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arXiv2026

Linear Algebra Foundations of Efficient Attention: A Phase Reversal in Rank Collapse Under SVD Compression

Linear algebra provides the framework of concepts (matrix rank, singular value decomposition (SVD), and eigendecomposition) that modern artificial intelligence employs to encode, compress, and propagate information through neural networks. This paper unifies fourteen separate peer-reviewed works analyzing the usage of these techniques in the context of transformer-based foundation model research, focusing on three areas of the topic: derivations and properties of self-attention matrices' output rank, compression methods that purposefully utilize this phenomenon, and the low-rank key-value (KV) cache projection and its semiseparable-matrix duality to linear attention and state-space structured models. We were motivated to conduct this work after observing an open problem in this literature: the interplay of the mentioned compression methods with natural rank collapse of the network. With this paper, we report an original finding that using SVD compression of attention projections actually has the opposite effect on the rank collapse of the network: while it strongly suppresses it at initialization, it accelerates on pretrained models (for GPT-2 124M, GPT-2 Medium 355M, and Pythia-160M) with minimal risk of object aliasing artifacts appearing (verified on all compression ratios) and is consistent across four rank estimation methods. A controlled causal decomposition of the effect in both settings showed that the reason for this behavior can be explained by the choice of the subspace SVD makes when compressing the matrix better than the reduction of the operator norm it achieves, explaining roughly 76% of the effect at initialization and 83% on the pretrained weights, providing a refinement to the calibration-aware compression viewpoint and an explanation of why it outperformed naive SVD truncation.

cs.LG↗

arXiv2026

Formation of structural attractors in neuromorphic systems

This paper examines the theory of Invariant Structural Learning (ISL), which proposes a non-optimization approach to concept formation. Learning is interpreted as convergence to structural attractors in a hypergraph space, rather than as the minimization of a global loss function. The paper presents the ISL model, including its mathematical formalization, computational verification, and a hypothetical neurobiological interpretation. The mathematical section introduces the formal apparatus of the structural reduction process and proves its finite convergence, the existence and uniqueness of class structural attractors, and the self-organization of attractor maps. The computational section demonstrates the feasibility of the proposed approach on classical image recognition tasks, utilizing the proposed learning mechanism without backpropagation and with extremely small training datasets. Finally, the neurobiological section formulates hypotheses regarding the possible implementation of structural attractors in dendritic trees, neural coding as a projection of internal attractor dynamics, and the development of neural architectures supporting the proposed learning concept. These hypotheses are discussed in the context of modern experimental data in the fields of dendritic computations, synaptic plasticity, and the structural organization of neural circuits. The proposed neurobiological mechanisms are presented as testable hypotheses rather than established biological facts. The results demonstrate the mathematical consistency and computational feasibility of the proposed model, while the neurobiological hypotheses outline potential directions for its experimental verification.

cs.AI↗

arXiv2026

Asymmetric Coupling Anisotropy for Causal Information Filtering in Physical Reservoirs

We demonstrate a physical mechanism for causal information filtering in a physical reservoir computing (PRC) by exploiting asymmetric coupling anisotropy. Using a network of coupled Duffing oscillators, we show that the directionality of internal coupling induces a spatial gradient in the effective potential, establishing a deterministic upstream-to-downstream information flow. This anisotropy allows for the selective amplification of semantic drifts, triggering a macroscopic saddle-node bifurcation as a physical interlock before global computational failure. Through spatiotemporal analysis of a 50-node system under traveling wave inputs, we confirm that local phase transitions effectively purge anomalous information while preserving the computational integrity of the remaining nodes. The results suggest that the intrinsic causality of the reservoir's topology provides a robust framework for autonomous reliability and fault-tolerant physical intelligence.

nlin.AO↗

arXiv2026

Minimizing the Effect of Sleep Deprivation in the Forward-Forward Algorithm

This paper addresses the challenge posed by sleep deprivation in the Forward-Forward algorithm, where separating the two passes in this algorithm and imbalancing the data processing in the passes is considered an imitation of the cognitive processes observed in humans suffering from sleep deprivation. Previous research has demonstrated that sleep deprivation in the Forward-Forward algorithm has a catastrophic effect on learning efficacy. To mitigate this issue, we explore several approaches; these include alternative activation, optimized loss function, and threshold tuning. To simulate periodic rest, we reduce the number of positive passes in alternating epochs, creating short break phases. We additionally investigate the potential of caffeine-induced stimulation to enhance performance during sleep-deprived conditions. Experimental evaluations conducted on the MNIST and Fashion-MNIST datasets demonstrate that these modifications improve accuracy under the context of sleep deprivation. For example, a 2%-62% accuracy gain is observed in a severe sleep deprivation setting (16 positive or awake periods and 1 negative or sleep period). The approaches also enhance the resilience of the algorithm and its alignment with the adaptive mechanisms of human cognition.

