From field-scale to large-scale spectral libraries: Tabular foundation models in soil spectroscopy

# From field-scale to large-scale spectral libraries: Tabular foundation models in soil spectroscopy
Source: [https://arxiv.org/html/2608.00608](https://arxiv.org/html/2608.00608)
1\]organization=Osnabrück University, Joint Lab Artificial Intelligence and Data Science, city=Osnabrück, country=Germany 2\]organization=Leibniz Institute for Agricultural Engineering and Bioeconomy \(ATB\), Department of Agromechatronics, city=Potsdam, country=Germany 3\]organization=German Research Center for Artificial Intelligence \(DFKI\), Cooperative and Autonomous Systems \(CAS\), city=Osnabrück, country=Germany

###### Abstract

Visible and near\-infrared \(vis\-NIR\) and mid\-infrared \(MIR\) spectroscopy enable rapid, cost\-effective prediction of soil properties\. Yet, translating high\-dimensional, highly collinear spectra into accurate soil property predictions remains challenging, particularly when employing machine learning\. We systematically investigated regression models and dimensionality reduction approaches for spectroscopic modeling across 85 regression tasks from open benchmark datasets in pedometrics spanning field\-scale digital soil mapping and a global soil spectral library\. We compared an in\-context learning tabular foundation model \(TabPFN\), a convolutional neural network \(CNN\), rule\-based regression \(Cubist\), Random Forest, and partial least squares regression \(PLSR\) using full spectra as well as features derived from principal component analysis \(PCA\) and partial least squares \(PLS\) latent variables\. TabPFN consistently delivered the best overall performance across scales, including large spectral library tasks with tens of thousands of soil samples\. Notably, TabPFN applied directly to full spectra already surpassed all classical baselines, showing that explicit dimensionality reduction is not strictly required for strong performance\. Further improvements were achieved through PLS, which proved to be an effective dimensionality reduction strategy for all models\. Combining PLS latent variables with TabPFN yielded the best predictions overall\. Our findings provide evidence\-based guidance for spectroscopic calibration model selection across operational scales, demonstrating that the long\-standing advantages of PLSR and modern tabular foundation models complement each other in chemometrics\.

###### keywords:

Chemometrics\\sepPedometrics\\sepDigital Soil Mapping\\sepMachine learning\\sepTabular foundation models

## 1Introduction

Diffuse reflectance spectroscopy enables the rapid and non\-destructive estimation of material properties from their characteristic molecular absorption signatures\(frei2019diffuse\)\. It is therefore widely used as a cost\-effective analytical technique across various environmental disciplines, including soil science\. In the infrared region in particular, certain soil minerals and organic compounds exhibit distinct absorption features arising from the vibrations of their chemical bonds\(stoner1981characteristic;ben1999soil\)\. The resulting spectral fingerprint contains information about the soil’s composition, from which soil properties such as texture, organic carbon, pH, and concentrations of certain nutrients can be inferred\(viscarrarossel2006visible\)\. Accordingly, both visible and near\-infrared \(vis\-NIR\) and mid\-infrared \(MIR\) spectroscopy are increasingly used ex situ in soil laboratories as a substitute for costly laboratory analyses\(nocita2015soilspectroscopy\)as well as in situ in the field through proximal soil sensing \(PSS\) for high\-resolution soil mapping\(soriano\-disla2014performance;gebbers2019proximal\)\.

Translating spectral signals into soil property predictions requires robust predictive models, which act as the critical backbone of soil spectroscopy\(nocita2015soilspectroscopy\)and combine insights from chemometrics, the application of mathematical and statistical methods to chemical data\(brown2020chemometrics\), and pedometrics, the application of mathematical and statistical methods in soil science\(webster1994pedometrics\)\. Knowledge from these disciplines enables the efficient spatial prediction of soil properties across the landscape, the central aim of digital soil mapping \(DSM\)\(mcbratney2003dsm;minasny2016dsm\)\.

Owing to its flexibility in modeling the relationship between dependent and independent variables, machine learning \(ML\) has become the predominant approach for developing such predictive models in DSM\(wadoux2020machine\)\. In soil spectroscopy specifically, these models operate on a structured, tabular representation of reflectance spectra, placing the task on common methodological ground with numerous other scientific domains where tabular ML is prevalent\. However, soils present unique challenges for ML modeling\. Soils exhibit great physical and structural complexity\(Jenny1941factors\), with highly heterogeneous composition varying across spatial and temporal scales: soil properties fluctuate at the microscopic scale due to complex pore structures and mineralogical diversity, at the macro and field scales due to environmental and anthropogenic factors, and over time due to high temporal dynamics in properties such as moisture and nutrient content\(herrick2023practical;young2008microbial\)\.

Moreover, the specifics of diffuse reflectance spectra pose modeling challenges of their own\. Spectral measurements can be strongly affected by particle\-size heterogeneity and light scattering, by the overlap of absorption features arising from multiple interacting soil constituents, and by variability in water content and other environmental factors when acquired in situ\(ben1999soil;soriano\-disla2014performance\)\. As a consequence, spectra almost never respond to a single soil property unambiguously\(gebbers2019proximal\)\. In addition, spectrometers output hundreds to thousands of spectral variables\(wang2022spectral\), creating high\-dimensional feature spaces\. At the field scale, where financial and practical constraints typically limit the number of soil samples\(soderstrom2016adaptation;schmidinger2024effect\), this yields unfavorable feature\-to\-sample ratios and the curse of dimensionality\(dossantos2023improving;correa2025overfitting\)\. At larger scales, where national and global soil spectral libraries may contain tens of thousands of samples, the high dimensionality instead introduces substantial computational overhead\(viscarrarossel2016global;gamagedara2025application\)\. On top of that, neighboring spectral bands are highly correlated, further complicating the application of ML in soil spectroscopy\(dossantos2023improving;wang2022determination;wang2022spectral\)\.

These challenges have historically shaped a distinct modeling landscape for soil spectroscopy, favoring approaches that differ from standard tabular ML practice\. Despite its origins in the 1970s\(wold1975soft\), partial least squares \(PLS\) regression \(PLSR\) remains one of the most widely used methods for quantitative spectral analysis of soil to this day\(e\.g\.,gyawali2025measuring;reyes2024spectral;pace2024soil\)\. Its longevity is well founded: PLSR is exceptionally well suited to spectral data, as it jointly addresses dimensionality reduction and regression while inherently handling multicollinearity and noise\(soriano\-disla2014performance;viscarrarossel2006visible;janik1998can\)\. Convolutional neural networks \(CNNs\) have more recently attracted interest for soil spectroscopy\(e\.g\.,huang2025using;ng2019convolutional\), as the ordered nature of spectral wavelengths and their high intercorrelation are well suited to convolutional kernels\. While these approaches handle dimensionality within the model itself, an alternative strategy is to address it explicitly through dimensionality reduction\(e\.g\.,correa2025overfitting;safanelli2025open;schmidinger2025limesoda\)or feature selection as a preprocessing step\(e\.g\.,rodriguez\-albarracin2024soil;cui2026improving\)\. This offers flexibility in the choice of regression model and enables practitioners to leverage advances in general\-purpose tabular ML as they arise\.

