arXiv:2605.30942v1 Announce Type: new
Abstract: Modern vision models process images in a single feed-forward pass, which limits their ability to recover missing evidence or refine uncertain representations under incomplete observations. Inspired by the iterative nature of human perception, we introduce PRISM (Progressive Reasoning through Iterative Slot Memory), a pyramid vision architecture that reasons over images through iterative refinement. At a high level, PRISM groups visual features into object-centric representations, retrieves relevant patterns from a learned memory, and iteratively refines the representation to resolve ambiguity and recover missing information. This organize-recall-refine process operates recurrently across multiple scales, enabling progressive improvement of visual representations. Across standard vision tasks, including image classification, object detection, and semantic segmentation, PRISM achieves competitive performance while demonstrating improved robustness under incomplete observations such as occlusion. These results suggest that iterative reasoning with structured representations and memory is a promising direction for building more resilient and adaptive vision models. Source code and models will be released.
Science Journals
arXiv:2605.30941v1 Announce Type: new
Abstract: Supercontinuum generation is a key technology in nonlinear optics, supporting a wide range of applications in frequency metrology and spectroscopy. Integrated photonics offers a promising route toward compact and efficient supercontinuum sources, yet extending the bandwidth while maintaining high spectral flatness remains a central challenge. Here we demonstrate an integrated broadband supercontinuum source based on segment-chirped periodically poled lithium niobate (SC-PPLN) nanophotonic waveguides. By discretizing the chirped poling profile into independently optimized segments, this approach enables high-fidelity ferroelectric domain inversion with near-ideal duty cycles and establishes broadband quasi-phase matching, overcoming the domain inhomogeneity and efficiency limitations commonly encountered in conventional chirped poling. The engineered phase-matching landscape supports efficient wavelength conversion and simultaneous activation of multiple second- and third-order nonlinear processes. Experimentally, we achieve a spectrally flat supercontinuum spanning three optical octaves, from 320 nm in the ultraviolet to 2600 nm in the mid-infrared. These results establish segment-chirped poling as a practical strategy for broadband wavelength conversion and supercontinuum generation in integrated photonics.
arXiv:2601.21645v2 Announce Type: replace
Abstract: We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and output spaces, there is a parameter choice yielding the same end-to-end function such that its layers are equivariant with respect to some group actions on the latent spaces. Our result assumes that the parameters of the model are identifiable in an appropriate sense. This identifiability property has been established in the literature for a large class of networks, to which our results apply immediately, while it is conjectural for others. The theory we develop is grounded in an abstract formalism, and is therefore architecture-agnostic. Overall, our results provide a mathematical explanation for the emergence of equivariant structures in the weights of neural networks during training -- a phenomenon that is consistently observed in practice.
arXiv:2508.08204v2 Announce Type: replace
Abstract: There has been much recent interest in evaluating large language models for uncertainty calibration to facilitate model control and modulate user trust. Inference time uncertainty, which may provide a real-time signal to the model or external control modules, is particularly important for applying these concepts to improve LLM-user experience in practice. While many of the existing papers consider model calibration, comparatively little work has sought to evaluate how closely model uncertainty aligns to human uncertainty. In this work, we evaluate a collection of inference-time uncertainty measures, using both established metrics and novel variations, to determine how closely they align with both human group-level uncertainty and traditional notions of model calibration. We find that numerous measures show evidence of strong alignment to human uncertainty, even despite the lack of alignment to human answer preference. For those successful metrics, we find moderate to strong evidence of model calibration in terms of both correctness correlation and distributional analysis.
arXiv:2605.31346v1 Announce Type: cross
Abstract: Zeroth-order (black-box) optimization is applied when gradients are unavailable and objective evaluations rely on expensive simulations. In many such applications, the oracle fidelity is tunable: higher-accuracy queries reduce noise but incur higher computational costs. To capture this trade-off, we study an accuracy-aware wall-clock model where each query with fidelity $\delta$ has a cost $c(\delta)$, and we minimize the total time $T_{\mathrm{total}} = \sum_{k=1}^{N} c(\delta_k)$, subject to a target accuracy constraint. We show how the choice of oracle type, noise model, and optimization scheme induces explicit wall-clock-optimal choices for the algorithmic parameters. For instance, we demonstrate that accelerated methods can be wall-clock inferior to non-accelerated schemes. Furthermore, we characterize the conditions under which a constant fidelity strategy is optimal in the Big-O sense. Our framework provides a unified methodology to translate convergence guarantees into practical fidelity and batching recommendations.
arXiv:2602.16165v2 Announce Type: replace
Abstract: Training LLMs as interactive agents for multi-turn decision-making remains challenging, particularly in long-horizon tasks with sparse and delayed rewards, where agents must execute extended sequences of actions before receiving meaningful feedback. Most existing reinforcement learning (RL) approaches model LLM agents as flat policies operating at a single time scale, selecting one action at each turn. In sparse-reward settings, such flat policies must propagate credit across the entire trajectory without explicit temporal abstraction, which often leads to unstable optimization and inefficient credit assignment.
