arXiv:2606.03208v1 Announce Type: new
Abstract: We have demonstrated highly-sensitive photon counting in the infrared based on the two-photon absorption (2PA) in a silicon avalanche photodiode, where the required photon energy for inducing effective conductivity was provided by an intense mid-infrared (MIR) field at 3 $\mu$m. The used MIR pumping scheme could not only benefit from the enhanced 2PA coefficient in the non-degenerate regime, but also eliminate the detrimental background noises due to the pump harmonic excitation of the pump. Consequently, the enhancement factor for the signal counting rate unprecedented reached to about $10^{5}$ with input infrared pulses at the femtojoule level. Additionally, the noise equivalent power was substantially improved by two orders of magnitude comparing to conventional schemes with near-infrared pumping. Therefore, the presented configuration might provide an alternative to realize sensitive infrared detection and imaging with desirable features of room-temperature operation, no phase-matching requirement, and broadband responding window, which would find a variety of applications including remote ranging, sensitive sensing, biochemical imaging, and trace spectroscopy.
Science Journals
arXiv:2606.03584v1 Announce Type: new
Abstract: Equilibrium Propagation (EP) is a physics-based training framework that has primarily been employed in energy-based models, including continuous Hopfield networks, nonlinear resistive networks and coupled phase oscillators. However, EP's practical applications have so far remained limited to relatively small-scale problems. Predictive coding networks (PCNs), another class of energy-based models rooted in computational neuroscience, are typically trained with a specialized algorithm and have likewise not yet been demonstrated at large scale. In this work, we develop an EP-based training method for PCNs which combines the centered variant of EP with a novel equilibration scheme for PCNs. Using this approach, we train a 10-layer convolutional PCN (VGG10) on full-size ImageNet, achieving 13.23\% test error rate on the top-5 classification task, close to the 12.2\% backpropagation baseline. To our knowledge, this is the first demonstration of both PCNs and EP-based training at ImageNet scale. These results significantly extend the scalability of both approaches and suggest that the primary challenges in scaling EP in other physical systems may come more from the computational properties of these systems than from inherent limitations of the EP framework.
arXiv:2606.03214v1 Announce Type: new
Abstract: In this study, we evaluate the performance of skin lesion classification using ResNet-based convolutional models, focusing on the impact of demographic bias in training data, particularly variations in patient sex and age. We use linear programming to generate datasets with controlled demographic characteristics, allowing systematic investigation of bias effects. Three learning strategies are evaluated: a single-task model, a reinforcing multi-task model, and an adversarial learning scheme. Our sex-based analysis indicates that sex-specific training datasets optimise model performance. Notably, including male patients in the training data improved performance for the male subgroup, even in female-majority cases. Reinforcing and adversarial learning schemes narrowed or eliminated bias gaps in balanced and female-majority datasets. However, these strategies proved less effective in male-majority settings, where models continued to perform better for males than females. The two learning schemes showed marginal bias reduction compared to the baseline model in predominantly male patient populations. Age-based analysis demonstrates comparable baseline performance across the three model approaches, with performance declining across age categories. Younger groups consistently achieve the highest performance, regardless of training data distribution. Although balanced training yields optimal results for the youngest age category, performance decreases in older categories. We find that sex biases arise mainly from data imbalances, while age biases consistently favour younger groups regardless of distribution. These distinct mechanisms require targeted mitigation strategies. Additionally, cross-dataset validation on two external datasets revealed that domain shifts notably affect performance and patterns of demographic bias.
arXiv:2606.03245v1 Announce Type: cross
Abstract: Concepts of calibration formalize the compatibility between probabilistic predictions and the respective outcomes. In a nutshell, the outcomes ought to be indistinguishable from random draws from the predictive distributions. In this paper, we review, extend, and bridge notions of calibration that have been proposed for classification and regression tasks. Particular emphasis is given to hierarchical relations between the various notions, as they apply to general real-valued data, continuous outcomes, count data, nominal classes, and binary outcomes. To highlight a number of contributions, we introduce the notion of modal calibration for nominal outcomes, we distinguish full, partial, and average calibration in this setting, and we show that double probability integral transform (PIT) calibration is logically independent of previously proposed concepts of calibration for discrete outcomes. Furthermore, we generalize extant results on concepts of calibration that are expressed in terms of properties or functionals of the predictive distributions, such as means, quantiles, or event probabilities. Throughout the paper, we illustrate the concepts and their hierarchical relations in worked examples, and we provide algorithmic tools that support the construction of instructive examples and counterexamples.
