arXiv:2607.07029v1 Announce Type: new Abstract: Reinforcement learning (RL) policies can be unsafe and vulnerable to attacks. Ensuring their reliability is often a pain point as existing automated testing methods target only selected environments, testing scenarios, and RL algorithms. To address this, we propose a comprehensive framework for testing single- and multi-agent RL policies under varying conditions. Our implementation of this framework, Gimitest, is an open-source tool that supports various gym frameworks and allows for modifications of their integrated components. This article describes the framework and details Gimitest's functionality and architecture. It showcases its effectiveness in testing multiple RL policies in environments such as the official Farama Gymnasium and PettingZoo.
Science Journals
arXiv:2607.07034v1 Announce Type: new Abstract: We introduce Intrinsic Green's Learning (IGL), a framework that models a target function on a manifold as the solution to a linear PDE whose source term is learned from data. Rather than approximating the target directly, IGL learns a source and integrates it against a Green's kernel. An encoder discovers a low-dimensional coordinate chart on the manifold where both the source and the kernel decompose as low-rank tensors, collapsing a high-dimensional integral into independent one-dimensional integrals with cost linear in the intrinsic dimension. A two-stage algorithm separates coordinate discovery from source fitting, a near-convex linear solve, preventing the dimensional collapse of joint training. Learnable gates on each coordinate automatically discover the intrinsic dimension of the manifold. We validate IGL on synthetic manifolds and on MNIST, where it simultaneously achieves near-optimal classification and automatic recovery of the intrinsic dimension.
arXiv:2607.07035v1 Announce Type: new Abstract: The architecture of deep feedforward neural networks is ubiquitous in deep learning, either as a whole system or as a subnetwork of other architectures, and thus its mechanism is a key ingredient of the black box of neural networks. On the basis of the simplest two-layer ReLU network, this paper systematically studies the mechanism of deep feedforward ReLU networks with multiple hidden layers and successfully explains the training solution obtained by the back-propagation algorithm. The concept of a path, especially in terms of the relationships between paths, plays a central role in uncovering the mystery of the black box. It is shown that a unit of a deep ReLU network can form a piecewise linear manifold to divide the input space, instead of a hyperplane of the two-layer case. How to efficiently use the hidden-layer units to produce both linear functions and partitions of the input space is also a central problem. The principles of a two-layer ReLU network can be generalized to the deeper case to a large extent, such as multiple strict partial orders and continuity restriction. The combination of the basic and simple principles proposed can yield complicated instantiations including the training solutions, and in this sense the black box of deep feedforward ReLU networks is revealed.
arXiv:2607.07678v1 Announce Type: new Abstract: Rotary Position Embeddings (RoPE) provide transformers with a fixed grid of positional frequencies, yet trained models use these frequencies highly non-uniformly. We study what determines this frequency usage and propose a data-centered explanation: RoPE frequencies are selected to match the relative-distance structure of the training data. Viewing each frequency as a positional lens, we formalize a field-resolution tradeoff and show that, for a data-induced dependency profile of width $W$, the optimal frequency scales as $1/W$. This frequency-matching principle explains controlled observations on synthetic and text-based data, and suggests that the mid-low frequency bands observed in language models arise from the multi-scale dependency structure of natural language. We further connect frequency selection to position-interpolation-based length generalization: scaling frequencies down expands the effective field while reducing resolution. This helps when longer-context dependencies are approximate dilations of those seen during training, but can fail when relevant dependencies do not scale with context length. Empirically, we show that natural language exhibits approximate self-similarity across positional scales, explaining why test-time frequency scaling can support long-context generalization. Overall, our results identify a data-driven mechanism behind emergent RoPE frequency usage and show that long-context generalization depends on two forms of scale matching: between learned frequencies and training-time dependencies, and between frequency scaling and how those dependencies extend to longer contexts.