We propose HiPER, a novel Hierarchical Plan-Execute RL framework that explicitly separates high-level planning from low-level execution. HiPER factorizes the policy into a high-level planner that proposes subgoals and a low-level executor that carries them out over multiple action steps. To align optimization with this structure, we introduce a key technique called hierarchical advantage estimation (HAE), which carefully assigns credit at both the planning and execution levels. By aggregating returns over the execution of each subgoal and coordinating updates across the two levels, HAE provides an unbiased gradient estimator and provably reduces variance compared to flat generalized advantage estimation.
Empirically, HiPER achieves state-of-the-art performance on challenging interactive benchmarks, reaching 97.4\% success on ALFWorld and 83.3\% on WebShop with Qwen2.5-7B-Instruct (+6.6\% and +8.3\% over the best prior method), with especially large gains on long-horizon tasks requiring multiple dependent subtasks. These results highlight the importance of explicit hierarchical decomposition for scalable RL training of multi-turn LLM agents.
arXiv:2605.30434v1 Announce Type: new
Abstract: Real-world data analysis is inherently iterative, yet existing benchmarks mostly evaluate isolated or short interactive tasks, leaving agents' ability to track evolving analytical context over long horizons untested. We introduce LongDS, a benchmark for long-horizon, multi-turn data analysis where agents must maintain, update, restore, and compose evolving analytical states. LongDS comprises 68 tasks constructed from real-world Kaggle notebooks, spanning 2,225 turns across six domains including Geoscience, Business, and Education. Tasks are designed around state-evolution patterns (e.g., counterfactual perturbation, rollback, multi-state composition), with an average dependency span of 11.3 turns. Evaluating five state-of-the-art models, we find that the best model reaches only 48.45% average accuracy, performance drops nearly 47 points from early to late turns, and long-horizon errors account for 52%--69% of failures. Further analysis shows that additional agent steps do not necessarily improve performance, suggesting that the key bottleneck is maintaining a correct analytical state rather than increasing interaction budget. We release LongDS to support research on reliable long-horizon agentic data analysis. Code and data will be released at https://github.com/zjunlp/DataMind.
arXiv:2605.30431v1 Announce Type: new
Abstract: Recent progress in video diffusion models has enabled remarkable generative fidelity, yet leveraging these priors for restoration remains limited by the strong coupling between conditional and unconditional branches in standard classifier-free guidance. We introduce a training-free framework that enhances distorted and low-resolution videos by decoupling these signals in time. Our proposed Decoupled Time Guidance (DTG) evaluates the unconditional branch at a cleaner diffusion timestep, providing a lookahead prior that preserves geometry while suppressing replication of warped content. This temporal bias is annealed throughout sampling, allowing the model to transition from structure correction to detail refinement without retraining. Combined with any off-the-shelf restoration module in a plug-and-play manner, our approach improves perceptual coherence and restores plausible structure in AIgenerated and real-world videos alike. To facilitate evaluation, we curate GenWarp480, a benchmark of 4,400 distorted 480p videos synthesized from diverse text-to-video models. GenWarp480 focuses on characteristic generative degradations such as warped faces, body misalignments, and spatial artifacts, providing a purpose-built testbed for assessing robustness to generative errors. Extensive experiments demonstrate that our method achieves significant improvements in structural fidelity and temporal stability without any model training.
arXiv:2601.20774v2 Announce Type: replace
Abstract: Multitask learning and related frameworks have achieved tremendous success in modern applications. In multitask learning problem, we are given a set of heterogeneous datasets collected from related source tasks and hope to enhance the performance above what we could hope to achieve by solving each of them individually. The recent work of arXiv:2006.15785 has showed that, without access to distributional information, no algorithm based on aggregating samples alone can guarantee optimal risk as long as the sample size per task is bounded.