arXiv:2606.03915v1 Announce Type: new
Abstract: We propose PatchScene, a novel diffusion-based framework for large-scale LiDAR scene completion. Unlike existing methods that rely on global latent representations or dense voxel grids, PatchScene adopts a patch-based voxel diffusion paradigm that explicitly generates fine-grained geometry within localized 3D regions. To ensure coherent reconstruction at both spatial and temporal scales, we introduce a confidence-guided spatio-temporal fusion mechanism that integrates overlapping patches and adjacent frames in a unified generative process. Furthermore, we design an Annular-Flow diffusion strategy that leverages the radial density pattern of LiDAR scans to progressively propagate high-fidelity information from near-range to far-range regions, enabling spatially unbounded scene completion. Extensive experiments on the SemanticKITTI benchmark demonstrate that PatchScene achieves state-of-the-art performance across all standard metrics, surpassing previous approaches in both geometric accuracy and temporal consistency. Remarkably, the model trained on 20 m LiDAR ranges generalizes effectively to 50 m scenes without retraining, highlighting its strong scalability and generalization capability for real-world autonomous driving applications.
arXiv:2606.03355v1 Announce Type: new
Abstract: Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration (APIC), a population-level extension of KOH that leverages Neural Processes to perform scalable Bayesian inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, APIC enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka-Volterra system, and the advection-diffusion PDE with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.
arXiv:2606.03357v1 Announce Type: new
Abstract: When prompting SLMs for psychometric assessments, researchers assume the outputs reflect semantic reasoning. We evaluate this premise across 13 open-weights models (0.6B to 14B parameters) using a prompt variation framework that separates semantic signals from prompt artifacts. By systematically varying personas, instructions, items, and option symbols, we find that artifactual variance frequently overpowers the semantic signal. In these cases, models predominantly reflect prompt compliance rather than simulated psychological traits. While these findings limit SLM utility in psychometrics, our framework provides a diagnostic tool to identify destructive artifacts and isolate semantic understanding for future frontier-model research.
arXiv:2606.03365v1 Announce Type: new
Abstract: Embedding models (KGEMs) constitute the main link prediction approach to complete knowledge graphs. Standard evaluation protocols emphasize rank-based metrics such as MRR or Hits@$K$, but usually overlook the influence of random seeds on result stability. Moreover, these metrics conceal potential instabilities in individual predictions and in the organization of embedding spaces. In this work, we conduct a systematic stability analysis of multiple KGEMs across several datasets. We find that high-performance models actually produce divergent predictions at the triple level and highly variable embedding spaces. By isolating stochastic factors (i.e., initialization, triple ordering, negative sampling, dropout, hardware), we show that each independently induces instability of comparable magnitude. Furthermore, for a given model, hyperparameter configurations with better MRR are not guaranteed to be more stable. Moreover, voting, albeit a known remediation mechanism, only provides a limited enhancement of stability. These findings highlight critical limitations of current benchmarking protocols, and raise concerns about the reliability of KGEMs for knowledge graph completion.
arXiv:2606.03369v1 Announce Type: new
Abstract: We identify two constructions from different mathematical traditions. In linear logic and realisability, logical types are generated rather than fixed in advance: one begins with a universe of realisers equipped with execution, uses orthogonality to test their interactions, and takes types to be the biorthogonally closed subsets. In enriched Isbell duality, a quantitative relation induces an adjunction whose fixed points form a category, its nucleus. These constructions proceed by different means; we show that, in the present setting, they produce the same objects. The shared datum is minimal: an associative product, called execution, and a real-valued measurement, with no compatibility assumed between them. The failure of the measurement to be additive is at once the relation defining orthogonality and the quantitative relation whose Isbell nucleus we form, and the types cut out by orthogonality are exactly the fixed points of the associated adjunction. The identification pays off in both directions. The most natural product of types fails to be associative; repairing this failure forces a different notion of type, sensitive to both sides of a composite, on which the induced product is associative and, when execution has units, carries two residuals. What emerges is a noncommutative Lambek calculus, derived directly from execution and orthogonality rather than imposed. In the reverse direction, each such type, read on the categorical side, generates a quantitative relation of its own, and with it a derived adjunction and a further generation of types; these derived types are again types of the original situation, computed by the residuals of the Lambek calculus. We also prove a coherence theorem for the threefold arrangements of this construction and, in the finite-dimensional case, give explicit formulas for the product.