arXiv:2607.07066v1 Announce Type: new Abstract: Transformers have demonstrated a remarkable ability to learn algorithmic reasoning, yet mechanistic analyses have mostly focused on globally invertible operations such as cyclic addition and group composition. In this work, we investigate how small transformers learn modular integer multiplication over composite moduli, a fundamentally non-invertible operation due to the presence of zero-divisors. We propose the monoid extension: a localized generalization of Group Composition via Representation (GCR) that suggests the learned computation does not rely on a single global representation space. Instead, the model partitions the input space into local hierarchical algebraic regions, where group-like structure survives and Fourier mechanisms can be applied. In transformers trained on square-free modular multiplication, we find that embeddings organize around these regions, attention exhibits class-sensitive routing and low-rank write directions, and local character features explain a large fraction of the model's output logits. Our results suggest that representation-theoretic mechanisms previously identified for group operations can extend beyond groups to more general structures.
arXiv:2607.07494v1 Announce Type: new Abstract: Gradient communication is a primary scaling bottleneck in large language model (LLM) pretraining. Communicating gradients in low-precision formats, such as FP8 and NVFP4, can significantly reduce the communication volume. Existing methods quantize gradients via linear or nonlinear mappings in Euclidean space, often degrading model performance because highly anisotropic gradients incur direction-dependent distortion. We present GIFT, a geometry-informed gradient scaling method that performs low-precision communication in geometry-aware coordinates. By transforming gradients into a near-isotropic space before quantization, GIFT makes low-precision representations substantially more faithful to their high-precision counterparts. GIFT only changes the coordinate system used for low-precision gradient communication and does not change the optimizer, training recipe, communication collective, or low-precision format. We also develop a simplified geometry-aware transformation algorithm with low-rank approximation and selective application to balance the computation overhead and communication reduction. We examine the empirical convergence of GIFT using Llama-300M and Llama-600M models. Our results show that GIFT reduces the end-to-end pretraining time of Llama-600M by 7.6% on 64 NVIDIA GH200 Superchips, while improving the downstream task preservation profile over direct Euclidean FP8 communication under the same optimizer and communication path.
arXiv:2607.07101v1 Announce Type: new Abstract: Proprioception is fundamental to robotic manipulation, yet standard fusion methods often treat it as an isolated vector lacking explicit alignment with visual tokens. Without a direct correspondence between 3D kinematics and 2D feature maps, manipulation policies struggle to ground the robot's state within the scene, frequently underperforming even vision-only baselines. To address this, we introduce GeoProp, a lightweight, plug-and-play adapter that aligns proprioception with vision through explicit geometric grounding and spatial feature sampling. GeoProp projects the robot state onto the image plane to sample localized visual features, constructing a grounded state token. It then injects state-derived spatial priors into the corresponding visual features via FiLM modulation. To capture motion intent, GeoProp further samples features at a short-horizon predicted coordinate derived from recent kinematics, providing look-ahead visual context. Across 67 tasks, GeoProp improves Diffusion Policy by 8.7% on 63 simulation tasks and pi_0 by 4.0% on the RoboTwin subset, and yields a 10.6% average gain across both policy families in the real world, while adding only 2-3% to the parameter count. These results demonstrate that GeoProp is a simple yet high-impact inductive bias for generalist embodied policies. Project page: https://alibaba-damo-academy.github.io/GeoProp/.
arXiv:2502.05906v2 Announce Type: replace Abstract: We consider a strategic M/M/1 queueing model under a first-come-first-served regime, where customers are split into two classes and class $A$ has priority over class $B$. Customers can decide whether to join the queue or balk, and, in case they have joined the queue, whether and when to renege. We study the equilibrium strategies and compare the equilibrium outcome and the social optimum in the two cases where the social optimum is or is not constrained by priority.