Among dimensionality reduction techniques in soil spectroscopy, principal component analysis \(PCA\) is a well\-established choice\(correa2025overfitting;safanelli2025open;schmidinger2025limesoda\)\. Its appeal is clear: PCA is simple, well\-understood, and can be paired with any downstream regression model\. Yet the persistent popularity of PLSR in soil spectroscopy, despite decades of ML advances, suggests that there are distinct advantages in the way PLS compresses spectral features\. Similar to PCA, PLS decomposes spectra into a reduced set of latent variables\. Unlike PCA, however, PLS is a supervised method: the decomposition maximizes the covariance between spectra and the soil property of interest, thereby producing latent variables that are inherently aligned with the prediction target\. Extending such target\-aware dimensionality reduction beyond the PLSR framework presents a promising opportunity: rather than restricting the extracted PLS latent variables to a linear model, as is done in PLSR, they could be used as input features for modern regression models, effectively combining target\-aware dimensionality reduction with the capacity of state\-of\-the\-art algorithms\. Despite the intuitive appeal of this idea, it has never been systematically evaluated in soil spectroscopy, having appeared as a dimensionality reduction choice only in a few isolated case studies\(e\.g\.,zhao2024integrating;liu2017combining;mouazen2010comparison\)\. Furthermore, whether it could enhance the performance of recent advances in pedometric modeling within DSM remains an open question\.

A recent development in tabular ML that holds particular relevance for pedometric modeling is the emergence of in\-context learning foundation models for tabular data\(hollmann2025accurate;hollmann2023tabpfn;muller2022transformers\)\. Unlike conventional ML approaches that require dataset\-specific training and hyperparameter optimization, these models are pre\-trained on large collections of synthetic tabular tasks, and perform inference by conditioning on a labeled training set provided as a context at prediction time\(hollmann2023tabpfn\)\. TabPFN \(Tabular Prior\-data Fitted Network\) is a pioneer of this paradigm\(hollmann2025accurate;hollmann2023tabpfn\), and has demonstrated strong performance on tabular datasets across diverse domains\(erickson2025tabarena;grinsztajn2025tabpfn\), including state\-of\-the\-art results in field\-scale DSM\(barkov2026modern\)\. Earlier versions of TabPFN, however, were constrained to datasets with limited numbers of samples and features\(hollmann2025accurate;ye2025closer\), creating a direct conflict with the high dimensionality characteristic of soil spectroscopy\. To address this limitation, combining PCA with TabPFN was proposed as a workaround both in DSM\(barkov2026modern\)and in general tabular ML\(ye2025closer\)\. TabPFNv2\.5\(grinsztajn2025tabpfn\)natively handles datasets with up to 100,000 samples and 2,000 features, aligning well with the scale of typical soil spectroscopic datasets both at the field scale and at the scale of national and global soil spectral libraries\. Initial exploratory studies in pedometrics suggest that these advances extend the potential of TabPFN beyond the field scale:huang2026zeroshotreported strong accuracy and generalization on subsets of a national soil spectral library of up to roughly 10,000 soil samples\. However, whether these strengths hold under the specific challenges of larger\-scale spectroscopic modeling remains an open question, both when applied directly to spectral data and when combined with typical dimensionality reduction strategies, warranting systematic investigation\.

While investigating these questions is essential, it is equally important to do so in a generalizable and fair manner\. Current benchmarking practice in DSM overwhelmingly relies on single\-dataset evaluations\(schmidinger2025limesoda\), even though single\-dataset conclusions are vulnerable to dataset\-specific biases and often fail to generalize\(boulesteix2017towards;niessl2022over;schmidinger2025limesoda\)\. This is particularly consequential in soil spectroscopy, where soil surveys are conducted with different objectives and produce datasets with fundamentally different characteristics\(chabrillat2019imaging\)\. In field\-scale DSM, a small number of highly localized soil samples are obtained to create high\-resolution maps for the needs of precision agriculture\. In national and global soil spectral libraries, which are compiled for environmental monitoring, large numbers of soil samples are collected with sparse spatial distribution, resulting in large datasets with high diversity and heterogeneity of soil properties\. A method that excels in one of these scenarios may not retain its advantages in the other, making cross\-scale evaluation necessary to draw transferable conclusions\. Further, to ensure fairness and reproducibility, it is necessary to employ openly accessible benchmark dataset collections\(e\.g\.,schmidinger2025limesoda;safanelli2025open\)\.

In this study, we systematically investigate modeling strategies and dimensionality reduction approaches for soil spectroscopy across multiple datasets and operational scales\. We evaluate whether the demonstrated strengths of TabPFNv2\.5 extend to the specific challenges of spectroscopic modeling, including the first application to large\-scale soil spectral library tasks involving tens of thousands of soil samples\. We further investigate whether the predictive performance of pedometric models can be enhanced by employing PLS latent variables as input features for both classical algorithms and tabular foundation models\. We compare our findings against established baselines and across datasets that span field\-scale to global spectral libraries, with openly accessible data and code to ensure fairness and generalizability of conclusions\. As a result of our study, we aim to provide evidence\-based guidance for practitioners selecting modeling strategies for soil spectroscopy across operational scales\.

## 2Materials and methods

### 2\.1Datasets

#### 2\.1\.1Field\-scale spectroscopy data

![Refer to caption](https://arxiv.org/html/2608.00608v1/x1.png)Figure 1:Spatial distribution of the 13 field\-scale soil spectroscopy datasets from the LimeSoDa benchmark collection employed in this study\. The datasets span seven countries across three continents, encompassing diverse geological settings, spectrometer instruments, study area sizes, and measurement protocols\. Base map source: Natural Earth\.The high dimensionality of spectral features combined with the small sample sizes typical of field\-scale soil surveys commonly leads to unfavorable feature\-to\-sample ratios and complicates modeling\(dossantos2023improving;correa2025overfitting\)\. To draw generalizable conclusions about field\-scale soil spectroscopy modeling strategies, we employed the Precision Liming Soil Datasets \(LimeSoDa\)\(schmidinger2025limesoda\), an open\-access benchmark dataset collection of field\- and farm\-scale high\-resolution DSM datasets that aggregates data from multiple independent soil surveys across diverse geographical and geological settings\.

