scales at an exponentially decaying order with respect to the multi-dimensional frequency magnitude. When a noise channel with unitary Kraus operators and probabilities $\{p_k\}$ is taken into account, the variance is further suppressed by a factor $\left(\sum_k p_k^2\right)^{Q}

20.
arXiv (CS.AI) 2026-06-12

Before You Think: System 0, AI-Mediated Cognition and Cognitive Colonization

arXiv:2606.13658v1 Announce Type: new Abstract: This paper examines three recent frameworks for understanding the cognitive and epistemic consequences of artificial intelligence: Tri-System Theory, Thinkframes, and System 0. It argues that while the first two capture important dimensions of AI's influence on individual reasoning and collective epistemic practices, System 0 occupies a theoretically distinctive position that neither can fully replicate. The paper introduces the concept of cognitive colonization, according to which AI systems can embed external interests within the architecture of the self in ways that are difficult for users to perceive. Because such systems are already widely deployed, understanding these invisible forms of influence is an urgent philosophical and practical task.

21.
arXiv (CS.AI) 2026-06-11

Categorical Prior Lock-in: Why In-Context Learning Fails for Structured Data

arXiv:2606.11961v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly used as conditional generators for structured data, relying on in-context learning (ICL) to adapt to new distributions without parameter updates. We investigate the limits of ICL for structured generation under distribution mismatch, using high-cardinality tabular data as a controlled test case, and identify a structural failure mode we term categorical prior lock-in: the inability of ICL to update the model's prior over token distributions inherited from pre-training. Across two 7B-parameter open-weight models, ICL improves numerical fidelity with additional examples but exhibits a sharp ceiling on categorical distributions, failing to reproduce rare classes entirely. Parameter-efficient fine-tuning (LoRA) overcomes these limitations but introduces measurable memorization risk and, in some cases, destabilizes structured output generation, highlighting a fundamental trade-off between adaptability and privacy.

22.
arXiv (CS.LG) 2026-06-11

FlexiBrain: Resolution-Agnostic Voxel-Level Encoding for Native fMRI

arXiv:2606.11500v1 Announce Type: cross Abstract: The success of large-scale deep learning models in neuroscience is fundamentally constrained by severe data heterogeneity. Native fMRI data aggregated from diverse sources exhibit substantial variation in both spatial and temporal resolutions. Consequently, most existing frameworks rely on lengthy, rigid preprocessing pipelines that enforce uniformity across datasets. This practice introduces two critical limitations: (1) potential degradation of subject-specific anatomical information; (2) significant computational overhead, often requiring hours of processing per subject. Here, we propose FlexiBrain, a resolution-agnostic voxel-level encoding framework for native fMRI based on Mamba-JEPA. FlexiBrain defines patch sizes in real-world physical units and employs a dynamic patch resizing, thereby bypassing destructive spatial standardization while enabling direct ingestion of data in native space. We instantiate the framework using an efficient Mamba-JEPA backbone to model high-dimensional 4D fMRI signals. Across five diverse downstream neuroscience tasks, FlexiBrain consistently outperforms recent state-of-the-art methods, achieving gains of up to 12 percentage points without external data augmentation. Importantly, FlexiBrain functions as a seamless plug-in module, substantially reducing preprocessing costs and accelerating the development of robust voxel-level fMRI foundation models. Code is available at https://github.com/OneMore1/FlexiBrain.

23.
arXiv (CS.AI) 2026-06-12

Real-rootedness of the Poincaré polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof

arXiv:2605.29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincaré polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne–Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi–Chen–Marcolli. The proof starts from the Keel–Manin–Getzler recurrence, but its main new idea is a bivariate deformation $F_m(y,t)$ of the Poincaré polynomial. This deformation reveals a hidden interlacing structure not visible in the one-variable recurrence. For fixed $t

24.
arXiv (CS.LG) 2026-06-15

SpikF-GO: Spiking Fourier Graph Operators for Multivariate Time Series Forecasting

arXiv:2606.13901v1 Announce Type: new Abstract: Spiking Neural Networks (SNNs) have emerged as an energy-efficient alternative to conventional neural networks, demonstrating strong performance in computer vision and robotics. More recently, SNNs have been applied to time series forecasting (TSF), with methods exploring spiking temporal backbones, spike-compatible positional encodings, Fourier-domain processing, and redesigned neuron dynamics. However, existing SNN forecasting approaches process variables independently, lacking explicit mechanisms for modeling inter-variable dependencies. This is a critical limitation in multivariate settings, where cross-variable correlations carry substantial predictive information. We propose Spiking Fourier Graph Operators (SpikF-GO), which addresses this gap by combining a hypervariate graph formulation in which every scalar observation becomes a graph node with spike-driven spectral processing. SpikF-GO introduces a Hard Concrete frequency gate for learnable sparse frequency selection and a Complex LIF gate that applies independent spiking neurons to real and imaginary Fourier components, preserving binary, event-driven computation throughout the spectral domain. We further present a variant incorporating Central Pattern Generator-based positional encodings for stronger long-range temporal modeling. Evaluated on eight benchmarks under a unified experimental protocol, SpikF-GO achieves the best average rank among all SNN methods and outperforms its ANN counterpart, FourierGNN, at reduced energy cost. SpikF-GO maintains competitive accuracy even at substantially smaller embedding dimensions, thereby achieving significant energy reductions. To our knowledge, this is among the first works to bring graph-based multivariate modeling into the spiking domain for TSF and the first to provide a unified comparison across SNN forecasting architectures under a common experimental protocol.

25.
arXiv (CS.LG) 2026-06-16

Transformers Learn the Mestre-Nagao Heuristic

arXiv:2606.15036v1 Announce Type: new Abstract: We train a two-layer transformer encoder to classify rational elliptic curves $E/\mathbb{Q}$ of conductor $\leq 10000$ as either rank 0 or rank 1 from the first 128 normalized Frobenius traces. We achieve >99% accuracy on both classes, and accuracy is essentially unchanged on test curves with no isogeny or quadratic-twist relative in the training set. We then apply techniques from mechanistic interpretability such as attention analysis, linear probing, activation patching, logit attribution, and neuron-level circuit analysis to reverse-engineer the algorithm the (centroid in function space) model learned. We find that a sparse circuit of 20 out of 512 layer-1 MLP neurons is sufficient for rank prediction under a linear probe with an AUROC of 0.992 at plateau, implementing a push-pull detector architecture of rank-0 and rank-1 detectors with a one-sided readout. However, we notice that the model has sub-optimal readout problems indicating a mismatch in rank-order between the readout pathway and the discriminative circuit. Critically, the learned input weights of the top discriminating neuron match the Mestre-Nagao sum heuristic weights $\log(p)/(p\cdot \log{B})$ with a Spearman coefficient $r = 0.997$ and Pearson coefficient $r = 0.952$: the model has learnt a result from analytic number theory from the Frobenius trace data alone. We additionally find that all 50 independently trained models concentrate CLS attention on prime positions at 2-50$\times$ the rate of composite positions. The CLS embedding encodes $\log{L(E,1)}$ with $R^2 = 0.962\pm 0.011$ across the 50 models (after controlling for the conductor). Activation patching analysis reveals that attention weights are dissociated from causal information flow. Additionally, the 50 solutions from training are near-identical in function space (with pairwise agreement $>$98.8%) despite large weight space barriers.