cs.LG↗

arXiv2026

DUA-D2C: Dynamic Uncertainty Aware Method for Overfitting Remediation in Deep Learning

Overfitting remains a significant challenge in deep learning, often arising from data outliers, noise, and limited training data. To address this, we previously proposed the Divide2Conquer (D2C) method, which partitions training data into multiple subsets and trains identical models independently on each. This strategy enables learning more consistent patterns while minimizing the influence of individual outliers and noise. D2C's standard aggregation typically treats all subset models equally or based on fixed heuristics (like data size), potentially underutilizing information about their varying generalization capabilities. Building upon this foundation, we introduce Dynamic Uncertainty-Aware Divide2Conquer (DUA-D2C), an advanced technique that refines the aggregation process. DUA-D2C dynamically weights the contributions of subset models based on their performance on a shared validation set, employing a novel composite score of accuracy and normalized prediction entropy. This intelligent aggregation allows the central model to preferentially learn from subsets yielding more generalizable and confident edge models, thereby more effectively combating overfitting. In this work, we provide a rigorous theoretical justification for this approach, analytically demonstrating how dynamic parameter fusion reduces model variance. Empirical evaluations on benchmark datasets spanning image, audio, and text domains demonstrate that DUA-D2C significantly improves generalization. Our analysis includes evaluations of decision boundaries, loss curves, and ablation studies, highlighting that DUA-D2C provides additive performance gains even when applied on top of standard regularizers like Dropout. This study establishes it as a theoretically grounded and effective approach to combating overfitting in deep learning. Our code is publicly available at: https://github.com/Saiful185/DUAD2C.

cs.LG↗

arXiv2026

OR-Agent: Bridging Evolutionary Search and Structured Research for Automated Heuristic Design

Automating heuristic design in complex, experiment-driven domains requires more than iterative mutation of solution algorithms. Current LLM-based evolutionary methods often rely on stochastic mutation loops that lack long-term strategic planning and a formal mechanism to learn from historical failures, leading to inefficient exploration and redundant trials. To address this, we present OR-Agent, a multi-agent research framework designed for automated heuristic design in optimization problems with rich experimental environments. OR-Agent organizes heuristic search as tree-based workflow that explicitly models branching hypothesis generation and systematic backtracking. Furthermore, to address the lack of adaptive learning in current agents, we introduce a hierarchical, optimization-inspired reflection system in which short-term reflections act as verbal gradients, long-term reflections as verbal momentum, and memory compression as semantic weight decay - collectively forming a principled mechanism for governing research dynamics. Extensive experiments on classical combinatorial optimization problems (e.g., TSP, CVRP, bin packing) and simulation-based cooperative driving scenarios demonstrate that OR-Agent outperforms strong evolutionary search baselines. All code and experimental data are publicly available at https://github.com/qiliuchn/OR-Agent.

cs.AI↗

arXiv2026

Towards Efficient Evaluation of Evolutionary Transfer Optimization: Case Studies on Task-Parameterized Applications

As evolutionary transfer optimization (ETO) scales to larger collections of related tasks, problem evaluation can become a major source of runtime growth. This work studies problem-side evaluation scaling in task-parameterized applications and reformulates application-specific serial computations into forms suitable for parallel execution. We organize evaluation scaling into two levels: the number of evaluated tasks and the workload within each task. In multi-task optimization, matrix-recursive kinematic-arm evaluation is reformulated using an accumulation-matrix representation of cumulative link directions. In sequential transfer optimization, pointwise B-spline trajectory evaluation is reformulated using a blending-matrix representation for trajectory and collision computations. Both reformulations maintain close numerical agreement with their reference evaluations and substantially reduce runtime, yielding $256.72\times$ and $93.91\times$ end-to-end speedups, respectively. These results demonstrate problem-side reformulation as a practical route toward scalable ETO. Both application implementations and experimental scripts are released as open source to support reproducibility and reuse.