arXiv:2607.07142v1 Announce Type: new Abstract: Low Earth Orbit (LEO) satellite Internet introduces rapid path variability, intermittent capacity shifts, and non-terrestrial delay dynamics that challenge transport-layer congestion control. Although Bottleneck Bandwidth and Round-trip propagation time (BBR) achieves high throughput in such environments, its aggressive bandwidth probing can cause excessive retransmissions and unstable pacing over LEO links. This paper presents a global experimental evaluation of BBR over a SpaceX Starlink testbed spanning six geographically distributed AWS endpoints and compares its behaviour against Cubic, Vegas, and Hybla under isolated and competing traffic scenarios. The measurements show that BBR consistently delivers superior throughput but incurs significantly higher retransmission overhead, revealing a critical throughput-stability trade-off in LEO satellite Internet. To address this limitation, we propose a Small Language Model (SLM)-guided BBR adaptation framework that learns phase-safe pacing-gain decisions from real Starlink traces. The framework combines a structured BBR state encoder, LoRA-based parameter-efficient fine-tuning, and a constrained networking head to generate feasible pacing actions with low inference latency. Evaluation using GPT-2, T5, GPT-Neo, and SmolLM2 shows that lightweight SLMs can retain BBR's throughput advantage while substantially reducing retransmissions, with performance comparable to larger language models but at much lower computational cost.
arXiv:2607.07584v1 Announce Type: new Abstract: 3GPP Integrated Access and Backhaul (IAB) allows operators to deploy outdoor mm-wave access networks in a cost-efficient manner, by reusing the same spectrum in access and backhaul. In IAB networks the performance bottleneck is the wireless backhaul segment, where efficient forwarding strategies are needed to effectively use the available capacity. In addition, the performance of the mm-wave IAB backhaul segment is contingent on the availability of line of sight (LoS) conditions in the selected deployment sites. To mitigate LoS dependence, in this paper, we propose to complement the mm-wave backhaul segment of IAB networks with additional Sub6 backhaul links, which contribute to the capacity and robustness of the backhaul network. We refer to IAB networks combining Sub6 and mm-wave links in the backhaul as Sub6 enhanced IAB networks. In this context, the main contribution of this paper is PHaul, a forwarding engine for Sub6 enhanced IAB networks that accomodates different traffic engineering criteria, and combines an offline path selection heuristic with an online Deep Reinforcement Learning (DRL) agent based on Proximal Policy Optimization (PPO). By leveraging a network digital twin of the IAB wireless backhaul, PHaul periodically samples the input traffic of the backhaul network and updates flow to path mappings, with execution times below 10 seconds in realistic backhaul topologies. We present an exhaustive performance evaluation, where we demonstrate that PHaul can achieve gains of up to 36\% in throughput efficiency and of up to 20\% in fairness, when compared against two alternative heuristics in a wide range of network configurations. We also demonstrate that PHaul is robust to differences between the network topologies considered in the training and inference phases, which can occur in practice due to link failures.
arXiv:2607.07173v1 Announce Type: new Abstract: Subject-driven personalized text-to-image generation requires a pretrained diffusion model to acquire a specific subject from a few reference images while preserving subject identity, following novel text prompts, and maintaining sample diversity. Existing optimization-based methods instantiate subject adaptation through full fine-tuning, textual embedding optimization, or low-rank parameter updates; PaRa further constrains personalization from the perspective of parameter rank reduction. However, a uniform low-rank constraint or a uniform adapter strength cannot explicitly distinguish the capacity requirements of different denoising stages. Moreover, inference-time candidate selection driven mainly by identity similarity may compress the selected samples in the visual representation space. We decompose the problem into two complementary components: SPaRa denotes training-side stage-aware low-rank adaptation, DCAL denotes inference-side distribution-calibrated candidate selection, and SPaRa-DCAL denotes the combined framework. Theoretical analysis shows that timestep-dependent scaling controls the effective perturbation magnitude of a low-rank adapter, while identity-biased candidate selection restricts the radius of selected features around the reference center under explicit conditions. Auditable experiments under the SDXL and DreamBooth 30-subject protocol show that DCAL improves 1-LPIPS, CLIP-I, DINO-I, and CLIP-T on a fixed LoRA candidate pool, while revealing a clear trade-off with CLIP/DINO pairwise diversity and pairwise LPIPS. These results indicate that personalized generation should be evaluated through identity consistency, text alignment, and representation diversity rather than identity metrics alone.