For the purpose of our investigation, we employed all LimeSoDa datasets that include features derived from soil spectroscopy, specifically from vis\-NIR and MIR spectroscopy\. For datasets that additionally contained features derived from other proximal soil sensors, such as apparent electrical resistivity, we retained only the spectroscopic features\. This selection resulted in 13 field\-scale datasets: eight produced with vis\-NIR spectroscopy and five with MIR spectroscopy\. Each resulting dataset includes three target soil properties: soil organic carbon \(SOC\) or soil organic matter \(SOM\), pH, and clay content\. These ground truth target soil properties were determined through wet chemistry laboratory analyses\. Since each dataset contains three target soil properties, this resulted in 39 separate regression tasks\.

![Refer to caption](https://arxiv.org/html/2608.00608v1/x2.png)Figure 2:Mean spectra of the individual spectroscopy datasets from LimeSoDa: \(a\) eight vis\-NIR datasets, and \(b\) five MIR datasets\. Each line is the per\-band mean spectrum across all soil samples of one dataset\. Colors differ to visually distinguish the individual datasets\. Vis\-NIR spectra are shown as reflectance against wavelength, and MIR spectra as absorbance against wavenumber\.The 13 selected datasets encompass a wide range of geological settings, spectrometer instruments, study area sizes, and measurement protocols\. The datasets span seven countries across three continents, with study sites in Brazil, China, France, Germany, Japan, Sweden, and Switzerland \(see Figure[1](https://arxiv.org/html/2608.00608#S2.F1)\)\. Geological settings range from glacial and fluvioglacial deposits, Cretaceous marls with aeolian and fluvial overburden, and Pleistocene periglacial slope deposits in Europe, to heavily weathered tropical soils developed on sandstone, volcanic rock, and diabase\. Spectroscopic measurements were obtained using a variety of instruments, including laboratory spectrometers \(e\.g\., Bruker Tensor 27 HTS\-XT, Bruker Optik, Ettlingen, Germany\) and portable handheld devices deployed in the field \(e\.g\., Agilent 4300, Agilent Technologies, Santa Clara, USA\)\. Study area sizes range from 0\.6 to 473 ha\. Dataset sizes are typical for field\-scale soil surveys, ranging from 32 to 460 soil samples\. The vis\-NIR spectra span the approximate spectral range of 350–2,500 nm, resulting in datasets with up to 2,151 spectral variables, while MIR spectra span approximately 550–5,400 cm\-1, resulting in datasets with up to 2,489 spectral variables\. The mean spectral signatures of individual vis\-NIR and MIR datasets are presented in Figure[2](https://arxiv.org/html/2608.00608#S2.F2)\. All datasets are openly accessible under a permissive license \(see[Code and data availability](https://arxiv.org/html/2608.00608#Sx1)\)\.

#### 2\.1\.2Large\-scale soil spectral library

![Refer to caption](https://arxiv.org/html/2608.00608v1/x3.png)Figure 3:Spatial distribution of soil samples in the Open Soil Spectral Library \(OSSL\) employed in this study\. The OSSL aggregates harmonized spectral data from multiple national and international soil spectral collections, providing near\-global spatial coverage\. Base map source: Natural Earth\.National and global soil spectral libraries compile large numbers of samples spanning diverse soil types, climatic zones, and parent materials\(e\.g\.,safanelli2025open;fohrafellner2026austrian;meszaros2025vis\)\. Their larger spatial scale results in greater heterogeneity in soil composition, and the aggregation of data across laboratories with different methods and instruments introduces additional variability\(safanelli2025open\)\. The high dimensionality of spectral data additionally introduces substantial computational overhead at this scale\(viscarrarossel2016global;gamagedara2025application\)\.

We employed the Open Soil Spectral Library \(OSSL\) for the large\-scale spectral library evaluation\(safanelli2025open\)\. OSSL is an open\-access global soil spectral library compiled by the Soil Spectroscopy for Global Good initiative that aggregates and harmonizes soil spectral data from multiple independent libraries with open or compatible data\-sharing policies\. Ground truth target soil properties were determined through wet chemistry laboratory analyses\. Spectral data were harmonized to common ranges and resolutions, and laboratory reference data were harmonized by mapping analytical methods to standardized guides and converting shared properties to unified target variables via published transformation rules\(safanelli2025open\)\. The resulting database contains over 135,000 entries with near\-global spatial coverage \(see Figure[3](https://arxiv.org/html/2608.00608#S2.F3)\)\.

![Refer to caption](https://arxiv.org/html/2608.00608v1/x4.png)Figure 4:Mean spectra of the individual spectroscopy regression tasks from OSSL: \(a\) 16 vis\-NIR regression tasks, and \(b\) 30 MIR regression tasks\. Each line is the per\-band mean spectrum across all soil samples for each target soil property\. Colors differ to visually distinguish the individual regression tasks\. Vis\-NIR spectra are shown as reflectance against wavelength, and MIR spectra as absorbance against wavenumber\.For the purpose of our investigation, we employed all MIR and vis\-NIR regression tasks from the OSSL for which the harmonized target soil property had at least 10,000 observations\. This resulted in 30 MIR and 16 vis\-NIR regression tasks, yielding a total of 46 separate regression tasks\. The target soil properties span a broad range of chemical, physical, and mineralogical attributes, including, among others, organic and total carbon, total nitrogen, pH, cation exchange capacity, particle size fractions \(clay, silt, sand\), extractable cations and nutrients, carbonate content, bulk density, water retention parameters, and electrical conductivity\.

The MIR spectra cover the spectral range of 600–4,000 cm\-1at 2 cm\-1intervals, resulting in 1,701 spectral variables per sample\. The vis\-NIR spectra span either 350–2,500 nm or 400–2,500 nm at 2 nm intervals, depending on the spectral coverage of the underlying source libraries \(e\.g\., the LUCAS library provides vis\-NIR spectra starting from 400 nm\), resulting in up to 1,076 spectral variables\. The mean spectral signatures associated with these regression tasks are shown in Figure[4](https://arxiv.org/html/2608.00608#S2.F4)\. Across the 46 regression tasks, dataset sizes range from 14,166 to 82,573 soil samples\. The OSSL is openly accessible under permissive licenses \(see[Code and data availability](https://arxiv.org/html/2608.00608#Sx1)\)\.