In this paper, we focus on understanding the statistical limits of multitask learning. We go beyond the no-free-lunch theorem in arXiv:2006.15785 by establishing a stronger impossibility result of adaptation that holds for arbitrarily large sample size per task. This improvement conveys an important message that the hardness of multitask learning cannot be overcame by having abundant data per task. We also discuss the notion of optimal adaptivity that may be of future interests.
arXiv:2605.30916v1 Announce Type: new
Abstract: AI benchmarks have well-documented limitations, with prior work examining contamination, saturation, and construct underspecification. Aggregation has received far less attention: benchmarks are typically summarized by uniformly averaging item-level scores, implicitly treating every test item as equally valuable. We model benchmarking as a multitask principal-agent game and show that the welfare loss from a benchmark is determined jointly by three item-level primitives: alignment with normative welfare priorities, marginal improvability, and performance variance. We translate the theory into an audit framework that ranks items along each of these three axes, and apply it to OLMES items using WORKBank for welfare, the EvoLM 4B suite for improvability, and the PolyPythias 410M panel for variance. The framework surfaces items that are Pareto-inferior within OLMES subject to a pro-worker welfare operationalization. All code is available at https://github.com/stair-lab/principal-agent-benchmarks.
arXiv:2605.31152v1 Announce Type: cross
Abstract: This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions. When the error is measured in $L^p([0,1]^d)$ norm and the approximator is a network with width $W$ and depth $L$, recent works have proven the supper approximation rate $\mathcal{O}((WL)^{-2s/d})$ for Besov space $\mathcal{B}^s_{q,r}([0,1]^d)$ under the Sobolev embedding condition $s/d>1/q-1/p$. In order to overcome the curse of dimensionality in this rate, we extent this result to anisotropic and mixed smooth function classes. We establish the approximation rate $\mathcal{O}((WL)^{-2\tilde{s}})$ for anisotropic Besov space $\mathcal{B}^{\boldsymbol{s}}_{q,r}([0,1]^d)$ with anisotropic smoothness $\boldsymbol{s}=(s_1,\dots,s_d)$ under the embedding condition $\tilde{s} > 1/q-1/p$, where the mean smoothness $\tilde{s} = (\sum_{i=1}^d s_i^{-1})^{-1}$. For mixed smooth Besov space $\mathcal{MB}^s_{q,r}([0,1]^d)$ with mixed smoothness $s>1/q-1/p$, we show that the approximation rate $\mathcal{O}((WL)^{-2s})$ holds up to logarithmic factors. Using these results, we also derive approximation bounds for the composition of anisotropic Besov functions. As an application, it is shown that deep ReLU neural networks can achieve minimax optimal rates up to logarithmic factors for a wide range of smooth function classes.
arXiv:2605.31107v1 Announce Type: cross
Abstract: The ability to identify nanometer-scale nuclei of new phases in atom probe tomography (APT) is often limited by the sensitivity of clustering algorithms to user-defined control parameters. Conventional approaches typically rely on the Euclidean distance metric and consider only solute atoms, thereby discarding the solvent atoms that contain most of the spatial information. Here, we introduce a coordination-number metric based on the composition and apply it to higher-order clustering. Using various metrics, we investigate percolation in typical APT structures. By scaling clustering properties to the corresponding percolation thresholds, we define a self-similar variable that is almost invariant with respect to metrics, clustering parameters, and structural disorder. This variable provides a relevant description of clustering and enables the formal transfer of optimal parameters between clustering methods. We also study the characteristic clustering behavior in small precipitates and quantify how the precipitate-matrix interface alters the composition spectrum and broadens the clustering curve. Finally, using simulations that incorporate finite spatial resolution, detection efficiency, and other APT reconstruction artifacts, we show that the approach based on coordination numbers effectively compensates for heterogeneous dilations and outperforms solute-density-based methods in all tested scenarios.
arXiv:2512.07615v4 Announce Type: replace
Abstract: Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or matrix-product states (MPS) data encodings have emerged as a technique to systematically reduce degrees of freedom, existing formulations do not extend to complex geometries and complex flow physics. Both capabilities are offered by lattice Boltzmann methods, for which we develop a generalized MPS formulation. This development marks a paradigm shift from classical methods that rely on explicit grid refinement for data reduction. Instead, our approach exploits non-local correlations in the MPS representation to systemically compress the global fluid state directly without modifying the underlying grid. We benchmark the proposed solver against classical LBM using three-dimensional flows through structured media and vascular geometries. The results confirm that the MPS formulation reproduces the reference solution with high fidelity while achieving compression ratios exceeding two orders of magnitude, positioning tensor networks or MPS encodings as a scalable paradigm for continuum mechanics on high-performance GPU hardware.