arXiv:2607.07181v1 Announce Type: new Abstract: Since self-orthogonal codes, few-weight codes, linear complementary dual codes(LCD codes, for short) and quantum codes have nice applications in coding theory and cryptography, they have received continuous attention. In 2024, by introducing the notion of the augment code, Heng et al.[30] constructed several classes of few-weight self-orthogonal codes basing on defining sets, which are introduced by Ding et al.[10] in 2007. In this manuscript, for two classes of defining sets, we consider the corresponding augmented codes, construct a class of projective four-weight self-orthogonal codes and three classes of four-weight self-orthogonal codes. And for two classes of these four-weight self-orthogonal linear codes, we determine the parameters of their dual codes. As applications, we construct two classes of LCD codes and a class of quantum codes. In particular, we prove that there exists a class of these LCD codes whose dual codes are almost optimal LCD codes according to the sphere packing bound, and a class of quantum codes are AMDS according to the quantum Singleton bound.
arXiv:2607.07082v1 Announce Type: cross Abstract: Data-Enabled Predictive Control (DeePC) has recently emerged as a framework for controlling unknown systems from data. However, its performance relies on the relevance of the collected data, and as such, disturbances lead to inevitable errors. This paper addresses this problem by proposing an augmentation of DeePC using Model-Free Disturbance Observer with Online Modification (MFDOOM). The method corrects output predictions based on previous prediction errors using a dedicated continuously updated Hankel matrix. We compare our method, both theoretically and through simulation, to other recent algorithms designed for time-varying systems in the DeePC framework. It is shown that for disturbances that can be modeled as the output of an autonomous linear time-invariant system, this approach can reduce tracking error and online-update burden compared with existing online DeePC variants.
arXiv:2607.07107v1 Announce Type: cross Abstract: A set of vertices $S$ of a directed graph $G$ is geodetic if every vertex of $G$ lies on a shortest path from a vertex of $S$ to a vertex of $S$. A directed graph is geodetic if there is at most one shortest path from every vertex of $G$ to every vertex of $G$. We prove the NP-completeness of the following decision problem. Given a directed acyclic planar geodetic graph $G$ and an integer $k$, does $G$ have a geodetic set with at most $k$ vertices? This implies that the question of whether $G$ has a strong or a monitoring geodetic set with at most $k$ vertices is also NP-complete for directed acyclic planar geodetic graphs. Furthermore, we prove that the number of vertices in a minimum geodetic set and the number of vertices in a minimum edge geodetic set can be computed in linear time for directed acyclic series-parallel graphs.
arXiv:2607.07196v1 Announce Type: new Abstract: Across robotics, World Models (WMs) are increasingly used to evaluate action policies by simulating the consequences of actions in an imagined world, and returning a success or safety verdict. Yet a verdict is only as trustworthy as the WM that produced it, and the WM itself needs to be certified. In video-generation WMs, fidelity metrics such as Fr\'echet Video Distance (FVD) reward visual realism, but ignore whether the world responds correctly to the policy's actions, including those unseen in training. Classical simulation-based validation assumes a trusted simulator evaluating an untrusted policy, whereas generative WMs are themselves unverified learned artifacts. Hence, we argue that any WM used as a test oracle must first be accredited before its verdicts can serve as evidence. Building on credibility practices from safety-critical simulation, including Verification, Validation & Accreditation (VV&A), Safety of the Intended Functionality (SOTIF), and scenario-based testing standards, we define an admissibility ladder (L0-L4) that a WM must climb before its closed-loop verdicts are accepted as assurance evidence. Our framework is embodiment-agnostic, and is instantiated in autonomous driving (AD), where assurance methods for traditional simulation are most mature. Applied to two driving WMs, the lower rungs reveal a reversal: the model that ranks higher on visual generation quality (L0) ranks lower on action-following (L1-L2), so visual fidelity does not predict the action-robustness a closed-loop verdict depends on.