arXiv:2505.20853v4 Announce Type: replace
Abstract: Fusing heterogeneous information remains a persistent challenge in modern data analysis. While significant progress has been made, existing approaches often fail to account for the inherent heterogeneity of object patterns across different semantic spaces. To address this limitation, we propose the Cooperation of Experts (CoE) framework, which encodes multi-typed information into unified heterogeneous multiplex networks. By overcoming modality and connection differences, CoE provides a powerful and flexible model for capturing the intricate structures of real-world complex data. In our framework, dedicated encoders act as domain-specific experts, each specializing in learning distinct relational patterns in specific semantic spaces. To enhance robustness and extract complementary knowledge, these experts collaborate through a novel large margin mechanism supported by a tailored optimization strategy. Rigorous theoretical analyses guarantee the framework's feasibility and stability, while extensive experiments across diverse benchmarks demonstrate its superior performance and broad applicability. Our code is available at https://github.com/strangeAlan/CoE.
arXiv:2606.03928v1 Announce Type: new
Abstract: Reasoning models improve accuracy through extended chains of thought, but their long outputs create a memory and compute bottleneck. KV cache eviction methods reduce this cost by evicting unimportant key-value pairs from the cache, yet they often yield worse accuracy than selection-based sparse attention alternatives, which keep the full KV cache. We identify key factors crucial to KV cache eviction accuracy. First, a small fraction of value states have abnormally large magnitudes, and evicting them causes catastrophic failure where models enter repetitive reasoning loops. Second, introducing stochasticity during eviction improves accuracy by increasing cache diversity. Based on these findings, we propose Value-aware Stochastic KV Cache Eviction (VaSE), a training-free recipe that protects large-magnitude value states and promotes diverse eviction decisions. Across six reasoning tasks, Qwen3 models using VaSE with 4x KV cache compression yield higher average accuracies than SOTA selection method at the same sparsity, while outperforming the strongest eviction method by more than 4%. Overall, VaSE bridges the gap between efficiency and accuracy, supporting FlashAttention2 and enabling a static memory footprint for reasoning models.
arXiv:2504.01206v3 Announce Type: replace
Abstract: Space-efficient streaming estimation of quantiles in massive datasets is a fundamental problem with numerous applications in data monitoring and analysis. While theoretical research led to optimal algorithms, such as the Greenwald-Khanna algorithm or the KLL sketch, practitioners often use other sketches that perform significantly better in practice but lack theoretical guarantees. Most notably, the widely used $t$-digest has unbounded worst-case error.
In this paper, we seek to get the best of both worlds. We present a new quantile summary, SplineSketch, for numeric data, offering near-optimal theoretical guarantees, namely uniformly bounded rank error, and outperforming $t$-digest by a factor of 2-20 on a range of synthetic and real-world datasets. To achieve such performance, we develop a novel approach that maintains a dynamic subdivision of the input range into buckets while fitting the input distribution using monotone cubic spline interpolation. The core challenge is implementing this method in a space-efficient manner while ensuring strong worst-case guarantees.
arXiv:2606.02739v1 Announce Type: new
Abstract: Audio tokenizers serve as the discrete interface between continuous audio and Audio Language Models (ALMs), but existing tokenizers often struggle to support both understanding and generation. Reconstruction-oriented codecs preserve acoustic fidelity but lack rich semantics, while semantic-aware tokenizers typically rely on separate semantic and acoustic streams, introducing redundancy or misalignment.
We propose \textbf{EntangleCodec}, a unified discrete audio tokenizer that learns caption-aligned semantic-acoustic representations before quantization. By aligning audio with rich captions rather than ASR transcripts, EntangleCodec captures linguistic content, speaker identity, emotion, prosody, and acoustic scenes within a compact token stream. A flow-matching diffusion decoder further enables high-quality reconstruction across speech, music, and general audio.
