arXiv:2512.15391v3 Announce Type: replace-cross Abstract: Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic propositional logic. We outline how this theorem may be proved semantically via the definability of bisimulation quantifiers, and how it generalizes to an open mapping theorem between Esakia spaces. We also discuss connections between uniform interpolation and research in categorical logic, algebra, and model theory.
Science Journals
arXiv:2605.00273v2 Announce Type: replace Abstract: Text-to-image diffusion models achieve impressive visual fidelity, yet they remain unreliable in multi-object generation. Despite extensive empirical evidence of these failures, the underlying causes remain unclear. We begin by asking how much of this limitation arises from the data itself. To disentangle data effects, we consider two regimes across different dataset sizes: (1) concept generalization, where each individual concept is observed during training under potentially imbalanced data distributions, and (2) compositional generalization, where specific combinations of concepts are systematically held out. To study these regimes, we introduce mosaic (Multi-Object Spatial relations, AttrIbution, Counting), a controlled framework for dataset generation. By training diffusion models on mosaic, we find that scene complexity plays a dominant role rather than concept imbalance, and that counting is uniquely difficult to learn in low-data regimes. Moreover, compositional generalization collapses as more concept combinations are held out during training. These findings highlight fundamental limitations of diffusion models and motivate stronger inductive biases and data design for robust multi-object compositional generation.
arXiv:2605.00358v2 Announce Type: replace Abstract: LLM parameter editing methods commonly rely on computing an ideal target hidden-state at a target layer (referred as anchor point) and distributing the target vector to multiple preceding layers (commonly known as backward spreading) for cooperative editing. Although widely used for a long time, its underlying basis have not been systematically investigated. In this paper, we first conduct a systematic study of its foundations, which helps clarify its capability boundaries, practical considerations, and potential failure modes. Then, we propose a simple and elegant alternative that replaces backward spreading with forward-propagation. Instead of optimizing the target at the last editing layer, we optimize the anchor point at the first editing layer, and then propagate it forward to obtain accurate and mutually compatible target hidden-states for all subsequent editing layers. This approach achieves the same computational complexity as existing methods while producing more accurate layer-wise targets. Our method is simple, without interfering with either the computation of the initial target hidden state or any other components of the subsequent editing pipeline, and thus constituting a benefit for a wide range of LLM parameter editing methods.
arXiv:2605.01446v3 Announce Type: replace Abstract: Support vector regression with Mean Absolute Percentage Error (MAPE) loss is theoretically well-motivated for forecasting applications where accuracy is evaluated in relative terms, but the sample-dependent dual box constraints it induces have not been addressed in the published SMO literature. We derive a Sequential Minimal Optimization algorithm for this setting and prove a structural-invariance result: the MAPE modification affects exactly two components of the SMO iteration -- working-set selection and analytic-update clipping -- leaving gradient bookkeeping and curvature computation identical to classical epsilon-SVR. Building on this invariance, we establish four efficiency improvements (asymmetric freeze-counters, warm-starting, block working-set updates of size four, and per-pair tolerance scaling) and resolve a previously-open convergence problem for the odd-symmetry kernel variant via adaptive spectral regularization. Numerical validation against three reference solvers across eleven synthetic configurations certifies solution agreement within standard tolerance. Wall-time benchmarks show the present algorithm achieves the lowest median runtime on every tested configuration against OSQP, MOSEK, and Clarabel. At production scale, the algorithm converges on the California Housing benchmark while the patched LIBSVM reference implementation reaches its iteration ceiling without satisfying optimality -- demonstrating the practical necessity of the theoretical efficiency mechanisms. An open-source R package and an explicit solver-adaptation recipe are provided.