cs.AI↗

arXiv2026

Large Language Models with At Most One Spike per Neuron

Leveraging their inherent sparse event-driven computation, spiking neural networks (SNNs) offer a promising path toward energy-efficient large language models (LLMs). Time-to-first-spike (TTFS) coding generates at most one spike per neuron within a time window, yielding extremely low firing rates. However, conventional TTFS SNNs are restricted to specific structures, making it challenging to encode certain blocks in LLM -- such as layer normalization and matrix multiplication --using TTFS. To overcome this limitation, we introduce a reference-based strategy specifically to encode the four core LLM components: embedding layers, layer normalization, attention-related operations and dropout. We construct a fully TTFS-based SNN architecture and train it end-to-end. Experiments on modern LLMs like BERT and GPT-2 demonstrate that our approach achieves performance comparable to ANN counterparts on natural language understanding and common-sense reasoning, while a clear gap remains on language modeling perplexity. To the best of our knowledge, this is the first work to scale a spiking LLM to 1.5 billion parameters using TTFS coding. We also report an estimate of spike-related energy; this is a spike-count proxy under an established cost model rather than a measurement on neuromorphic hardware.

cs.NE↗

arXiv2026

What Makes a Redundant Representation Remember? Lineage Isolation, Not Masking

Memory-based evolutionary algorithms for dynamic optimization often carry a redundant second copy of the genotype and expose only one copy to the objective, on the assumption that the shielded copy accumulates information about past optima. We show this assumption is false as usually implemented, and identify the structural property that actually determines whether the shielded copy retains information. We formalize such methods as a gated dual-copy representation with two independent design axes: a gating rule deciding which copy is evaluated, and an inheritance rule deciding whether the two copies mix across generations. A ablation shows retained information is governed almost entirely by the inheritance rule (21.4 vs. 1.3 bits) and is nearly invariant to the gating rule. Per-locus independent inheritance reshuffles cross-locus structure every generation, so shielding preserves the variance of the hidden copy while destroying the pattern that constitutes a memory. Under isolated inheritance the memory effect is real: against a single-copy baseline matched for representation budget, the method gains +0.010 AUC when optima recur periodically and loses 0.078 when they drift unidirectionally---a 0.089 separation under otherwise identical settings, which excludes explanations based on added capacity. We show the readout rate is also the corruption rate, predicting and confirming an interior optimum replicated across two implementations. We report one negative result with a mechanism: dual-copy representations lower the mutational error threshold, because gated expression is a selector rather than a joint decoder and therefore provides no coding gain. Finally, we document a benchmarking hazard: on dynamic benchmarks the choice of recombination operator alone shifted our baseline by 0.062 AUC, six times the effect size under study.

cs.NE↗

arXiv2026

Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problems

The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making traditional approaches such as exact mathematical models or heuristic methods prone to high computational overhead or reliant on the design of complex heuristic operators to achieve optimal or near optimal solutions. Meanwhile, although some recent learning-based methods can produce good performance for VRP with straightforward constraint scenarios, they often fail to effectively handle hard constraints that are common in practice. This study introduces a novel end-to-end framework that combines constraint-oriented hypergraphs with reinforcement learning to address vehicle routing problems. A central innovation of this work is the development of a constraint-oriented dynamic hyperedge reconstruction strategy within an encoder, which significantly enhances hypergraph representation learning. Additionally, the decoder leverages a double-pointer attention mechanism to iteratively generate solutions. The proposed model is trained by incorporating asynchronous parameter updates informed by hypergraph constraints and optimizing a dual loss function comprising constraint loss and policy gradient loss. The experiment results on benchmark datasets demonstrate that the proposed approach not only eliminates the need for sophisticated heuristic operators but also achieves substantial improvements in solution quality.

cs.LG↗

arXiv2026

Parameterized Hardness of Zonotope Containment and Neural Network Verification

Neural networks with ReLU activations are a widely used model in machine learning. It is thus important to have a profound understanding of the properties of the functions computed by such networks. Recently, there has been increasing interest in the (parameterized) computational complexity of determining these properties. In this work, we close several gaps and resolve an open problem posed by Froese et al. [COLT '25] regarding the parameterized complexity of various problems related to network verification. In particular, we prove that, for all $\ell\ge 2$, deciding positivity (and thus surjectivity) of a function $f:\mathbb{R}^d\to\mathbb{R}$ computed by an $\ell$-layer ReLU network is W[$\ell-1$]-hard when parameterized by the input dimension $d$. The case $\ell=2$ implies that zonotope non-containment (a problem that is of independent interest in computational geometry, control theory, and robotics) is W[1]-hard with respect to the ambient dimension $d$. Moreover, we show that approximating the maximum within any multiplicative factor and computing the $L_p$-Lipschitz constant for $p\in(0,\infty]$ in $\ell$-layer networks is NP-hard and W[$\ell-1$]-hard with respect to $d$. For $\ell\ge 3$, approximating the $L_p$-Lipschitz constant is NP- and W[$\ell-2$]-hard. We further show that the above problems are NP- and W[$t$]-hard (for all $t\ge 1$) with respect to $\ell$ for constant $d$. Notably, our hardness results imply that the naive enumeration-based methods for these fundamental problems running in $n^{(\ell-1) d}\cdot\operatorname{poly}(N)$ time are all essentially optimal under the Exponential Time Hypothesis.