arXiv:2605.31059v1 Announce Type: cross
Abstract: This paper characterizes the performance limits of optimal array designs using orthogonal and coherent waveforms for both linear and planar arrays. For orthogonal waveforms, we show that the single-target Cram\'er-Rao Bound (CRB) depends on the sum of the so-called spatial variances of the transmit (Tx) and receive (Rx) arrays, or equivalently, the spatial variance of the sum co-array weighted by the multiplicities of the virtual sensors. This reveals that CRB-optimal geometries are inherently redundant, highlighting a fundamental trade-off between mean squared error (MSE) and identifiability in parameter estimation. Moreover, we derive optimal Tx-Rx sensor allocations given a total sensor budget and show that unequal allocation (favoring the Rx) is optimal even for nonredundant arrays, questioning conventional designs. We extend our results to planar arrays, providing a new general condition that the spatial covariances of the Tx and Rx arrays should satisfy for the optimal waveforms to direct power in the target direction. Additionally, we establish a connection between Diophantine equations and array geometries with equal CRB, along with a constructive method for designing such arrays. Our work provides new guidelines for and insights into optimal array and waveform design with relevance in emerging active sensing multiple-input multiple-output systems.
arXiv:2605.30904v1 Announce Type: new
Abstract: Most visual tokenizers for image generation are bifurcated into two families with complementary limitations: continuous VAEs offer high-fidelity reconstruction but suffer from dense, entangled latents that are poorly suited for semantic control, whereas discrete VQ-based models enable autoregressive generation yet struggle with gradient sparsity, unstable training, and codebook collapse. In this work, we introduce MergeTok, a unified tokenizer that jointly optimizes continuous (VAE) and discrete (VQ) tokenizers within a encoder-decoder architecture, leveraging token merging techniques as a semantic bridge. By clustering similar tokens during encoding, MergeTok establishes a structural prior that provides dual supervision signals: (i) it imposes merged-token semantic alignment in the VAE branch, regularizing its latent space toward disentangled, semantic-aware representations; (ii) it derives group-wise constraints, promoting intra-group diversity and inter-group exclusivity that stabilize VQ training. MergeTok shows competitive reconstruction and generation performance on ImageNet-256, with substantially lower rFID than strong VAE and VQ models under matched token budgets, while producing semantically-organized token representations compatible with both autoregressive and diffusion generators. This shows that a single architecture can endow visual tokenizers with robust semantic organization and generator-friendly discreteness.
arXiv:2510.11683v3 Announce Type: replace
Abstract: A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) is the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation during training. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, they incur significant memory overhead due to the need to retain all MC samples for the gradient computation of non-linear terms in the RL objective, and thus restrict feasible sample sizes, leading to imprecise likelihood approximations and distorted RL objective. To address this, we propose \emph{Boundary-Guided Policy Optimization} (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, improving likelihood approximations and RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks. Our codes and models are available at \href{https://github.com/THU-KEG/BGPO}{https://github.com/THU-KEG/BGPO}.
arXiv:2510.10544v3 Announce Type: replace
Abstract: We derive a novel PAC-Bayesian generalization bound for reinforcement learning that explicitly accounts for Markov dependencies in the data, through the chain's mixing time. This contributes to overcoming challenges in obtaining generalization guarantees for reinforcement learning, where the sequential nature of data breaks the independence assumptions underlying classical bounds. The new bound provides non-vacuous certificates for modern off-policy algorithms such as Soft Actor-Critic. We demonstrate the practical utility of the bound through PB-SAC, a novel algorithm that optimizes the bound during training to guide exploration. Experiments across several continuous control tasks show that the proposed approach provides meaningful confidence certificates while maintaining competitive performance.
arXiv:2510.03415v3 Announce Type: replace
Abstract: Recent work asks whether large language models (LLMs) condition their reasoning on explicit rules rather than statistical regularities from pretraining. Program execution provides a canonical instance: formal semantics define behavior through symbolic transition rules that can be systematically altered under distribution shift. We investigate whether LLMs can condition their reasoning on formal semantics through program execution and introduce PLSemanticsBench, pairing featherweight C programs with two semantic systems -- small-step operational semantics and K semantics -- and probing four capabilities: composing rules for final states, selecting rules when state is unmutated, sustaining such conditioning over long traces, and following supplied rules under novel semantics. To decouple semantic reasoning from syntactic familiarity, we redefine familiar operators to induce symbol-meaning conflict and introduce novel symbols defined only through the supplied rules, and stress-test models on Human-Written, LLM-Translated, and Fuzzer-Generated splits with increasing structural complexity. Across 11 frontier LLMs, strong final-state accuracy under standard semantics (up to 90%) drops sharply -- by as much as 40--60% points -- under semantic mutations and increasing structural complexity. Only a handful of models achieve non-zero long-horizon conditioning accuracy, and even the best systems reach just 35%. Together, these results suggest that contemporary LLMs often rely on pretrained lexical associations rather than systematically conditioning on supplied formal rules. PLSemanticsBench is publicly available at https://EngineeringSoftware.github.io/PLSemanticsBench.