arXiv:2607.07350v1 Announce Type: new Abstract: Limited flight endurance significantly restricts the operational range of unmanned aerial vehicles (UAVs) in long duration missions such as surveillance and inspection, where multiple spatially distributed Areas of Interest (AOIs) must be visited. These tasks require efficient routing determining the sequence of visits which directly impacts mission time, energy consumption, and overall feasibility. Pairing UAVs with unmanned ground vehicles (UGVs) for mobile recharging offers a promising solution, but introduces a tightly coupled cooperative routing problem involving UAV route planning, UGV road constrained movement, energy management, and rendezvous scheduling under uncertainty. In this work, we present an integrated planning and autonomy framework for reliable field deployment. We formulate the problem as an energy constrained cooperative routing task and solve it using a Deep Reinforcement Learning (DRL) based planner that jointly optimizes the UAV visitation sequence and rendezvous locations with the UGV, outperforming baseline heuristics in minimizing total mission time. To bridge the gap between planning and execution, we introduce a standardized two layer YAML based mission API that captures environment states and structures lightweight, synchronized action sequences. This framework is supported by a complete autonomy stack using PX4/MAVSDK for UAV control and ROS 2/Nav2 for UGV navigation. Furthermore, we propose a lightweight Rendezvous Aware Replanner (RARP) that operates online to handle environmental uncertainties, reducing energy margin violations from 83.33% to 20.00%. The full system is validated through outdoor field experiments, demonstrating robust cooperative navigation and adaptability in dynamic tasks, including a search and rescue scenario with vision language model (VLM) based hazard detection
arXiv:2607.06650v1 Announce Type: cross Abstract: HDRL held its first HDRL wide strategy meeting in January 2026, pulling in a majority of HDRL member staff and selected HDRL grantees. Just over 40 people attended with a few more online to listen to over 30 lightning talks presented by their colleagues and leaders, participate in several breakout and group discussions, and cast 324 votes on over 50 strategic topic ideas contributed by the attendees. The many ideas generated by attendees can be grouped into seven themes which describe the overall breadth of discussion at the meeting. These themes included: Metadata, Standards, and Semantics Discovery, Search, and Recommendation Modernizing HDRL User experience Modernizing HDRL Staff experience Modernized, Scalable, and Dependable Infrastructure for Compute and Storage Metrics and Impact Assessment Community Engagement and Sustainability Considering the gathered information and the interconnections between the prioritized ideas we concluded that several strategic areas for action exist. This document provides an overview of contributed materials and post meeting strategic analysis.
arXiv:2405.16668v2 Announce Type: replace Abstract: Adversarial Imitation Learning (AIL) faces challenges with sample inefficiency because of its reliance on sufficient on-policy data to evaluate the performance of the current policy during reward function updates. In this work, we study the convergence properties and sample complexity of off-policy AIL algorithms. We show that, even in the absence of importance sampling correction, reusing samples generated by the $o(\sqrt{K})$ most recent policies, where $K$ is the number of iterations of policy updates and reward updates, does not undermine the convergence guarantees of this class of algorithms. Furthermore, our results indicate that the distribution shift error induced by off-policy updates is dominated by the benefits of having more data available. This result provides theoretical support for the sample efficiency of off-policy AIL algorithms. To the best of our knowledge, this is the first work that provides theoretical guarantees for off-policy AIL algorithms.