arXiv:2605.01616v2 Announce Type: replace Abstract: Human behavior is challenging to measure continuously at scale, yet traces of daily routines and well-being may be reflected in interactions with personal devices. We investigate whether encrypted smartphone network traffic can serve as a passive sensing signal for behavioral states related to sleep disturbance, stress, and loneliness. To capture both population-level patterns and individual-specific behavior, we employ a transformer-based model with user-specific adapters that learns representations of network activity while accounting for personal baselines and deviations from them. To improve interpretability, we further analyze these representations using sparse representation learning to identify latent behavioral features associated with distinct activity patterns. We relate the resulting features to sleep disturbance, stress, and loneliness using generalized estimating equations with Mundlak decomposition, enabling separation of stable between-person differences from within-person changes over time. Our analysis reveals that the three outcomes are characterized by different temporal dynamics: stress is predominantly associated with persistent between-person variation, loneliness is more strongly linked to within-person fluctuations, and sleep disturbance reflects a combination of both. Importantly, these within-person behavioral signals are not recovered by conventional handcrafted network-traffic features, highlighting the advantages of learned representations for longitudinal behavioral modeling. Overall, our findings demonstrate that encrypted network traffic contains interpretable behavioral information and can support passive, scalable monitoring of behavioral dynamics, particularly changes relative to an individual's typical pattern of activity.
arXiv:2605.02439v3 Announce Type: replace Abstract: Synthesizing realistic and diverse anomalous samples from limited data is vital for robust model generalization. However, existing methods struggle to reconcile fidelity and diversity, often hampered by distribution misalignment and overfitting, respectively.To mitigate this, we introduce Anomaly Preference Optimization,a novel paradigm that reformulates anomaly generation as a preference learning problem.Central to our approach is an implicit preference alignment mechanism that leverages real anomalies as positive references, deriving optimization signals directly from denoising trajectory deviations without requiring costly human annotation. Furthermore, we propose a Time-Aware Capacity Allocation module that dynamically distributes model capacity along the diffusion timeline,prioritizing structural diversity during highnoise phases while enhancing fine-grained fidelity in low-noise stages. During inference, a hierarchical sampling strategy modulates the coherencealignment trade-off, enabling precise control over generation. Extensive experiments demonstrate that significantly outperforms existing baselines,achieving state-of-the-art performance in both realism and diversity.
arXiv:2605.02676v4 Announce Type: replace Abstract: Optical skyrmionic textures, including N\'eel-type skyrmions and merons, have attracted significant attention across diverse physical systems for their promising applications in ultra-precise metrology, optical information processing, and quantum technologies. However, the lack of an effective approach for their on-chip directional transport and manipulation impedes their applications in photonic integrated devices. Here, we numerically demonstrate a photonic platform that utilizes topologically protected valley edge state to achieve robust on-chip directional transport of optical spin merons. These merons originate from spin-orbit coupling within the evanescent field at the valley photonic crystal surface and exist as eigenstates of the topologically protected edge state, ensuring their robust propagation even in the interface with defects. Leveraging the valley degree of freedom of topological edge states, we further achieve valley-locked spin merons, enabling flexible control over the polarity of spin merons. By endowing spin merons with topological protection in momentum space, our work provides an approach for robust on-chip transport and manipulation of spin merons, thereby paving the way for expanding their application in photonic systems.
arXiv:2605.05138v2 Announce Type: replace Abstract: We evaluate an initial coding-agent system for ARC-AGI-3 in which the agent maintains an executable Python world model, verifies it against previous observations, refactors it toward simpler abstractions as a practical proxy for an MDL-like simplicity bias, and plans through the model before acting. The system is intentionally direct: it uses a scripted controller, predefined world-model interfaces, verifier programs, and a plan executor, but no hand-coded game-specific logic. The agent-facing prompts, workspace, and controller contain no game-specific code, game-specific prompts, hand-coded heuristics, hidden solutions, or other game-specific information; the same agent and prompts are used across games. Because the coding agent has broad system access, we audit unintended information channels, describe earlier vulnerable harnesses, and explain how the current harness closes observed leakage channels while reducing benchmark-specific information exposure. We report results on the 25 public ARC-AGI-3 games. Each playthrough starts from a fresh agent instance and clean workspace, with no access to files or conversation state from earlier playthroughs. With GPT-5.5 high reasoning effort, the agent fully solved 15 games and achieved a mean per-game RHAE of 58.12%. With GPT-5.4 high reasoning effort, it fully solved 8 games and achieved a mean per-game RHAE of 41.29%. Performance on the private validation set, which is not yet available to us, remains to be tested. Overall, the results provide preliminary evidence that verifier-driven executable world models are a promising approach for ARC-AGI-3 agents. Full run artifacts are released with the code at https://github.com/astroseger/arc-3-agents-baseline1.