cs.CC↗

arXiv2026

MeEvo: Metacognitive Evolution Combined with Natural Evolution for Automatic Heuristic Design

Large Language Models (LLMs) have advanced Automatic Heuristic Design (AHD) by enabling heuristic generation through reasoning and code synthesis. In LLM-based AHD, the LLM reasons about algorithm design and generates executable heuristic code. Existing architectures adopt two main paradigms: Natural Evolution applies crossover and mutation to this code to explore diverse strategies, but discards the reasoning traces behind the design decisions, weakening knowledge retention; Metacognitive Evolution retains these reasoning traces and refines them through reflection, but lacks population-level recombination, limiting exploration. These limitations reduce search efficiency, stability, and solution quality on complex problems. To address this gap, we propose MeEvo, an AHD framework that cyclically couples Natural Evolution and Metacognitive Evolution with operator balance that shifts from exploration to exploitation. Natural Evolution explores heuristic code while recording LLM-generated reasoning traces, fitness values, errors and best heuristic into a shared history; Metacognitive Evolution then reflects on this history to generate improved heuristics that feed into the next Natural Evolution cycle. This design enables population-driven exploration and reflection-driven refinement to reinforce each other. Experiments on five optimization problems show that MeEvo achieves stronger performance and lower variance than tested LLM-based AHD architectures, especially on complex constrained tasks.

cs.NE↗

arXiv2026

Trust, but Verify: Rigorously Profiling Best-Effort High-Performance Computing for Digital Evolution

Developments in high-performance computing (HPC) technology continue to drastically increase quantities of available processing power. In the context of digital evolution, this explosive growth offers opportunities to advance both hypothesis-driven explorations of multi-scale biological phenomena and application-driven evolutionary optimization targeting hard problem domains. A particular opportunity arises from emerging next-generation AI/ML hardware accelerator platforms, such as the 880,000-processor Cerebras Wafer-Scale Engine (WSE). Such hardware, however, constrains on-device data storage and movement --- a challenge compounded by vulnerability to failures arising over numerous device components. Best-effort relaxations that depart from a traditional deterministic computing paradigm can help accommodate such constraints, but complicate reproducibility and risk introducing artifactual biases. We explore these concerns, developing a framework to measure runtime behavior of best-effort code and examining case studies of best-effort computing in digital evolution projects. The first case study applies best-effort CPU-cluster multiprocessing to a multicellularity evolution model, which provides 92% scaling efficiency at 64 processes ($2.1\times$ speedup) and exhibits robust median quality of service, even under hardware anomalies. The second case study examines WSE-based simulations, demonstrating best-effort strategies to track spatiotemporal population history --- through sparse, asynchronous device-to-host sampling that tolerates hardware faults. In sum, across potential forms and scopes of best-effort relaxation, we argue that digital evolution is uniquely positioned to contribute in developing post-deterministic HPC paradigms.

cs.NE↗

arXiv2026

Efficient Constant Optimization for Symbolic Regression with GPU-Accelerated Tree-Based Genetic Programming

Constant optimization refines the numerical coefficients of candidate expressions in tree-based genetic programming for symbolic regression. But its per-generation cost has led modern GPU-accelerated frameworks to omit it or restrict it to lightweight forms. We present a GPU-resident, batched Levenberg--Marquardt solver that optimizes constants across a structurally heterogeneous population of expression trees using a fixed number of population-wide CUDA launches per iteration. Reverse-mode automatic differentiation assembles the per-tree Jacobian in one backward sweep, making the dominant per-iteration cost independent of the number of constants per tree, and a double-precision delivery guard guarantees that returned constants are never worse than their initial values. On early-generation populations, the solver sustains up to $5.1{\times}10^{5}$ trees per second on an NVIDIA A100; at a GPU-saturated benchmark configuration it delivers roughly $9.9{\times}$ the throughput of Operon running on a 64-core EPYC 7763, while matching fp64-reference quality. Integrated in-process into EvoGP, the solver enables end-to-end search to recover governing equations on $10$ of $18$ constructed problems versus 0 for stock EvoGP. Our code is at https://github.com/TensorConv/CuSR.