arXiv:2509.22335v3 Announce Type: replace
Abstract: We investigate why deep neural networks suffer from loss of plasticity in continual learning, and thus fail to learn new tasks without reinitializing parameters. We show that this failure is preceded by Hessian spectral collapse at new-task initialization, where meaningful curvature directions vanish and gradient descent becomes ineffective. Analyzing a linearized ReLU network, we derive explicit $\epsilon$-rank conditions for successful training and prove that the loss-weighted Gram matrix is spectrally equivalent to the Generalized Gauss-Newton approximation, thereby relating NTK dynamics to Hessian curvature. Targeting spectral collapse directly, we then discuss the Kronecker factored approximation of the Hessian, which motivates two regularization enhancements: maintaining high effective feature rank and applying L2 penalties. Experiments on continual supervised and reinforcement learning tasks confirm that combining these two regularizers effectively preserves plasticity.
arXiv:2408.10441v3 Announce Type: replace
Abstract: For many low-resource languages, the only available language models are large multilingual models trained on many languages simultaneously. Despite state-of-the-art performance on reasoning tasks, we find that these models still struggle with basic grammatical text generation in many languages. First, large multilingual models perform worse than bigrams for many languages (e.g. 24% of languages in XGLM 4.5B; 43% in BLOOM 7.1B) using FLORES perplexity as an evaluation metric. Second, when we train small monolingual models with only 125M parameters on 1GB or less data for 350 languages, these small models outperform large multilingual models both in perplexity and on a massively multilingual grammaticality benchmark. To facilitate future work on low-resource language modeling, we release Goldfish, a suite of over 1,000 small monolingual language models trained comparably for 350 languages. These models represent the first publicly-available monolingual language models for 215 of the languages included.
arXiv:2605.30963v1 Announce Type: cross
Abstract: We present AMix-2, a protein-text foundation model that establishes protein as a native modality in large language models (LLMs), unifying protein understanding and sequence design within a single foundation model. AMix-2 is built upon two key ideas: (1) a unified protein-text formulation that embeds natural language and protein sequence in a shared token space, enabling one model to perform biological reasoning and conditional design instead of separate downstream task-specialized models; and (2) a block-wise diffusion language modeling backbone that combines causal generation across blocks with bidirectional context and iterative refinement within blocks. This scheme better matches the intrinsic nature of proteins than a strict left-to-right factorization. To evaluate protein foundation models under realistic generalization settings, we further introduce ProteinArena, a comprehensive benchmark with time-aware and homology-aware protocols across various understanding and design tasks, and with baselines covering classical bioinformatics tools, protein-specialized models and LLMs. On ProteinArena, AMix-2 outperforms frontier LLMs and demonstrates competitive performance to task-specific protein models. Controlled experiments further show that the diffusion-based paradigm generally surpasses its autoregressive counterpart, highlighting the advantage of flexible generation order for protein sequences. We release both AMix-2 and ProteinArena to facilitate open research in protein foundation models.