arXiv:2605.05936v2 Announce Type: replace Abstract: The primary objective of this work is the determination of fluences and characteristics of fast neutrons, other hadrons, and highly ionizing particles in the environment of the MoEDAL experiment at the Large Hadron Collider. These particles constitute an experimental background for the passive Nuclear Track Detectors (NTDs) used by MoEDAL to search for tracks potentially produced by Dirac magnetic monopoles, in particular by particles indistinguishable in NTD from monopoles. The study is based on data acquired by the Timepix hybrid silicon pixel detector network, which represents the first and only active detector system installed and operated as part of the MoEDAL experiment from 2013 to 2018. The Timepix detector network enables real-time measurements of mixed radiation fields, including the composition, spectral properties, and directional characteristics of individual radiation components across different regions of the MoEDAL experimental area. The paper presents detailed results of the radiation field analysis with emphasis on neutrons and highly ionizing particles, including their directional distributions. The first results demonstrating the spatial tracking capabilities of the Timepix detectors are also reported, illustrating the reconstruction of particle direction and energy-loss profiles from individual detector frames.
arXiv:2605.11855v2 Announce Type: replace Abstract: Sequence learning is dominated by Transformers and parallelizable recurrent neural networks (RNNs) such as state-space models, yet learning long-term dependencies remains challenging, and state-of-the-art designs trade power consumption for performance. The Bistable Memory Recurrent Unit (BMRU) was introduced to enable hardware-software co-design of ultra-low power RNNs: quantized states with hysteresis provide persistent memory while mapping directly to analog primitives. However, BMRU performance lags behind parallelizable RNNs on complex sequential tasks. In this paper, we identify gradient blocking during state updates as a key limitation and propose a cumulative update formulation that restores gradient flow while preserving persistent memory, creating skip-connections through time. This leads to the Cumulative Memory Recurrent Unit (CMRU) and its relaxed variant, the $\alpha$CMRU. Experiments show that the cumulative formulation dramatically improves convergence stability and reduces initialization sensitivity. The CMRU and $\alpha$CMRU match or outperform Linear Recurrent Units (LRUs) and minimal Gated Recurrent Units (minGRUs) across diverse benchmarks at small model sizes, with particular advantages on tasks requiring discrete long-range retention, while the CMRU retains quantized states, persistent memory, and noise-resilient dynamics essential for analog implementation.
arXiv:2605.12213v2 Announce Type: replace Abstract: LLM-based conversational AI agents struggle to maintain coherent behavior over long horizons due to limited context. While RAG-based approaches are increasingly adopted to overcome this limitation by storing interactions in external memory modules and performing retrieval from them, their effectiveness in answering challenging questions (e.g., multi-hop, commonsense) ultimately depends on the agent's ability to reason over the retrieved information. However, existing methods typically retrieve memory based on semantic similarity to the raw user utterance, which lacks explicit reasoning about missing intermediate facts and often returns evidence that is irrelevant or insufficient for grounded reasoning. In this work, we introduce Goal-Mem, a goal-oriented reasoning framework for RAG-based agentic memory that performs explicit backward chaining from the user's utterance as a goal. Rather than progressively expanding from retrieved context, Goal-Mem decomposes each goal into atomic subgoals, performs targeted memory retrieval to satisfy each subgoal, and iteratively identifies what information from memory should be retrieved when intermediate goals cannot be resolved. We formalize this process in Natural Language Logic, a logical system that combines the verifiability of reasoning provided by FOL with the expressivity of natural language. Through extensive experiments on two datasets and comparing to nine strong memory baselines, we show that Goal-Mem consistently improves performance, particularly on tasks requiring multi-hop reasoning and implicit inference.