### 2\.2Modeling

To compare modeling strategies fairly, all regression tasks were evaluated under a common protocol: \(i\) spectral preprocessing, \(ii\) feature\-wise standardization, \(iii\) optional dimensionality reduction, and \(iv\) regression\. The components of this protocol are described in the following subsections\.

#### 2\.2\.1Spectral preprocessing and standardization

All spectra were preprocessed using the standard normal variate \(SNV\) transformation\(barnes1989standard\)\. SNV is a row\-wise normalization that centers each spectrum to zero mean and scales it to unit standard deviation across wavelengths\. SNV allows correcting for multiplicative effects of particle size and light scattering that are prevalent in diffuse reflectance spectroscopy of soil\(barnes1989standard;safanelli2023interlaboratory\), and is consistently identified among the most effective preprocessing approaches for soil spectroscopy across spectral regions and modeling algorithms\(safanelli2023interlaboratory;safanelli2025open;vestergaard2021evaluation\)\.

Following SNV, feature\-wise standardization \(centering to zero mean and scaling to unit variance\) was applied, with standardization statistics computed on the training samples of the respective fold\.

#### 2\.2\.2Dimensionality reduction

Two dimensionality reduction strategies were evaluated as preprocessing steps prior to regression: principal component analysis \(PCA\) and partial least squares \(PLS\) projection\.

PCA involves the decomposition of the feature matrix𝐗\\mathbf\{X\}\(in our case,IIsoil samples×\\timesJJspectral variables\)\. This is commonly achieved via singular value decomposition \(SVD\):

𝐗=𝐑​𝚫​𝐕⊤,\\mathbf\{X\}=\\mathbf\{R\}\\,\\boldsymbol\{\\Delta\}\\,\\mathbf\{V\}^\{\\top\},\(1\)where𝐑\\mathbf\{R\}and𝐕\\mathbf\{V\}are orthonormal matrices and𝚫\\boldsymbol\{\\Delta\}is a diagonal matrix of singular values\. The principal components of𝐗\\mathbf\{X\}are the columns of𝐑​𝚫\\mathbf\{R\}\\boldsymbol\{\\Delta\}, ordered by the variance of𝐗\\mathbf\{X\}they explain\. Retaining only the firstnncomponents yields a reduced set of features that can be used with any regression model to predict𝐘\\mathbf\{Y\}, making PCA an unsupervised dimensionality reduction method\. The orthogonality of the resulting components is naturally suited to spectroscopic data, as it eliminates the multicollinearity inherent in neighboring spectral bands\. However, because the decomposition is performed on𝐗\\mathbf\{X\}alone, there is no guarantee that the components explaining the most variance in𝐗\\mathbf\{X\}will be the most relevant for predicting𝐘\\mathbf\{Y\}\.

PLS, in contrast, searches for a set of components, commonly referred to as latent variables, that maximize the covariance between𝐗\\mathbf\{X\}and𝐘\\mathbf\{Y\}\. While PLS is classically computed using iterative algorithms such as Nonlinear Iterative Partial Least Squares \(NIPALS\), it can be expressed through SVD in a manner directly analogous to PCA\(abdi2010partial\)\. In this formulation, the cross\-covariance matrix𝐗⊤​𝐘\\mathbf\{X\}^\{\\top\}\\mathbf\{Y\}is decomposed as

𝐗⊤​𝐘=𝐖​𝚯​𝐂⊤,\\mathbf\{X\}^\{\\top\}\\mathbf\{Y\}=\\mathbf\{W\}\\,\\boldsymbol\{\\Theta\}\\,\\mathbf\{C\}^\{\\top\},\(2\)where𝐖\\mathbf\{W\}and𝐂\\mathbf\{C\}are orthonormal matrices and𝚯\\boldsymbol\{\\Theta\}is a diagonal matrix of singular values reflecting the covariance between𝐗\\mathbf\{X\}and𝐘\\mathbf\{Y\}\. The latent variables are obtained as𝐋=𝐗𝐖\\mathbf\{L\}=\\mathbf\{X\}\\mathbf\{W\}, ordered by decreasing covariance\. Retaining the firstnnlatent variables yields a reduced set of features that best capture the covariance structure between𝐗\\mathbf\{X\}and𝐘\\mathbf\{Y\}\. Since the decomposition involves𝐘\\mathbf\{Y\}, these selected latent variables can be used directly to estimate𝐘^\\hat\{\\mathbf\{Y\}\}, effectively performing PLSR\. Equally, the selected latent variables can serve as features for any regression model, making PLS a supervised dimensionality reduction method that addresses potential limitations of PCA\.

#### 2\.2\.3Regression models

Six regression models were evaluated: Linear regression, PLSR, Random Forest, Cubist, CNN, and TabPFN\.

Linear regression models the relationship between dependent and independent variables using a linear equation\. When multiple independent variables are used, it is referred to as multiple linear regression \(MLR\)\. MLR is a well\-established baseline in pedometric modeling\. A common variant of MLR employed in soil spectroscopy is principal component regression \(PCR\), where MLR is fitted on principal components extracted via PCA as input features\(e\.g\.,kuhn2025tracking;tavakoli2023predicting;paltseva2022prediction\)\.

PLSR, similarly to PCR, performs linear regression on a reduced set of components\. Unlike PCR, PLSR extracts these components through simultaneous decomposition of features and the dependent variable \(see Section[2\.2\.2](https://arxiv.org/html/2608.00608#S2.SS2.SSS2)\), effectively combining linear regression with supervised dimensionality reduction\. PLSR is historically the most widely used algorithm in soil spectroscopy\(rossel2010using\)and is still one of the strongest baselines in contemporary DSM\(e\.g\.,hutengs2024enhanced;angelettidafonseca2022effect;carvalho2022combining\)\.

Random Forest\(breiman2001random\)is a randomized ensemble of decision trees regularized through bootstrap aggregation\. Random Forest is the most widely adopted ML algorithm in general pedometric modeling from PSS\(ding2025advancing;wadoux2020machine\)\. In soil spectroscopy, Random Forest is typically coupled with PCA or combined with iterative feature selection\.

Cubist is a rule\-based regression model that constructs a set of piecewise linear models organized as a decision tree, with optional committee boosting and instance\-based nearest\-neighbor correction\(quinlan1992learning\)\. Cubist has been widely adopted for pedometric modeling in DSM\(minasny2008regression\)with strong results in soil spectroscopy\(e\.g\.,sanderman2025application;agyeman2025prediction;safanelli2025open\)\.