EntangleCodec achieves reconstruction quality competitive with specialized codecs, outperforms all codec-based baselines on audio understanding by up to \textbf{+7.4\%} on MMAR, and supports both TTS and TTA generation in a unified framework. Furthermore, EntangleCodec-based audio language models demonstrate strong scaling behavior: even at \textit{0.6B} parameters, the model surpasses specialized continuous-representation LLMs with over \textit{13B} parameters across three benchmarks using \textbf{22$\times$} fewer parameters; scaling to \textit{8B} further establishes new state-of-the-art results on MMAR, highlighting that representation quality is as critical as model scale in audio language modeling. Code and model weights are available at https://github.com/luckyerr/EntangleCodec.
arXiv:2606.02908v1 Announce Type: new
Abstract: Multi-turn user-facing agents must infer user intent from incomplete requests, collect missing information through dialogue and tools, and execute valid actions. A training trajectory records this process as an interleaved sequence of user messages, agent responses, tool calls, etc. Synthesizing sufficiently complex trajectory has become a central route to train agents: existing pipelines often increase difficulty by composing multiple user requests into longer tasks, producing write-intensive trajectories that train sequential execution.
We argue that a single write decision can itself be difficult when the agent must gather and compare substantial read-tool evidence before its arguments become identifiable, a challenge that write-intensive data alone cannot address. Guided by this insight, we propose WRIT (\uline{W}rite-\uline{R}ead \uline{I}ntensive \uline{T}rajectory Synthesis), a pipeline for synthesizing multi-turn agent training trajectories along two complexity axes: the number of write decisions in a task and the evidence burden of each individual decision. WRIT first generates write-intensive and read-heavy tasks. It then diversifies user behavior instructions to reflect realistic conversational variation, and finally simulates agent-user interactions in an executable environment to produce complete training trajectories. The resulting data trains agents not only for longer task execution, but also for robust, evidence-grounded decision making under high information load. With only 2K synthesized trajectories, a 4B model trained on WRIT outperforms GPT-5.1 no-think on $\tau^2$-bench and substantially reduces inference-time token usage, showing that compact SFT data can convert part of expensive test-time reasoning into efficient agent behavior.
arXiv:2606.03247v1 Announce Type: new
Abstract: Document-grounded dialogue systems (DGDS) utilize knowledge from external documents to answer domain-specific user questions. Existing solutions typically divide documents into independent passages for retrieval and response generation. This approach, however, neither makes good use of structural information within documents nor provides enough (document) context for knowledge selection and responses. This paper proposes SF-Re2G to address such issues systematically. Firstly, we seek to improve a passage representation by contrasting it with others of the same section, thus improving the retrieval performance. Secondly, a structure-enhanced reranker is built, leveraging the fact that multiple grounding passages of one dialog turn tend to be in the same neighborhood. Specifically, candidates from the retrieval are grouped into subgraphs according to the document structure. The reranker will rescore the candidate integrating its group information. Finally, the chosen passages are used for responses, taking into account the subgraph context for better generation. Experimental results on two DGDS datasets validate our method for both Chinese and English.
arXiv:2606.03351v1 Announce Type: new
Abstract: We present a framework to generalize the standard b-ary Gray code to get the k-bonacci ones obtained in [5] as well as many others by using theoretical tools that allow to make calculations on lists. We introduce the notion of Z-Gray product, from which we deduce sequences of lists of finite words avoiding a predefinite list Z of factors and which satisfy a power-associativity property as well a generalizations of the classical flipping digit property.
arXiv:2606.03965v1 Announce Type: new
Abstract: Large language models improve final-answer accuracy through extended chain-of-thought reasoning, but often spend tokens inefficiently and offer little inference-time control. Existing efficient reasoning methods control thinking length by shortening, early-stopping, or compressing traces, leaving how the model thinks implicit. In this paper, we propose Agentic Chain-of-Thought Steering (ACTS), which formulates reasoning steering as a Markov decision process where a controller agent adaptively steers a frozen reasoner during inference. At each step, the controller observes the reasoning trace and remaining thinking budget, then issues a steering action consisting of a reasoning strategy and a steering phrase that initiates the next reasoner step. This enables budget-aware strategy control for efficient reasoning while preserving the reasoner's generation continuity. We initialize the controller agent from our constructed synthetic steering trajectories with multi-budget augmentation, and further optimize it via reinforcement learning with budget-conditioned reward shaping. Experiments across multiple benchmarks show that ACTS matches full-thinking performance with substantial token savings, and enables controllable accuracy-efficiency trade-offs across different reasoners and tasks. The code is available at https://github.com/Andree-9/ACTS.