arXiv:2604.27460v4 Announce Type: replace-cross Abstract: In this letter, we study a model-based inverse problem for infinite-horizon linear-quadratic differential games with descriptor dynamics. Given an observed feedback strategy profile, we seek to identify all cost functions that rationalize it as a feedback Nash equilibrium; this collection is referred to as the solution set. We characterize the solution set, show that it is rectangular and convex, and provide an algorithm for computing an admissible realization whenever it is nonempty. We also show that, compared with the corresponding inverse problem for standard state-space dynamics, descriptor dynamics modify the geometry of the solution set and may reduce identifiability. Finally, we illustrate the results with numerical examples.
arXiv:2605.28831v2 Announce Type: replace Abstract: Long-horizon memory question answering often requires sparse evidence from heterogeneous histories, including events, object states, visual observations, temporal relations, and causal steps. Existing memory interfaces expand reader context, retrieve semantically related chunks, or expose graph neighborhoods, but they are not explicitly designed to select compact evidence for a fixed reader. We propose Structured Spatiotemporal Scene--Event Memory (S3Mem), a query-time memory interface that writes textual, visual, and agent-use histories into structured scene--event units and routes compact evidence packs to the reader. Its router scores candidate units, query anchors, and anchor--support links, enabling both single-hop selection and short multi-hop evidence chains without reader fine-tuning or test-time training. Across LoCoMo, EMemBench Visual Games, and AMA-Bench, S3Mem provides a strong score--token trade-off, with the clearest gains on localized event, state, temporal, causal, or provenance evidence. On LoCoMo, S3Mem reaches \(0.48\) F1 and \(0.40\) BLEU with (1{,}073) evidence tokens per question, about \(15.8\times\) fewer than the LoCoMo reference. On EMemBench Visual Games, it obtains the best F1 and second-best accuracy with only \(189\)tokens.On AMA-Bench, it is not the highest-scoring method, but remains competitive while using the fewest reader-visible evidence tokens.
arXiv:2606.00568v2 Announce Type: replace Abstract: Bulk gene expression profiling, which aggregates pooled RNA across cells within a biological sample, remains important in the single-cell era because it is typically less noisy, more sensitive, and more cost-effective than single-cell assays. Accordingly, a growing body of computational methods seeks to recover causal relations among genes from bulk expression data. However, aggregation is a lossy, non-invertible coarsening of the underlying cellular system, and it remains unclear whether and under what conditions causal relations are recoverable from aggregated bulk gene expression data. To answer this, we formalize recoverability under aggregation through two notions of consistency: functional-form consistency and conditional-independence consistency. We then derive necessary and sufficient conditions for recoverability, showing that these properties are preserved only under linear aggregations (e.g., sum/mean) coupled with affine structural equations. To assess the practical plausibility of these conditions, analyses of four bulk and four single-cell gene expression datasets further reveal that the estimated pairwise regulatory functions among genes deviate from linearity in both data types, providing limited empirical support for the linearity assumptions required for recoverability. Together, these results caution against recovering causal relations from aggregated bulk expression data without strong additional assumptions.
arXiv:2606.00706v2 Announce Type: replace Abstract: Cross-modal remote sensing image retrieval aims to retrieve semantically related scenes across heterogeneous sensing modalities. This remains challenging because paired observations may differ substantially in imaging physics, spatial resolution, spectral configuration, and visual appearance. Moreover, a single retrieval projection trained with one objective may be insufficient to jointly support cross-modal semantic alignment and same-modal neighbourhood preservation. We propose CR-JEPA, a Cross-modal Retrieval Joint-Embedding Predictive Architecture for dual-modality remote sensing retrieval. The model uses modality-specific stems, a shared transformer trunk, and JEPA-style predictive objectives to estimate masked latent target features within and across modalities. Inspired by LeJEPA, we apply Sketched Isotropic Gaussian Regularization to raw retrieval projections to stabilize embeddings and mitigate collapse. CR-JEPA further employs a decoupled-head design with a unified retrieval head for same-modal retrieval and a cross-modal retrieval head for cross-modal search. We evaluate CR-JEPA on BEN-14K, CBRSIR_VS, and DSRSID. On BEN-14K, CR-JEPA improves S1 to S2 retrieval from 61.23% to 75.82% and S2 to S1 retrieval from 63.73% to 75.40% over X-JEPA, while also achieving competitive same-modal retrieval with fewer parameters.