CNN is a neural network architecture in which learnable filters \(commonly referred to as kernels\) perform discrete convolution operations \(typically implemented as spatially localized cross\-correlations\) by sliding across the input with a defined step size \(commonly referred to as stride\)\. CNNs are designed for data characterized by a grid\-like topology, with foundational applications in image recognition\(lecun2002gradient\)\. The naturally ordered structure and high intercorrelation of neighboring spectral bands in soil spectroscopy present a setting that is well suited for the application of CNNs, enabling learning directly from the spectra without the need for dimensionality reduction\. Therefore, CNNs attracted considerable interest in soil spectroscopy, with initial applications on two\-dimensional \(2D\) representations of spectra drawing inspiration from computer vision\(padarian2019usinga\), and moving to more principled one\-dimensional \(1D\) convolutional architectures operating directly on the spectral sequence in subsequent works\(ng2019convolutional\)\. In addition to the CNN baseline, we evaluated an ensemble of CNN models that aggregates predictions from multiple independently trained models\.barkov2026moderndemonstrated that deep ensembles mitigate the inherent variability of individual artificial neural network training runs, thus allowing CNN performance to be assessed under the most favorable conditions\.

TabPFN \(Tabular Prior\-data Fitted Network\) is an in\-context learning foundation model for tabular data\(hollmann2025accurate;hollmann2023tabpfn\)\. TabPFN is pre\-trained once on a large collection of synthetic tabular tasks, learning to capture the interactions among features and observations of any given tabular dataset\. For a new dataset, TabPFN treats the labeled training data as a context \(a “context set”\) and predicts by relating each test observation to this context set, effectively learning “in\-context” entirely at prediction time\. Because of this, TabPFN requires no dataset\-specific training or hyperparameter optimization\. TabPFN has demonstrated strong performance on general tabular benchmarks\(grinsztajn2025tabpfn\)and state\-of\-the\-art results in pedometric modeling within DSM\(barkov2026modern\)\. In the present study, we investigated TabPFNv2\.5\(grinsztajn2025tabpfn\), which has been shown to natively handle datasets with up to 100,000 samples and 2,000 features\(erickson2025tabarena\)\.

#### 2\.2\.4Experimental setup

The performance of the regression models and dimensionality reduction approaches was evaluated using nested cross\-validation\(varma2006bias\)\. For both the LimeSoDa and OSSL datasets, 5\-fold outer cross\-validation was employed, with folds created by random splitting\. The same fold partitions were used across all model and dimensionality reduction configurations within each dataset\. Hyperparameters of each model were optimized within an inner validation loop\. When dimensionality reduction was applied, the number of retained components for PCA or latent variables for PLS was treated as an additional hyperparameter\. For the field\-scale LimeSoDa datasets, inner validation used 5\-fold cross\-validation\. For the large\-scale OSSL datasets, an inner holdout split \(20% of the outer training set\) was used instead to reduce computational cost\. Hyperparameters were optimized using Bayesian optimization with the Tree\-structured Parzen Estimator \(TPE\) algorithm\(bergstra2011algorithms\)as implemented in Optuna\(akiba2019optuna\)\. Further details on the hyperparameter search spaces and training configurations are provided in Appendix[B](https://arxiv.org/html/2608.00608#A2)\. All experiments were run on dedicated hardware, with linear regression, PLSR, and Cubist run on a single core of an AMD EPYC 7742 central processing unit \(CPU\), Random Forest on two AMD EPYC 7742 CPUs with trees parallelized across 128 cores, and CNN and TabPFN on an NVIDIA L40S 48 GB graphics processing unit \(GPU\)\. To support reproducibility, source code is provided openly, together with all software dependencies and their exact versions used in the experiments \(see[Code and data availability](https://arxiv.org/html/2608.00608#Sx1)\)\.

Predictive performance on each regression task was assessed using the root mean squared error \(RMSE\),

RMSE=1n​∑i=1n\(yi−y^i\)2,\\mathrm\{RMSE\}=\\sqrt\{\\frac\{1\}\{n\}\\sum\_\{i=1\}^\{n\}\(y\_\{i\}\-\\hat\{y\}\_\{i\}\)^\{2\}\},\(3\)whereyiy\_\{i\}andy^i\\hat\{y\}\_\{i\}denote the observed and predicted values for theii\-th test sample, andnnis the number of samples in the held\-out test fold\. RMSE was used both as the optimization objective during hyperparameter optimization and as the metric for assessing generalization on the outer test folds\.

Since the evaluated regression tasks involved soil properties with different scales and units, ranking based on RMSE was employed\(rosset2005rankingbased;nariya2023paired\)\. Mean and median ranks of different models and the dimensionality reduction configurations served as the primary measure of relative performance\.

## 3Results

![Refer to caption](https://arxiv.org/html/2608.00608v1/x5.png)Figure 5:Ranking of 14 model and dimensionality reduction configurations evaluated across 39 field\-scale regression tasks from the LimeSoDa dataset collection, showing: \(a\) mean ranks, and \(b\) distribution of ranks across tasks, with the large dot marking the median rank\. Ranking is based on RMSE\. Lower ranks indicate better predictive performance\.![Refer to caption](https://arxiv.org/html/2608.00608v1/x6.png)Figure 6:Ranking of 14 model and dimensionality reduction configurations evaluated across 46 regression tasks from the Open Soil Spectral Library \(OSSL\), showing: \(a\) mean ranks, and \(b\) distribution of ranks across tasks, with the large dot marking the median rank\. Ranking is based on RMSE\. Lower ranks indicate better predictive performance\.Results are reported separately for the 39 field\-scale LimeSoDa tasks and the 46 OSSL spectral library tasks\. Figures[5](https://arxiv.org/html/2608.00608#S3.F5)and[6](https://arxiv.org/html/2608.00608#S3.F6)summarize the mean and median ranks and rank distributions of the 14 model and dimensionality reduction combinations\. Across both dataset groups, a similar ordering of models and their variants emerged\.

TabPFN delivered the strongest performance overall\. On both LimeSoDa and OSSL, the three TabPFN variants outperformed all other configurations, with PLS TabPFN ranked first in both settings\. On the field\-scale datasets, the advantage of TabPFN variants over the remaining configurations was most evident, while on the large\-scale spectral library, performance across top\-ranking configurations was more comparable, yet TabPFN variants still achieved the best results\. Notably, even without a separate dimensionality reduction step, TabPFN achieved the best or near\-best results in both dataset groups\.