arXiv:2605.30358v1 Announce Type: new
Abstract: Quantum computing remains in the Noisy Intermediate-Scale Quantum (NISQ) era, where the performance is highly constrained to noise. Addressing the limitation often requires hardware-facing capabilities beyond gate-sequence circuit specification, including mid-circuit measurement and classical feedback for quantum error correction (QEC), precise timing control for dynamical decoupling (DD), and pulse-level waveform access for calibration. OpenQASM-3 was introduced to expose exactly these capabilities, providing a hardware-level programming interface. However, despite the rapid progress of large language models in code generation, there is still no dataset specifically designed to train and evaluate LLMs on OpenQASM-3 programs that involve its advanced hardware-oriented features. To address this gap, we introduce QASM-Eval, the first comprehensive dataset designed to train and evaluate LLMs on OpenQASM-3. Rather than focusing on quantum algorithm design or reasoning, QASM-Eval explicitly targets the language's hardware-facing features. QASM-Eval comprises an expert-verified test set of 100 tasks and a training set of 4,000 tasks, systematically covering classical logic, timing scheduling, pulse control, and complex real-world workflows. To automatically validate generated programs, we check syntax, quantum states and program timeline using an extended verifier. Our evaluation reveals that while state-of-the-art LLMs struggle heavily in OpenQASM-3 coding tasks, targeted fine-tuning on QASM-Eval yields significant gains. QASM-Eval provides a crucial benchmark and training foundation to accelerate the development of reliable LLM assistants for hardware-facing quantum programming in NISQ era. Data and code: https://github.com/fuzhenxiao/QASM-Eval
arXiv:2508.13447v2 Announce Type: replace
Abstract: This work continues the one commenced in \cite{m24}, where the key idea is that individual stances on a social matter can be modeled as positions of particles in physics. Here, we develop an effective thermodynamic framework for the statistical description of collective social systems based on a mechanical representation of individual stances. In this approach, each individual is modeled as a point-like particle evolving in an abstract stance-space, where the dynamics are characterized by position-dependent inertial response functions. The resulting many-particle system is treated within an equilibrium statistical description analogous to the canonical ensemble of statistical mechanics.
Using this framework, we derive the corresponding partition function and introduce emergent macroscopic observables analogous to pressure, volume and temperature, interpreted here as collective statistical properties of the social system. For a particular class of position-dependent mass functions, the resulting equation of state acquires an ideal-gas-like form, suggesting a degree of macroscopic universality despite microscopic heterogeneity among individuals. The formalism is further extended to open social systems through the introduction of a chemical potential associated with population exchange among social groups. This extension naturally allows the treatment of variable particle number and multispecies social configurations within the same equilibrium framework.
The present work is intended as an exploratory phenomenological contribution to sociophysics and complex systems research, aimed at investigating whether collective social behavior may admit effective macroscopic statistical descriptions analogous to those encountered in statistical physics.
arXiv:2605.30708v1 Announce Type: cross
Abstract: All embodied agents are fundamentally patterns in physiological or other excitable media, blurring the distinction between objects and processes. Emergent patterns with complex behaviors, such as Gliders in the Game of Life and virtual patterns in Lenia, are powerful model systems in which to understand the properties and origins of behavioral traits in novel agents. To evaluate the behavior of patterns in Lenia, we introduce regions into their environment from which no sensory information is available - in effect, making creatures blind to parts of their surroundings. Complementing the conventional concept of infotaxis, we find that creatures tend to avoid these regions, a behavior we term agnosiophobia. To explain this behavior, we map each test creature's sensitivity to targeted occlusions and interpret the results in the language of dynamical systems. We observe Lenia creatures taking advantage of their freedom to change heading in order to achieve what appears to be a more fundamental goal: the preservation of their morphology. This work illustrates the beginning of an important roadmap to understand how emergent agents' behavioral propensities interact with the informational, not only tangible, topography of their world.
arXiv:2605.30532v1 Announce Type: cross
Abstract: We study true self-avoiding walk (TSAW) as a mechanism for improving empirical integral estimation via Markov chain Monte Carlo (MCMC). We consider finite-state adaptive sampling dynamics associated with an irreducible Markov kernel $P$ on a finite set, with stationary distribution $\pi$, in which the transition probabilities are penalized according to empirical overuse.
Our main result is that the empirical occupation counts $L_t(i)$ and transition counts $N_t(i,j)$ of the resulting TSAW-based walk satisfy \[ L_t(i)-t\pi_i = O(\sqrt{\log t}) \quad\text{and}\quad N_t(i,j)-t\pi_iP_{ij}=O(\sqrt{\log t}) \qquad\text{almost surely} \] for every state $i$ and every edge $(i,j)$ with $P_{ij}>0$. Consequently, for every bounded function $f:V\to\mathbb R$, the error of our integral estimator converges as \[ \left|\frac1t\sum_{s=0}^{t-1} f(X_s)-\sum_{i\in V}\pi_i f(i)\right| = O\left(\frac{\sqrt{\log t}}{t}\right) \qquad\text{almost surely}. \]
These results show that, in contrast with the usual $t^{-1/2}$ error scaling for empirical averages under standard random-walk-based methods, TSAW-based estimator yields empirical integral errors of order $O(\sqrt{\log t}/t)$ almost surely, thereby achieving a substantially sharper dependence on the sample size $t$.