arXiv:2607.07401v1 Announce Type: new Abstract: While whole-body multimodal medical imaging scanners have been increasingly recognized for more effective medical applications, the excessive long acquisition time in PET-MR scanning is a major obstacle in more efficient clinical practice. Deep learning-based MRI translation provides a potential solution to reduce scan duration. However, current models often focus on specific anatomical regions and face challenges for whole-body scans that consists of highly heterogeneous feature distributions mainly due to (1) different anatomical regions across whole-body, and (2) lesions or pathological tissues. This paper tackles the challenges through a novel Heterogeneity-Adaptive Diffusion Schrodinger Bridge (HA-DSB) framework. By explicitly modeling translation as stochastic transport between source and target distributions, HA-DSB incorporates region context embeddings derived from a vision-language model (VLM) to enable region-specific modeling. To enhance fidelity of the pathological tissue, lesion-aware metabolic prior from PET is integrated directly into the bridge dynamics through a dual-stage guidance mechanism. Specifically, a PET-guided noise modulation module adaptively scales spatial diffusion perturbations during the forward process, while PET features are leveraged during the reverse process to selectively amplify lesion-relevant structures via an attention mechanism. Experiments demonstrate the superiority of our method across different body regions in whole-body MRI translation and show improved translation quality in lesion areas under PET guidance. Our code is available at Github.
arXiv:2607.07380v1 Announce Type: new Abstract: Large language models (LLMs) achieve a strong performance in question answering (QA), but remain prone to hallucinations and suffer from limited transparency. Retrieval-augmented generation (RAG) can improve factuality, yet decisions about when and how to retrieve from external resources are typically based on opaque policies or computationally inefficient multi-step prompting procedures. We propose an uncertainty-aware framework for adaptive QA based on explicit signals derived from LLM internal representations. We distinguish between knowledge insufficiency and knowledge ambiguity or conflict, and efficiently estimate these from hidden states in a single forward pass. These signals guide system behaviour: RAG is triggered when knowledge is insufficient, while additional reasoning is applied when ambiguity or conflict is high. By grounding adaptive decisions in decomposed and efficiently estimable uncertainty signals, this approach provides a transparent and practical alternative to existing retrieval and reasoning strategies supporting the design of interpretable user-facing tools.
arXiv:2606.31615v2 Announce Type: replace Abstract: Exceptionally, a bunched electron beam can get trapped by its own spontaneously emitted synchrotron undulator radiation in the self-interaction scheme of TES (Tapering Enhanced Superradiance). In this scheme, excess radiative energy is extracted from the beam by tapering the undulator after the bunch trapping. To avoid slippage of the radiation wavepacket away from the bunch, the interaction takes place in a waveguide with a slow group velocity mode. Here we study the time domain waveform of the Electric Field and the radiation energy buildup in this scheme. We compare its analytical theory and numerical simulations in an ideal exemplary setup based on a rectangular waveguide and a planar undulator
arXiv:2607.07127v1 Announce Type: cross Abstract: Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials. Its Boltzmann distributions are parametrized analytically by coupling constants, but these bare parameters are weak predictors of observables -- extracting physics typically requires extensive simulation. While normalizing flows have emerged as effective samplers at fixed couplings, it remains difficult to interpret what these networks have learned. This raises a natural question: can the physics be read off directly from the flow network parameters themselves, and can those parameters be generated for unseen theories? We propose lattice field theory as a testbed for neural network interpretability: because the target physics is qualitatively well-understood and smoothly varying, it provides ideal synthetic data with known ground truth. To this end, we introduce JEPAWG, a Joint-Embedding Predictive Architecture-based Weight Generator that maps couplings directly to flow weights via a learned latent space. On a scalar theory at lattices of size $6^2$ to $11^2$, the JEPAWG latent space recovers the correct intrinsic dimension of the underlying manifold, locates the phase transition, and encodes a finite-size shift aligned with the 2D Ising exponent $\nu \approx 1$, allowing us to uncover physical structure by studying the network weights alone. This suggests the fascinating idea of treating the network weights as a new type of physical observable. As a generator, JEPAWG also interpolates and extrapolates to unseen couplings effectively and remains robust to weight-space discontinuities introduced by multi-seed training data, outperforming PCA, AE, and VAE baselines.