MENTIS: What Belief Changes Under Alignment? Measuring Multi-Scale Latent Torsion in Language Models
arXiv:2606.01060v2 Announce Type: replace Abstract: Preference alignment has substantially improved the observable behavior of large language models, yet it remains unclear what alignment changes internally. Aligned systems still fail under jailbreaks, prompt injection, and retrieval-time corruption, suggesting behavior-level evaluation alone is incomplete. Post-training should leave measurable traces in internal computation. We ask: when an instruction-tuned (IT) model becomes a preference-aligned (PA) model, what geometric structure changes, where do those changes concentrate, and how selectively do they vary across concepts, prompts, and model families? We introduce MENTIS, a geometry-first framework for measuring alignment-induced internal reorganization in paired checkpoints. MENTIS compares IT and PA models using a primary layerwise covariance-based torsion norm (T1), a secondary spectral torsion diagnostic (T2), and an Energy-Radiance-Activation measure (ERA) for depth localization. Across four 7-8B model pairs on LITMUS, our study reveals that alignment-induced change is selective rather than uniform: normative concepts exhibit larger torsion shifts than factual concepts on average; torsion is negatively correlated with contextual entropy; and peak effects localize to architecture-specific mid-to-late layers. The same pattern appears across word-level, prompt-level, and model-level analyses. These results suggest preference alignment leaves structured, depth-localized geometric signatures in internal computation beyond what behavior-level evaluation alone can reveal.
arXiv:2606.01205v2 Announce Type: replace Abstract: Vision-language navigation (VLN) for UAVs demands grounding free-form instructions into 6-DoF flight under partial observability. While Vision-Language-Action (VLA) models excel at semantic reasoning, they suffer from brittleness due to geometric inconsistency and dynamics mismatch. To address this, we propose ImagineUAV, an imagination-driven framework leveraging cascaded world-action modeling. Instead of direct regression, ImagineUAV employs a latent video diffusion model to generate instruction-conditioned future observations, explicitly imagining environmental evolution, from which 6-DoF motions are inferred via an action extractor. A kinodynamic planner then refines these estimates into collision-free trajectories. Additionally, a step-distilled inference pipeline ensures real-time execution. With only 1.3B parameters, ImagineUAV outperforms prior VLN and VLA baselines on benchmarks and real-world flights, validating the practicality of imagination-driven aerial navigation.
arXiv:2606.02351v2 Announce Type: replace Abstract: Bayesian optimization (BO) is a popular and effective approach for tuning expensive, noisy experiments, but requires the formulation of an explicit objective function. Preferential BO (PBO) removes this requirement by learning from pairwise human feedback, yet existing methods struggle to efficiently optimize beyond low- and medium-dimensional problems due to their global search approaches. We address this limitation by developing a family of local PBO methods that transfer key ideas from high-dimensional BO to the preferential setting. In particular, we introduce local PBO methods which adapt trust-region and derivative-informed local search to pairwise preference feedback, where the latter exploits first- and second-order derivatives of the Laplace-approximated GP posterior. Our benchmark on GP sample paths, standard optimization benchmark functions, and policy-search tasks shows that local PBO methods are especially effective in high-dimensional and complex landscapes with steep optima. Compared with global preference-based baselines, they can substantially reduce cumulative regret, making them particularly useful for real-world preference-based optimization tasks such as policy search.
