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Models whose predictions depend on only a handful of well-constrained parameter combinations, termed sloppy models, are ubiquitous in nonlinear stochastic systems. The information-geometric approach to sloppiness advocates using the symmetrized Kullback--Leibler divergence and its associated Hessian, the Fisher Information Matrix (FIM), as the natural loss function. However, prior applications have relied on analytically known or parametrically fitted distributions. In practice, for general agent-based or stochastic models the distribution must be estimated from simulation data. I demonstrate, using Kirman's ant recruitment model as a worked example, that a standard kernel density estimate (KDE) converges to the analytical FIM eigenvectors and eigenvalues with simulation budgets accessible in practice. I derive the analytical Hessian in closed form, show numerical convergence of the KDE-based estimate as a function of simulation data, and demonstrate how the stiff direction enables efficient phase exploration across the model's unimodal and bimodal regimes.
Patchy particles have proven to be a prominent model for studying the self-assembly behavior of various systems, ranging from finite clusters to bulk crystal assemblies, and from synthetic colloidal particles to viruses. The patchy particle model is flexible, but it also comes with its own pitfalls -- the potential design space is infinite. Many efforts have been put into building inverse-design frameworks that efficiently design patchy particles for targeted assembly behaviors. In contrast, little work has been done on investigating the interplay between different types of parameters that can be optimized for patchy particles, such as patch location, patch size, and patch binding energies. Here, by utilizing molecular dynamics with automatic differentiation, we elucidate the relationships between different potential optimization parameters and provide general guidelines on how to approach patchy particle design for various types of finite clusters. Specifically, we find that the design parameter landscape is highly dependent on the floppiness of the target structure, and we can identify stiff and sloppy parameters by computing the Hessians of all optimization parameters.
In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff' combinations of the parameters and is unchanged as other `sloppy' parameter combinations vary by orders of magnitude. We contrast examples of sloppy models (from systems biology, variational quantum Monte Carlo, and common data fitting) with systems which are not sloppy (multidimensional linear regression, random matrix ensembles). We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form, with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.
What can we learn about language from studying how it is used by ChatGPT and other large language model (LLM)-based chatbots? In this paper, we analyse the distinctive character of language generated by ChatGPT, in relation to questions raised by natural language processing pioneer, and student of Wittgenstein, Margaret Masterman. Following frequent complaints that LLM-based chatbots produce "slop," or even "bullshit," in the sense of Frankfurt's popular monograph On Bullshit, we conduct an empirical study to contrast the language of 1,000 scientific publications with typical text generated by ChatGPT. We then explore whether the same language features can be detected in two well-known contexts of social dysfunction: George Orwell's critique of political speech, and David Graeber's characterisation of bullshit jobs. Using simple hypothesis-testing methods, we demonstrate that a statistical model of sloppy bullshit can reliably relate the Frankfurtian artificial bullshit of ChatGPT to the political and workplace functions of bullshit as observed in natural human language.
Although sloppy interpretation is usually accounted for by theories of ellipsis, it often arises in non-elliptical contexts. In this paper, a theory of sloppy interpretation is provided which captures this fact. The underlying idea is that sloppy interpretation results from a semantic constraint on parallel structures and the theory is shown to predict sloppy readings for deaccented and paycheck sentences as well as relational-, event-, and one-anaphora. It is further shown to capture the interaction of sloppy/strict ambiguity with quantification and binding.
We explore the relationship among model fidelity, experimental design, and parameter estimation in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physics that must be included to explain collective behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which details are relevant/irrelevant vary among potential experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model's inadequacy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the error in the model renders it less predictive than it was in the sloppy regime where model error is small. We introduce the concept of a \emph{sloppy syste
Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring \emph{in vivo} biochemical parameters is difficult, and collectively fitting them to other data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a `sloppy' spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our m
Transmission spectroscopy is among the most fruitful techniques to infer the main opacity sources present in the upper atmosphere of a transiting planet and to constrain the composition of the thermosphere and of the unbound exosphere. Not having a public tool able to automatically extract a high-resolution transmission spectrum creates a problem of reproducibility for scientific results. As a consequence, it is very difficult to compare the results obtained by different research groups and to carry out a homogeneous characterization of the exoplanetary atmospheres. In this work, we present a standard, publicly available, user-friendly tool, named SLOPpy (Spectral Lines Of Planets with python), to automatically extract and analyze the optical transmission spectrum of exoplanets as accurately as possible. Several data reduction steps are first performed by SLOPpy to correct the input spectra for sky emission, atmospheric dispersion, the presence of telluric features and interstellar lines, center-to-limb variation, and Rossiter-McLaughlin effect, thus making it a state-of-the-art tool. The pipeline has successfully been applied to HARPS and HARPS-N data of ideal targets for atmosphe
Non-equilibrium transportation of particles through a restricted space (such as porous media or narrow channels) significantly differs from free space. With a simple model of two types of particles competing to transport via a passive single-lane channel connecting two chemical baths, we find two dynamical modes of transportation -- the dud mode and the ratchet mode. At the ratchet mode, the gradient flow of one type of particle forces the other into a transient anti-equilibrium flow against its gradient. At the dud mode, the two types of particles both flow according to their gradients. This counter-intuitive non-equilibrium effect can be explained by a sloppy gear mechanism. In addition to the anti-gradient flow observed in the ratchet mode, we find that the non-equilibrium sloppy gear mechanism suppresses the flow of one particle while allowing the flow for the other. This mechanism provides a general theoretical framework to explain and design the selective transportation of particles via passive channels.