arXiv:2607.07390v1 Announce Type: new Abstract: Nonverbal communication through head and neck movement is fundamental to human social signalling, yet how robotic neck morphology translates motion into communicative information remains poorly understood. We present an information-theoretic framework characterising robot neck movement as a communication channel, quantifying information transmitted and energy expended across varied configurations. Using a robotic neck platform, we recorded 84 video stimuli spanning three rotational degrees of freedom (DoF), varying amplitude, acceleration, and frequency, measuring Shannon entropy of pixel-change signals alongside energy consumption. A perceptual study validated communicative interpretations of each motion. While humans typically engage one axis per gesture, robots are unconstrained by biological architecture, motivating tests up to 3 DoF. Yet communicative information peaks at two DoF and decreases at three despite rising energy cost, a phenomenon we term the morphological information bottleneck. Motion parameter effects were parameter-dependent, some additive, others non-linear. We introduce the Motor Information Space, a framework mapping entropy against energy to expose communicative efficiency across morphologies, in which the optimal configuration achieves 5.26 bits at competitive energy cost. Perception data further confirm multi-axis movements reduce clarity. These findings challenge the assumption that anatomical completeness improves robotic expressiveness, establishing a quantitative basis for morphological design in robots, especially humanoids.
arXiv:2607.07197v1 Announce Type: cross Abstract: Achieving a genuine quantum advantage relies on two distinct non-classical resources that restrict efficient classical simulation: entanglement and magic (nonstabilizerness). We investigate the interplay between these resources by characterizing the Pareto frontiers of extreme magic at fixed entanglement for systems of two qutrits ($d=3$) and two ququints ($d=5$). Unlike the case of two qubits, the Schmidt spectrum for two qutrits features two independent entanglement parameters, resulting in two-dimensional Pareto surfaces. For the lower frontier, we recast the minimal magic as a compact function of concurrence and negativity, with a maximal value of $\ln 2$. For the upper frontier, we determine the maximal stabilizer R\'enyi entropy to be $M_2 = \ln(81/17) \approx 1.561$, which tightens the previous theoretical bound of $\ln 5\approx 1.609$ and improves on earlier numerical estimates. The maximum magic is achieved at eighteen distinct maxima categorized into three families of six permutation-equivalent spectra. We provide analytical expressions for the maximal magic in the neighborhood of each maximum and for the corresponding maximally magical states which turn out to be Weyl-Heisenberg-covariant fiducial states for mutually unbiased bases. Finally, numerical analysis of two ququints ($d=5$) reveals six permutation-inequivalent maxima with a peak magic value of $M_2 = \ln(625/49) \approx 2.546$. Based on these findings, we conjecture that the maximal magic for a bipartite system of two qudits with prime dimension $d$ is given by $\ln [ d^4 / (2d^2 - 1) ]$, which reproduces the previously known value for qubits, as well as the values derived here for qutrits and ququints.
arXiv:2607.07500v1 Announce Type: new Abstract: Time series classification (TSC) is dominated by a two-stage paradigm: train a feature encoder -- either from scratch on the target dataset or via pretraining on large corpora -- and then fit a task-specific classifier on top. While effective, this decoupling optimizes representation learning independently of the classification objective, requires per-dataset training, and prevents the model from exploiting label information during inference. We introduce TimEE, a 4.5M-parameter foundation model for end-to-end TSC via in-context learning. Given a labeled support set and a query time series, TimEE directly outputs a predicted class distribution in a single forward pass with no per-dataset training required. Following the prior-data fitted network (PFN) framework, TimEE is meta-trained exclusively on synthetic TSC tasks, where each task contains time series with distinct class identities arising from structured distributional shifts in the generative process. Despite seeing no real time series during pre-training, TimEE ranks first in ROC AUC (and third on accuracy) on the UCR benchmark among all compared methods, which include both foundation models and supervised deep learning baselines. To our knowledge, TimEE is the first purely synthetic-pretrained model to reach state-of-the-art performance on the UCR benchmark. These results establish end-to-end ICL with synthetic priors as a compelling, largely unexplored direction for TSC, with scaling, prior design, and richer generation mechanisms as natural avenues for improvement. Code is publicly available at http://github.com/automl/timee.