arXiv:2606.07118v2 Announce Type: replace Abstract: Simulation is central to robot learning, yet the sim-to-real gap remains a major bottleneck. Existing approaches often tackle visual or dynamic gaps separately, overlooking how these individual mismatches accumulate and propagate throughout the robot's state evolution. In this paper, we introduce QuadVerse, an integrated framework that uses reconstructed scenes as a calibration substrate for aligning visual perception, physical interaction, and actuator dynamics. From captured RGB videos, we reconstruct geometry-constrained 3D Gaussian Splatting (3DGS) scenes that support batched photorealistic ego-view rendering and collision-ready semantic mesh extraction. The meshes further enable contact calibration by initializing spatially varying friction priors and refining them through trajectory-based posterior search. To address remaining actuator discrepancies, QuadVerse trains a residual dynamics compensator by replaying real-world trajectories on the contact-calibrated terrain, reducing the entanglement between terrain-induced contact errors and actuator non-idealities. Experiments show that QuadVerse improves reconstruction quality and locomotion tracking over relevant baselines. Leveraging this foundation, we demonstrate robust zero-shot visual-navigation policy deployment without task-specific real-world rollouts.
arXiv:2505.08908v3 Announce Type: replace-cross Abstract: Many researchers apply classical statistical decision theory to evaluate treatment choices and learn optimal policies. However, because this framework relies solely on realized outcomes under chosen actions and ignores counterfactuals, it cannot assess the quality of a decision relative to feasible alternatives at the unit level, which is an important requirement in some settings. For example, in pretrial bail decisions, a judge must balance crime prevention upon release against the risk of imposing unnecessary burdens on arrestees. A central challenge in this framework is identification: since only one potential outcome is observed per unit, counterfactual risk is typically not identifiable. We show that, under strong ignorability, counterfactual risk is identifiable if and only if the loss is additive in the potential outcomes. We further demonstrate that additive counterfactual losses can yield treatment recommendations that differ from those based on standard losses when more than two treatment options are available. We show that additive counterfactual losses capture not only decision accuracy but also decision difficulty, whereas standard losses reflect accuracy alone. Finally, we introduce a symbolic linear inverse program that determines whether a given counterfactual loss yields an identifiable risk, without requiring data.
arXiv:2506.14266v3 Announce Type: replace-cross Abstract: Countless biological processes are fueled by energy-rich molecules like ATP and GTP that supply energy with extreme efficiency. However, designing similar energy-delivery schemes from the bottom up, essential for the development of powered nanostructures and other \emph{de novo} machinery, presents a significant challenge: how can an energy-rich structure be stable in solution yet still deliver this energy at precisely the right time? In this paper, we present a purely physical mechanism that solves this challenge, facilitating energy transfer akin to ATP hydrolysis, yet occurring between synthetic nanostructures without any biochemical interactions. This targeted energy delivery is achieved by exploiting a differentiable state-based model to balance the energy profiles that govern the structural transitions in the two nanostructures, creating a coupled relaxation pathway with minimal barriers that facilitates energy delivery. We verify the effectiveness and robustness of this mechanism through Langevin Dynamics simulations, demonstrating that a bath of the high-energy structures can systematically and repeatedly drive the target structure out of equilibrium, enabling it to perform tasks. As the mechanism operates only through explicit physical forces without any biochemistry or internal state variables, our results present generic and far-reaching design principles, setting the stage for the next generation of synthetic nanomachines.
arXiv:2506.20573v4 Announce Type: replace-cross Abstract: Public datasets, crucial for modern machine learning and statistical inference, often contain low-quality or contaminated samples that can harm model performance. This creates a need for principled prefiltering procedures that a data provider can apply to protect the accuracy of a range of potential downstream statistical and learning procedures simultaneously. In this work, we formalize and analyze Learner-Agnostic Robust data Prefiltering (LARP), the problem of designing prefiltering procedures with guarantees on the worst-case loss over a pre-specified set of learners. We establish the feasibility of LARP in two theoretical settings, by providing upper-bound guarantees on the worst-case loss. Our theoretical results indicate that protecting heterogeneous learner sets via LARP comes at the price of some performance loss compared to individual, learner-specific prefiltering; we call this gap the price of LARP. To assess this gap in performance, we empirically measure the price of LARP across image and tabular tasks. We further explore potential benefits of LARP from the perspective of saving on repeated data curation efforts, in a game-theoretic model where the downstream learners can split the cost of the single prefiltering.