arXiv:2606.03378v1 Announce Type: new
Abstract: Much of software development revolves around understanding the relationship between software changes and their effects. If we could learn and predict those relationships, such predictions could benefit several areas of software engineering. While recent advances in artificial intelligence have shown great promise in software engineering tasks, predicting the semantics of code without executing it remains a big challenge. In this paper, we present Neural Change Prediction, a novel and fundamental technique to learn and predict associations between software changes and their dynamic effects on program behavior. Specifically, for a given program and test inputs, we automatically apply numerous mutations to the code and observe how these changes alter the program's output. From these (changes to software, changes in behavior)-pairs, we create models that: (1) for a desired change in behavior, predict where and how the code should be changed (feature localization, software evolution, and software repair); and (2) for a given code change, predict how this code change affects the output (effect prediction). We have conducted a detailed case study on CSS configuration files and an evaluation on Python programs to demonstrate the generality and wide applicability of Neural Change Prediction. While Neural Change Prediction requires numerous mutations (and thus numerous executions of the program under test), Neural Change Prediction is fully automatic and does not require any prior knowledge of the code or its semantics, making it applicable to any software artifact that can be executed and whose output can be observed.
arXiv:2606.03386v1 Announce Type: new
Abstract: While AI and machine learning for cyber attack prediction have advanced, a critical gap persists between theoretical research and practical operational deployment. Building on Ankalaki et al. (2025), this paper provides a comprehensive analysis of 150+ benchmark datasets and 200+ studies to identify and prioritize five implementation hurdles: (1) temporal dataset obsolescence, (2) narrow attack scope, (3) real-time model interpretability, (4) inadequate adversarial robustness, and (5) privacy/ethical concerns. We introduce a novel gap-prioritization framework that evaluates these limitations based on detection impact, implementation cost, and remediation time. Our analysis identifies dataset obsolescence and adversarial robustness as the highest-priority gaps, while highlighting model interpretability as the most cost-effective path for resource-constrained environments. To bridge the research-practice divide, we provide a practical implementation roadmap and a dataset quality assessment framework that classifies 45 benchmarks into production-ready, research-only, and unusable categories. This work translates academic findings into actionable decision-support tools for robust, production-oriented AI-driven cyber defense.
arXiv:2606.03397v1 Announce Type: new
Abstract: Muography is a non-invasive imaging technique that uses cosmic-ray muons, commonly divided into transmission (absorption) and scattering muography. For transmission muography, the inversion algorithm critically determines reconstruction quality. However, widely used schemes may produce smearing artifacts when measurement locations are limited and data are sparse. We develop an optimized Metropolis--Hastings (M--H) algorithm that mitigates smearing and retrieves sharper, more accurate density distributions without auxiliary data. Additionally, we implement an inverse distance weighting (IDW) approach to reconstruct the air--rock interface from muon measurements. The optimized M--H algorithm is applied in Monte Carlo simulations and applied to field data from the TianQin Tunnel experiment using the MuGrid-v2 detector. The IDW-reconstructed air--rock interface is validated against Light Detection and Ranging (LiDAR) measurements. In simulations, the optimized M--H algorithm improves high-density anomaly detection precision from $42\%$ to $100\%$ at threshold $5.1\,\mathrm{g/cm^3}$, with gains of $6\%$ to $42\%$ across other threshold and low-density scenarios, together with the TianQin Tunnel reconstructions, these results demonstrate the effectiveness of the proposed approach.
arXiv:2606.03398v1 Announce Type: new
Abstract: Formal languages have proven to be effective conduits to understand the inner mechanisms of transformers. Past work has shown that transformers trained on next token prediction over counter languages learn representations consistent with an underlying stack structure. Beyond representational analysis, this paper investigates the causal role of these representations. Linear probes are trained to predict the stack depth at each token from the model's hidden states, and a principal representation direction is extracted from the probe. Ablation of this direction from the model causes sequential accuracy to collapse to near 0%, providing strong empirical evidence that the stack representation is not just learned, but is causally necessary for model performance.