Dynamic models of biochemical networks typically consist of sets of non-linear ordinary differential equations involving states (concentrations or amounts of the components of the network) and parameters describing the reaction kinetics. Unfortunately, in most cases the parameters are completely unknown or only rough estimates of their values are available. Therefore, their values must be estimated from time-series experimental data. In recent years, it has been suggested that dynamic systems biology models are universally sloppy so their parameters cannot be uniquely estimated. In this work, we re-examine this concept, establishing links with the notions of identifiability and experimental design. Further, considering a set of examples, we address the following fundamental questions: i) is sloppiness inherent to model structure?; ii) is sloppiness influenced by experimental data or noise?; iii) does sloppiness mean that parameters cannot be identified?, and iv) can sloppiness be modified by experimental design? Our results indicate that sloppiness is not equivalent to lack of structural or practical identifiability (although they can be related), so sloppy models can be identifiab
In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases, models are sloppy, that is, exhibit an exponential hierarchy of parameter sensitivities. We propose a parameter classification scheme based on how the sensitivities scale at long observation times. We show that for oscillatory models, either with a limit cycle or a strange attractor, sensitivities can become arbitrarily large, which implies a high effective-dimensionality on the model manifold. Sloppy models with a single fixed point have model manifolds with low effective-dimensionality, previously described as a "hyper-ribbon". In contrast, models with high effective dimensionality translate into multimodal fitting problems. We define a measure of curvature on the model manifold which we call the \emph{winding frequency} that estimates the linear density of local minima in the model's parameter space. We then show how alternative choices of fitting metrics can "unwind" the model manifold and give low winding frequencies. This prescription translate
The description of complex systems requires a progressively larger number of parameters. However, in practice, it often happens that a small subset of parameters suffices to describe the dynamics of the system itself: these combinations are usually referred to as \textit{stiff} combinations. In turn, the remaining combinations, called \textit{sloppy}, only play a minor role in the dynamics of the system, hence provide little information on it. While this effect can reduce model complexity, it can also limit the estimation precision when the stiff and sloppy combinations are unknown to the experimenter, and one is forced to estimate the potentially sloppy model parameters. We explored how such a sloppy behavior can be controlled and counteracted via quantum weak measurements in the estimation of two sequential phases. We showed that the introduction of a weak measurement of variable strength in-between the two phases allows to switch from a fully sloppy setup to a fully determined one where both phases can be estimated with quantum-limited precision. Our work provides an important insight of sloppiness detection in quantum systems, with promising applications in quantum metrology an
The characterization of electric and magnetic dipole moments (EDM and MDM) in quantum systems is central to fundamental physics and quantum sensing. While EDM searches provide powerful probes of CP violation within and beyond the Standard Model, precise MDM estimation is crucial for high-precision magnetometry and the development of quantum sensors. In this work, we address the ultimate precision limits for separate and simultaneous estimation of both dipole moments in a generic two-level system coupled to electromagnetic fields. We analyze three classes of quantum probes/strategies: unitary and depolarizing dynamics, and thermal equilibrium states. For each, we derive the quantum Fisher information (matrix), identify optimal probes, and determine the ideal operating conditions, such as evolution times and temperatures, that maximize estimation precision. We further assess the compatibility and sloppiness of the statistical models, showing that orthogonal dipole moments configurations enable joint estimation of EDM and MDM, whereas parallel configurations are intrinsically sloppy, permitting only the estimation of a single parameter combination. Our results provide a unified metrol
This work introduces a stochastic hierarchical optimization framework inspired by Sloppy Model theory for the efficient calibration of physical models. Central to this method is the use of a reduced Hessian approximation, which identifies and targets the stiff parameter subspace using minimal simulation queries. This strategy enables efficient navigation of highly anisotropic landscapes, avoiding the computational burden of exhaustive sampling. To ensure rigorous inference, we integrate this approach with a probabilistic formulation that derives a principled objective loss function directly from observed data. We validate the framework by applying it to the problem of plasma-surface interactions, where accurate modelling is strictly limited by uncertainties in surface reactivity parameters and the computational cost of kinetic simulations. Comparative analysis demonstrates that our method consistently outperforms baseline optimization techniques in sample efficiency. This approach offers a general and scalable tool for optimizing models of complex reaction systems, ranging from plasma chemistry to biochemical networks.