cs.NE↗

arXiv2026

Understanding Autonomous Driving Datasets by Describing Differences between Image Subsets in Natural Language

Understanding the composition of large-scale autonomous driving datasets is essential for safety, robustness, and reliable operation across domains. For example, domain shift between locations could lead to the operating environment being misaligned with the training data, resulting in potentially dangerous performance degradation. Yet, existing data analysis pipelines largely rely on metadata, predefined labels, or manual inspection, which provide limited semantic insight or do not scale. This paper studies set difference captioning: given two subsets of images, the goal is to produce a natural-language hypothesis describing differences between the target and reference set. Building on a two-stage formulation, we adapt the method to autonomous driving by focusing on object-centric patches derived from object detection, which simplifies aggregation and enables attribution of differences to specific object instances or categories. To evaluate this setting in-domain, we introduce a new benchmark, AD-Diff Bench. Low-concentration experiments assess the suitability of set-difference-captioning approaches to sparse, real-world differences. We restrict our experiments to open-weight models to support reproducibility and ease of deployment. The proposed benchmark and analysis provide a step towards practical, human-interpretable dataset introspection for autonomous driving datasets. Our implementation and benchmark dataset are available at https://github.com/KIT-MRT/AD-Diff

cs.CV↗

arXiv2026

Prospective Coding Improves Learning in Deep Continuous-Time Recurrent Networks

Temporal integration gives continuous-time recurrent networks memory, but in deep stacks it also delays bottom-up signals and attenuates top-down errors. We develop Recursive Quadrature Filters (RQFs), biologically motivated complex-valued temporal filters that are a special case of diagonal state-space models (SSMs), and ask whether this failure mode can be addressed by making each layer's bottom-up input prospective. Starting from an energy model, we derive the RQF dynamics and show that each RQF is a band-pass filter whose learnable parameters control its tuning frequency and bandwidth. We then make each layer's bottom-up input prospective using a parameter-free two-tap update that leaves the recurrent transition and parallel scan unchanged. We extend this correction to general diagonal SSMs and show that it mitigates depth-dependent gradient attenuation when temporal gradients are truncated, i.e., spatial-only backpropagation. We evaluate the intervention in RQFs, S5, and ORGaNICs (a nonlinear gated RNN) trained using full backpropagation through time (BPTT) and spatial-only backpropagation. Under full BPTT, prospective variants match or outperform their non-prospective controls in every model and configuration. A non-residual width-32 six-layer RQF reaches 96.09% accuracy on raw-audio Speech Commands with 31.9k parameters; a width-64 six-layer RQF reaches 83.56% on the 16,384-step Path-X task. These results identify RQFs as a parameter-efficient recurrent substrate and prospective-input coding as an input-side correction for deep continuous-time recurrent networks.

cs.LG↗

arXiv2026

CompEvo: Competition-Induced Evolution for Multi-Agent in News-Driven Time Series Forecasting

News-driven time series forecasting uses evolving textual events together with historical observations to predict future values, supporting applications such as market risk monitoring and resource scheduling. In multi-agent settings, two challenges still remain. The first is degeneration of thought, where agents converge to similar evidence-seeking behaviors. The second is insufficient theoretical grounding, where strategy updates are often heuristic and lack a principled formulation. To address the above challenges, we propose CompEvo, a competition-induced evolution framework for multi-agent news-driven time series forecasting. For theoretical grounding, we introduce an evolutionary game formulation to guarantee equilibrium existence and optimization convergence. Building on this formulation, we construct a trainable multi-agent evolution framework that integrates strategy execution, fitness-based differentiable selection, and competition-induced strategy evolution. CompEvo enables heterogeneous agents to explore diverse news evidence, converts forecasting feedback into differentiable influence weights, and evolves agent strategies under competitive pressure to preserve effective logic while maintaining diversity. Experiments on four real-world datasets show that CompEvo reduces RMSE by 27.3% and MAPE by 26.2% on average over strong baselines. Further analysis indicates that CompEvo successfully maintains diverse and specialized agent behaviors.

cs.NE↗

arXiv2026

Quality-diversity in dissimilarity spaces

The theory of magnitude provides a mathematical framework for quantifying and maximizing diversity. We apply this framework to formulate quality-diversity algorithms in generic dissimilarity spaces. In particular, we instantiate and demonstrate a very general version of Go-Explore with promising performance.

cs.AI↗