arXiv:2606.03164v1 Announce Type: new
Abstract: Artificial intelligence systems that model and support human cognition require reliable measures of cognitive state. We present the Focus Performance Score (FPS) from the Pulse Focus mobile Stroop application and evaluate whether it measures attentional control during color-word conflict resolution. We conduct behavioral, neural, and formula validation analyses. Behavioral results (N=466, 111,133 trials) show that FPS captures the Stroop interference effect, tracks individual differences in attentional control, and demonstrates strong test-retest reliability. Neural validation using the DMCC55B fMRI dataset (N=55) shows that the primary FPS component, mean incongruent reaction time, is significantly associated with anterior cingulate cortex activation, a key neural substrate of conflict monitoring. Formula validation identifies and resolves structural redundancy within the scoring framework and provides convergent support for the weighting design. Together, these findings establish FPS as a behaviorally valid, reliable, and neurally grounded measure of attentional control. FPS provides a defensible behavioral signal for evaluating human attentional state and supports future work on attention-aware human-AI interaction and physiological state modeling.
arXiv:2606.03678v1 Announce Type: new
Abstract: Generating safety-critical scenarios is essential for validating and improving autonomous driving systems, yet it inherently requires maximizing adversariality to expose failures while preserving realism. Existing methods usually manage this trade-off with handcrafted heuristics, confining generation to known priors and overlooking underexplored patterns. While recent open-ended agentic evolution can push this limit, unconstrained general agents lack strict simulator grounding and tend to collapse the multi-objective tension into single-scalar maximization. Here we present EvoDrive, the first automated, LLM-based agentic evolution framework for multi-objective scenario generation. EvoDrive employs a simulator-grounded actor-critic architecture where a memory-driven actor iteratively proposes improvements to the generators and critics filter out implausible candidates, and a self-evolving world evaluator routes promising proposals to optimize simulation budgets. EvoDrive further maintains a Pareto archive of evaluated candidates to preserve diverse attack-realism trade-offs and guide future evolution via simulation feedback. Benchmark results on MetaDrive and CARLA show that EvoDrive not only significantly expands the Pareto frontier across various generators, but also produces valuable scenarios for policy training.
arXiv:2606.03259v1 Announce Type: new
Abstract: Translation quality depends on purpose: the same source text demands different translations depending on audience, tone, and communicative intent. Yet MT models and metrics treat translation as a fixed mapping from source to target. LLMs enable users to explicitly specify purpose alongside source text, yet this capability has not been evaluated at scale. We introduce a systematic evaluation of purpose-driven MT across 50 languages, 5 model sizes and 8 text domains. We find that (1) explicit instructions substantially improve translation adaptedness, with larger gains on informal domains (conversation, social media), for larger model sizes and for higher-resource languages; (2) instructions outperform semantically-matched few-shot examples and paragraph-level context; (3) traditional MT metrics fail to capture adaptation quality, often penalizing adapted translations; (4) when curated instructions are unavailable, models can self-generate them from surrounding document context, closing up to 80% of the adaptedness gap to curated instructions. Our results establish that purpose-adapted MT is a viable and measurable capability of LLMs, while highlighting the need for purpose-aware metrics.
arXiv:2606.03679v1 Announce Type: new
Abstract: Learning-based and physics-informed methods are increasingly used for inverse estimation in controlled nonlinear dynamical systems. However, in many such approaches, the theoretic requirements that make unknown-input reconstruction meaningful, namely well-posedness in the sense of Hadamard, are often disregarded or weakly addressed through generic regularization terms with no explicit guarantees. In this work, we adopt a complementary viewpoint in which these control-theoretic and structural conditions inform the estimator design and constrain its training. We thus develop a physics-informed input-state neural estimator for joint unknown-input and state estimation in nonlinear controlled systems with partial measurements. In the present work, this general framework is instantiated on a model of autonomic cardiac regulation, provides a concrete study case. The estimator is formulated as an inverse neural map conditioned on time and measured outputs, and is trained under data fidelity and dynamical consistency constraints. To ensure it complies with the same structural requirements imposed in robust estimation, we derive left-invertibility conditions by differential-algebraic elimination and embed the resulting constraints directly into the training objective. We further analyze a priori the stability of the inverse mapping to output perturbations and derive a conservative Lipschitz bound that guides the tuning of cost functional hyper-parameters. The framework is evaluated on simulated data, where ground truth data is available, and on two distinct datasets of real cardiovascular recordings. The results show that incorporating control-theoretic solvability constraints into physics-informed learning improves the reliability of inverse inference beyond forward consistency alone.