Cubist was the strongest classical baseline\. PLS Cubist ranked directly behind the TabPFN variants in both dataset groups and clearly improved over Cubist on full spectra and PCA Cubist\. CNN showed moderate performance overall, with better results on the large\-scale spectral library\. The CNN ensemble variant consistently outperformed a single CNN and showed a reduced spread of ranks overall, especially noticeable on the field\-scale datasets\. Random Forest did not perform competitively in either dataset group\. PLS latent variables as inputs improved Random Forest relative to full spectra and PCA components, but not sufficiently to close the gap to the best\-performing models\.

A consistent ordering was also observed among dimensionality reduction strategies\. PLS was the most effective strategy across both dataset groups\. PLSR was the best\-performing linear model and consistently outperformed both linear regression and PCR\. The benefit of PLS as a feature extraction method extended to the other models as well\. Using PLS latent variables instead of full spectra or PCA components improved Cubist, Random Forest, and TabPFN in most configurations\. PCA provided some improvement over full spectra, especially on the large\-scale spectral library, but compared to PLS these improvements were smaller and less consistent\.

Since ranks may obscure the magnitude of the differences between different approaches, we additionally report the relative RMSE difference of every configuration to the per\-task best model in Figure[A1](https://arxiv.org/html/2608.00608#A1.F1), Appendix[A](https://arxiv.org/html/2608.00608#A1)\. The relative results confirm the hierarchy observed in rankings: the top\-ranked TabPFN configurations consistently achieved the best or near\-best achievable RMSE, while the classical approaches showed much larger and more frequent gaps\.

Across all 85 regression tasks, the results point to a consistent and stable hierarchy of modeling approaches\. TabPFN was the strongest model family overall, PLS was the most effective dimensionality reduction method, and PLS Cubist was the strongest baseline outside the TabPFN family\.

![Refer to caption](https://arxiv.org/html/2608.00608v1/x7.png)Figure 7:Runtime scaling of the benchmarked models\. Left: full hyperparameter tuning plus final fit, as a function of training\-set size\. Right: prediction time as a function of test\-set size\. Axes are log–log\. Each point corresponds to one regression task, reported as the median wall\-clock time across its cross\-validation folds\. CNN and TabPFN were run on a GPU, while the remaining models were run on a CPU\.The wall\-clock training and prediction times for each evaluated regression task are shown in Figure[7](https://arxiv.org/html/2608.00608#S3.F7)\. The figure includes a selection of the best\-performing models in this study together with commonly used ones: PLSR, CNN, TabPFN, PLS TabPFN, and PLS Cubist\.

The left panel in Figure[7](https://arxiv.org/html/2608.00608#S3.F7)shows the median wall\-clock time for model training, including hyperparameter optimization\. Training time increased with the size of the training set for all models and configurations except TabPFN applied directly to the spectra\. Since TabPFN requires no hyperparameter optimization, its training included only a single model fit \(which, in TabPFN specifically, corresponds to just processing and caching the context set\)\. As a result, TabPFN had the lowest training time of all configurations, and it remained almost constant with respect to the training set size, only marginally increasing for the larger datasets\. Among the remaining models, PLS Cubist and CNN had the highest training times, reaching up to approximately 43 h and 20 h of median wall\-clock time per fold, respectively, on the largest tasks\.

The right panel in Figure[7](https://arxiv.org/html/2608.00608#S3.F7)shows the median wall\-clock time for predicting the test set, after the model with the best hyperparameters had been selected and fitted\. CNN, despite having one of the highest training times, predicted in well under a second even for the largest test sets, taking up to 10 ms on field\-scale and up to 679 ms on large\-scale datasets\. The same held for PLSR, with up to 959 µs \(below 1 ms\) on field\-scale and up to 371 ms on large\-scale datasets\. TabPFN, by contrast, showed noticeably higher prediction times that scaled with dataset size\. On field\-scale tasks its prediction time still remained below one second \(up to 917 ms median wall\-clock time across folds\), but on large\-scale tasks it grew substantially, reaching up to 24\.1 min\. Reducing the spectra to PLS latent variables lowered TabPFN prediction time by about 61% \(to up to 9\.6 min on the largest tasks\), while the scaling with dataset size persisted\. Interestingly, PLS Cubist showed prediction times of comparable magnitude to PLS TabPFN and scaled almost identically\. On the large\-scale library, the prediction times of TabPFN, PLS TabPFN, and PLS Cubist all grew approximately quadratically with test\-set size\.

## 4Discussion

Vis\-NIR and MIR spectroscopy holds great promise to make large\-scale physicochemical analysis faster, cheaper, and less laborious than traditional laboratory procedures\. The necessary step to turn this promise into practice is to develop robust and performant predictive models, motivating considerable interest in deep learning approaches\. Tabular foundation models, which preserve the advantages of deep learning while removing the burdens of dataset\-specific training and hyperparameter optimization, are thus a particularly welcome advancement and have already been speculated to become a default pedometric modeling choice even amid the complexities of spectroscopic data\(barkov2026modern;huang2026zeroshot\)\. Our results show that their benefits extend to large\-scale spectroscopy modeling, and open new paths toward further improvements\.

### 4\.1Do tabular foundation models scale to large soil spectral libraries?

In previous exploratory works,barkov2026modernandhuang2026zeroshotshowed that TabPFN delivers strong results for soil spectroscopy, withbarkov2026modernproposing it as a new default for field\-scale datasets andhuang2026zeroshottaking an initial step toward exploring how it scales further\. Nonetheless, the question of whether it would scale to large spectral libraries still stands\. This is a fair question, especially given the scale at which these models were first developed: prior\-data fitted networks were introduced on small synthetic tabular tasks of 100 observations\(muller2022transformers\), and the first version of TabPFN was trained and evaluated on datasets of only up to roughly 1,000 observations\(hollmann2023tabpfn\), bringing the common expectation that tabular foundation models are mostly constrained to settings with limited data availability\. Established deep learning approaches such as CNNs, by contrast, have shown great potential in soil spectroscopy, with their main limitation being poor performance on small sample sizes, which further calls into question whether changing the modeling approach to a tabular foundation model is necessary at all when large amounts of data are available\. In our study, however, TabPFN excelled across fundamentally different scales, including soil property prediction tasks involving tens of thousands of ground\-truth soil samples, extending recent DSM evidence beyond the field\-scale applications ofbarkov2026modernand the national soil spectral library examined byhuang2026zeroshot\. Such scalability did not happen by chance: scaling in\-context learning beyond small datasets was identified early on as both a practical need and a technical challenge, and became an important line of research\(qu2025tabicl\)\. TabPFNv2\.5 followed this path by scaling its synthetic pre\-training to substantially larger sample and feature counts and by implementing architectural decisions such as feature subsampling across underlying ensemble members\(grinsztajn2025tabpfn\)\. Tabular foundation models thus now appear to be a viable option for spectroscopic modeling across all operational scales\.