arXiv:2507.08920v4 Announce Type: replace-cross Abstract: We introduce AMix-1, a powerful protein foundation model built on Bayesian Flow Networks and empowered by a systematic training methodology, encompassing pretraining scaling laws, emergent capability analysis, in-context learning mechanism, and test-time scaling algorithm. To guarantee robust scalability, we establish a predictive scaling law and reveal the progressive emergence of structural understanding via loss perspective, culminating in a strong 1.7-billion model. Building on this foundation, we devise a multiple sequence alignment (MSA)-based in-context learning strategy to unify protein design into a general framework, where AMix-1 recognizes deep evolutionary signals among MSAs and consistently generates structurally and functionally coherent proteins. This framework enables the successful design of a dramatically improved AmeR variant with an up to $50\times$ activity increase over its wild type. Pushing the boundaries of protein engineering, we further empower AMix-1 with an evolutionary test-time scaling algorithm for in silico directed evolution that delivers substantial, scalable performance gains as verification budgets are intensified, laying the groundwork for next-generation lab-in-the-loop protein design.
arXiv:2509.07709v2 Announce Type: replace-cross Abstract: Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional non-equilibrium phases beyond the Mermin-Wagner limit or dissipative state preparation demand a systematic analysis of quantum many-body phases out of equilibrium. Akin to the equilibrium case, this requires the computation of the low-lying eigenstates of Lindbladians, a problem challenging conventional approaches for simulating quantum many-body systems. Here, we undertake a first step to overcome this limitation and introduce a tensor-network-based framework to systematically compute not only steady states, but also low-lying excited states for large, driven quantum many-body systems. Our framework is based on recent advances utilizing complex-time Krylov spaces, and we leverage these ideas to create a toolbox tailored to solve the challenging non-Hermitian eigenvalue problem ubiquitous in open quantum systems. At the example of the interacting Bose-Hubbard model driven by dissipation-assisted hopping, we demonstrate the high efficiency and accuracy. From a reliable finite-size scaling analysis of the spectral gap, we find strong evidence for nonlinear hydrodynamic behavior consistent with Kardar-Parisi-Zhang-type superdiffusive relaxation and establish the existence of exponentially accelerated, anomalous relaxation. This method unlocks the capability of spectral analysis of generic open quantum many-body systems, suitable also for non-Markovian environments.
arXiv:2512.11000v2 Announce Type: replace-cross Abstract: Representations pervade our daily experience, from letters representing sounds to bit strings encoding digital files. While such representations require externally defined decoders to convey meaning, conscious experience is fundamentally different: a neural state corresponding to perceiving a red square cannot alternatively encode the experience of a green triangle. This intrinsic property of consciousness suggests that conscious representations must be unambiguous in a way that conventional representations are not. We formalize this intuition using information theory, defining representational ambiguity as the conditional entropy H(I|R) over possible interpretations I given a representation R. Through experiments on neural networks trained to classify MNIST digits, we demonstrate that relational structures in network connectivity can unambiguously encode representational content. From relational structure alone, we achieve perfect (100%) accuracy for dropout-trained networks and 38% for standard backpropagation (chance: 10%) in identifying output neuron class identity, despite identical task performance, demonstrating that representational ambiguity can arise orthogonally to behavioral accuracy. We further show that spatial position of input neurons, relevant to phenomenal properties like visual field location, can be decoded from network connectivity with R^2 up to 0.844. These results provide a quantitative method for measuring representational ambiguity in neural systems and demonstrate that neural networks can exhibit the low-ambiguity representations posited as necessary (though not sufficient) by theoretical accounts such as narrow representationalism and IIT.