When two successive squeezing operations with the same phase are applied to a field mode, reliably estimating the amplitude of each is impossible because the output state depends solely on their sum. In this case, the quantum statistical model becomes sloppy, and the quantum Fisher information matrix turns singular. However, estimation of both parameters becomes feasible if the quantum state is subjected to an appropriate scrambling operation between the two squeezing operations. In this work, we analyze in detail the effects of a phase-shift scrambling transformation, optimized to reduce sloppiness and maximize the overall estimation precision. We also compare the optimized precision bounds of joint estimation with those of stepwise estimation methods, finding that joint estimation retains an advantage despite the quantum noise induced by the residual parameter incompatibility. Finally, we analyze the precision achievable by general-dyne detection and find that it may approach the optimal precision in some regimes.
We demonstrate that, even when there are moderate overlaps in the inputs of sloppy or accurate double-word addition algorithms in the QD library, these algorithms still guarantee error bounds of $O(u^2(|a|+|b|))$ in faithful rounding. Furthermore, the accurate algorithm can achieve a relative error bound of $O(u^2)$ in the presence of moderate overlaps in the inputs when rounding function is round-to-nearest. The relative error bound also holds in directed rounding, but certain additional conditions are required. Consequently, in double-word multiplication and addition operations, we can safely omit the normalization step of double-word multiplication and replace the accurate addition algorithm with the sloppy one. Numerical experiments confirm that this approach nearly doubles the performance of double-word multiplication and addition operations, with negligible precision costs. Moreover, in directed rounding mode, the signs of the errors of the two algorithms are consistent with the rounding direction, even in the presence of input overlap. This allows us to avoid changing the rounding mode in interval arithmetic. We also prove that the relative error bound of the sloppy addition
Multiparameter quantum estimation becomes challenging when the parameters are incompatible, i.e., when their respective symmetric logarithmic derivatives do not commute, or when the model is sloppy, meaning that the quantum probe depends only on combinations of parameters leading to a degenerate or ill-conditioned Fisher information matrix. In this work, we explore the use of scrambling operations between parameter encoding to overcome sloppiness. We consider a bosonic model with two phase-shift parameters and analyze the performance of second- and third-order nonlinear scrambling using two classes of probe states: squeezed vacuum states and coherent states. Our results demonstrate that nonlinear scrambling mitigates sloppiness, increases compatibility, and improves overall estimation precision. We find third-order nonlinearity to be more effective than second-order under both fixed-probe and fixed-energy constraints. Furthermore, by comparing joint estimation to a stepwise estimation strategy, we show that a threshold for nonlinear coupling exists. For coherent probes, joint estimation outperforms the stepwise strategy if the nonlinearity is sufficiently large, while for squeezed
It is widely accepted that the brain operates near a critical state, characterized by neural avalanches that follow power-law distributions. However, the functional rationale for why neural systems attain criticality remains unclear. Here, we present a theoretical framework that links efficient coding to criticality in neural populations. Using a Gaussian population coding model, we demonstrate that maximizing Fisher information under resource constraints naturally leads to the emergence of soft modes and diverging correlation lengths, which are hallmarks of criticality. By introducing spatial structure, we unify two distinct perspectives of criticality: statistical criticality with diverging correlation lengths and dynamical criticality with critical slowing down as well as bifurcation. Furthermore, this framework provides a natural explanation for the sloppiness observed in neural systems. Numerical simulations confirm that optimization results in power-law response, providing a mechanistic link between efficient coding, sloppiness and the critical brain hypothesis.
Multiparameter quantum estimation theory plays a crucial role in advancing quantum metrology. Recent studies focused on fundamental challenges such as enhancing precision in the presence of incompatibility or sloppiness, yet the relationship between these features remains poorly understood. In this work, we explore the connection between sloppiness and incompatibility by introducing an adjustable scrambling operation for parameter encoding. Using a minimal yet versatile two-parameter qubit model, we examine the trade-off between sloppiness and incompatibility and discuss: (1) how information scrambling can improve estimation, and (2) how the correlations between the parameters and the incompatibility between the symmetric logarithmic derivatives impose constraints on the ultimate quantum limits to precision. Through analytical optimization, we identify strategies to mitigate these constraints and enhance estimation efficiency. We also compare the performance of joint parameter estimation to strategies involving successive separate estimation steps, demonstrating that the ultimate precision can be achieved when sloppiness is minimized. Our results provide a unified perspective on th
Multi-parameter statistical models may depend only on some functions of the parameters that are fewer than the number of initial parameters themselves. Such \emph{sloppy} statistical models are characterized by a degenerate Fisher Information matrix, indicating that it is impossible to simultaneously estimate all the parameters. In a quantum setting, once an encoding is fixed, the same can happen for the Quantum Fisher Information matrix computed from a sloppy quantum statistical model. In addition to sloppiness, however, further issues of quantum incompatibility can arise. We take a fully Gaussian case-study to investigate the topic, showing that by appropriately scrambling the quantum states in between the encoding of two phase-shift parameters a Mach-Zehnder interferometer, not only sloppiness can be lifted, but also the quantum incompatibility can be put identically to zero, maintaining an enhanced scaling of precision and the covariance of the model with respect to exact values of the parameters.