Moreover, the advances introduced in TabPFNv2\.5 move us toward modeling directly on the spectra, without the dimensionality reduction step previously proposed as a workaround for the feature\-size limits of earlier versions, both in soil spectroscopy\(barkov2026modern\)and in general tabular ML\(ye2025closer\)\. Practitioners can thus employ TabPFN on spectroscopic data with minimal preprocessing while still achieving state\-of\-the\-art predictive performance\. This also reframes the role of dimensionality reduction: rather than a workaround imposed by model constraints, strong dimensionality reduction can instead be employed deliberately and contextually to obtain better results, as we discuss next\.

### 4\.2On the role of PLS in soil spectroscopy

Although TabPFN applied directly to spectra already outperformed established modeling approaches, our results show that further consistent improvements remain attainable, most immediately through dimensionality reduction, with the strongest and most consistent gains coming from supervised, target\-aware PLS\. This is an intuitive insight: PLSR has persisted in soil spectroscopy for decades\(soriano\-disla2014performance;viscarrarossel2006visible;gyawali2025measuring;reyes2024spectral;pace2024soil\), and our findings suggest that the strength behind this longevity can be carried forward even as the field adopts tabular foundation models\.

PLSR was the strongest linear model across both dataset groups, consistent with its long track record, but more importantly, the advantages of its PLS decomposition extended well beyond PLSR itself\. Across Cubist, Random Forest, and TabPFN, pairing the regression model with extracted PLS latent variables consistently improved predictions relative to both full spectra and PCA components\. Combining this supervised feature extraction with TabPFN produced the overall best results in our study\. Ultimately, PLS proved to be an effective step for maximizing the capabilities of modern regression algorithms in soil spectroscopy\.

### 4\.3Does TabPFN shift the computational cost to the prediction step?

Besides showing the best predictive performance, TabPFN effectively eliminated the cost of model training\. As expected, this comes with trade\-offs at the prediction stage\. First, as an artificial neural network, TabPFN generally requires a GPU for optimal performance\. GPUs, being massively parallel processors, offer advantages such as efficient batch processing, but also present operational constraints in settings where such hardware is not readily available\. Second, although TabPFN removes the need for dataset\-specific training, it still requires a labeled context set of ground\-truth observations to make predictions\. This shifts the computational cost of modeling to the prediction stage, where it grows with the size of the dataset\. Most importantly, the attention mechanism in TabPFN incurs a computational complexity ofO​\(n2\+m2\)O\(n^\{2\}\+m^\{2\}\)with respect to sample sizennand feature countmm\(hollmann2025accurate\)\. Both terms are unfavorable when working with large spectroscopy libraries, as was directly reflected in the wall\-clock timings of our experiments \(Figure[7](https://arxiv.org/html/2608.00608#S3.F7)\)\.

However, placed in the context of models commonly used in soil spectroscopy, these costs appear neither critical nor unusual\. The reliance on a GPU is already common among deep learning approaches such as CNNs, and the scaling inference cost is likewise not unique to TabPFN\. Cubist, a long\-established model in soil spectroscopy, similarly showed near\-quadratic scaling of prediction time with test\-set size in our experiments\. This scaling is, of course, intuitive, and attributable to Cubist’s optional instance\-based nearest\-neighbor correction: for each test observation, Cubist locates the nearest training instances and adjusts the rule\-based prediction by the model’s residuals at those neighbors\(quinlan1992learning\)\. While this mechanism in Cubist aligns well with spectroscopy, where each observation carries a characteristic spectral signature and prediction by similarity to reference spectra is itself a long\-standing and effective strategy\(ramirez2013distance\), it ties prediction cost to the size of the training set, much like TabPFN’s reliance on a context set\. In our experiments, PLS Cubist and PLS TabPFN showed prediction times of comparable magnitude and similarly steep scaling: the high inference cost of high\-performing models in spectroscopy is not a new barrier introduced by tabular foundation models\.

Nevertheless, this higher inference cost is the principal trade\-off of current tabular foundation models, but several steps can already be taken to offset it\. An initial step, which we employ in this work, is to pair TabPFN with dimensionality reduction: projecting the spectra onto PLS latent variables directly targets the feature\-count \(m2m^\{2\}\) term of the complexity and, in our experiments, lowered TabPFN prediction time by about 61%\. Moreover, as tabular foundation models are still in their infancy, active research is rapidly addressing their inference cost in multiple directions\. More efficient architectures are being proposed, such as TabICLv2, achieving state\-of\-the\-art performance at a lower computational cost\(qu2026tabiclv2\), and more exploratory ideas even aim to remove the attention cost entirely\(tong2025mlps\)\. Whereas our approach reduces the feature\-count term, the sample\-count \(n2n^\{2\}\) term can be addressed in parallel, for instance by retrieving only the relevant local context\(thomas2024retrieval\)or by compressing the context into a compact, learnable form through parameter\-efficient fine\-tuning\(feuer2024tunetables\)\. Finally, in applications where inference latency is truly critical, TabPFN can act as a teacher to train a lightweight yet performant student model that predicts in milliseconds\(muller2023mothernet\)\. Taken together, the inference cost of tabular foundation models may seem high, but is already practically viable and set only to decrease further, making them a strong default choice for spectroscopy modeling\(barkov2026modern\)\.

### 4\.4Practical guidance, outlook, and future directions

Taken together, our results indicate that modern tabular foundation models such as TabPFN are a strong default choice for soil spectroscopy, even for large spectral libraries\. Applied directly to MIR or vis\-NIR spectra, TabPFN offers a simple yet highly performant baseline that requires minimal preprocessing and no dataset\-specific tuning\. When further improvements matter, drawing on the long\-standing strengths of PLSR through PLS TabPFN pushes predictive performance further\.

Several practical considerations should nonetheless be taken into account\. The most important is, as discussed above, the computational cost at inference time\. Although this cost remains practically viable, practitioners should remain mindful of it when working with very large datasets\. The choice of a dimensionality reduction strategy also carries practical implications\. PLS is target\-specific, so a specific projection must be fitted for each new soil property\. PCA, by contrast, is unsupervised, which makes it possible to incorporate spectroscopic measurements of soil samples that lack ground\-truth reference data, potentially improving feature extraction in scenarios where labeled samples are scarce but unlabeled spectra are abundant\. The choice between PLS, PCA, and full spectra ultimately depends on the operational context\.

While the dimensionality reduction methods investigated in this study were deliberately limited to PCA and PLS, other feature extraction techniques are also applicable in soil spectroscopy, such as independent component analysis for extracting statistically independent components\(rutledge2013independent\)\. Furthermore, PCA itself can be made more robust to outliers by deriving its eigenvalues and eigenvectors from robust estimators of the covariance or correlation matrix\(croux2000principal\), while PLS can be made more robust through downweighting outliers\(serneels2005partial\)\. Beyond feature extraction, dimensionality reduction can also be approached through feature selection, for example via sure independence screening\(fan2008sure\), recursive feature elimination\(eslamifar2025effective\), least absolute shrinkage and selection operator \(LASSO\)\(tibshirani1996regression\), or directly by applying chemometric domain knowledge of diagnostic absorption features\. Such strategies would be primarily attractive when the interpretability of individual spectral bands is required, and pairing them with modern tabular foundation models could be a promising direction for further investigation\.

Another important consideration is that, in our experimental setup, training and test samples were drawn from the same underlying population, corresponding to an independent and identically distributed \(IID\) evaluation\. Ensuring that a spectral library is representative of its intended prediction targets is, of course, a guiding requirement when building such libraries\(dorantes2022calibration\)\. In practice, however, many chemometric applications eventually face out\-of\-distribution \(OOD\) conditions: spectral libraries can fail to capture site\-specific variability\(dorantes2022calibration\), and models trained on a spectral library are sometimes applied to unseen sites and regions\(ng2022spike\)or to spectra acquired with different instruments and in different laboratories\(safanelli2023interlaboratory\)\. Because such distribution shifts are well known to degrade predictive performance\(e\.g\.,sun2026selfsupervised;hateffard2024evaluating\), whether the advantages of tabular foundation models observed here persist under OOD conditions requires further evaluation\. Early evidence from general tabular ML can provide an initial picture\. At sample sizes corresponding to field\-scale soil spectroscopy,purucker2026beyondfound tabular foundation models to be the leading model family even in the OOD setting\. At the larger sizes typical of global spectral libraries, however,purucker2026beyondshowed that this advantage narrowed: tabular foundation models ranked best on some aggregate metrics but were outperformed overall by ensembled variants of gradient\-boosted decision trees and multilayer perceptron\-based deep learning model RealMLP\(holzmueller2024realmlp\)\. We therefore regard a systematic OOD evaluation of tabular foundation models for soil spectroscopy as the most immediate extension of the present work\.

Looking ahead, the demonstrated effectiveness of tabular foundation models opens many concrete avenues for future research in spectroscopy and pedometrics\. One promising direction is uncertainty quantification: TabPFN can provide calibrated predictive distributions at no additional computational cost\(huang2026zeroshot;schmidinger2026kriging\), making uncertainty\-aware decision support a natural extension for spectroscopic applications\(schmidinger2026rejector\)\. Another opportunity lies in adapting the models themselves\. While the current paradigm of pre\-training on synthetic data already yields strong results, fine\-tuning on real\-world data can improve performance further\(garg2025realtabpfn\)\. Training tabular foundation models on real spectroscopic data could yield additional improvements and may eventually lead to spectroscopy\-specific or pedometrics\-specific foundation models\. Finally, practitioners should keep an eye on the rapidly evolving landscape of tabular foundation models more broadly\(e\.g\.,erickson2025tabarena\)\. During the preparation of this manuscript, further improvements were already introduced, including TabPFNv3\(grinsztajn2026tabpfn\)and TabICLv2\(qu2026tabiclv2\)\. TabICLv2 in particular may become a strong option for spectroscopic modeling owing to its open licensing, especially considering a potential shift of TabPFN toward a closed\-licensed software\-as\-a\-service model\. Overall, the benefits of tabular foundation models for soil spectroscopy are already evident, and with many avenues still left to explore, the field can be expected to advance considerably in the near future\.

## 5Conclusions

Tabular foundation models emerge as the best\-performing model family for soil property prediction from vis\-NIR and MIR spectroscopy\. Across 85 regression tasks from openly accessible field\-scale and large\-scale benchmark datasets, TabPFN consistently outperformed established approaches for spectroscopic pedometric modeling, including PLSR, Cubist, Random Forest, and CNN\. Importantly, this advantage extended to the large soil spectral library setting, where tasks involved tens of thousands of soil samples, thereby extending recent evidence for tabular foundation models in pedometrics beyond field\-scale DSM\. The best results were obtained with PLS TabPFN\. At the same time, TabPFN applied directly to full spectra already outperformed all classical baselines, showing that explicit dimensionality reduction is not strictly required for strong predictive performance in soil spectroscopy and offering practitioners a high\-performing workflow with minimal preprocessing\.

When opting for dimensionality reduction, the choice of strategy proved to matter\. Target\-aware dimensionality reduction achieved with PLS was most effective and consistently outperformed PCA across both field\-scale DSM and large soil spectral libraries\. This benefit was not limited to linear models, but extended to Cubist, Random Forest, and TabPFN\.

Among the conventional approaches, Cubist was the strongest overall baseline when paired with PLS, while PLSR remained the strongest linear model\. CNN showed moderate performance, benefited from larger datasets and ensembling, but ultimately did not surpass tabular foundation models\.

Taken together, our results provide straightforward guidance for pedometric practice\. We recommend tabular foundation models as the default modeling strategy for soil spectroscopy across operational scales\. When predictive accuracy is the main objective, pairing TabPFN with PLS latent variables could bring further improvements\. When a straightforward workflow is preferred, TabPFN on full spectra provides strong performance without dataset\-specific training or model\-specific hyperparameter optimization\. Overall, our results further position tabular foundation models as the strong default choice for soil spectroscopy within DSM\.

## Code and data availability

## Acknowledgements

This work was supported by the Lower Saxony Ministry of Science and Culture \(MWK\), via the zukunft\.niedersachsen program of the Volkswagen Foundation \(ZN4072\)\. Compute resources were supported by the Deutsche Forschungsgemeinschaft \(DFG, German Research Foundation\) project number 456666331\.

## Appendix ARelative performance across regression tasks

![Refer to caption](https://arxiv.org/html/2608.00608v1/x8.png)Figure A1:Relative performance of the 14 model and dimensionality reduction configurations on \(a\) the 39 field\-scale regression tasks from LimeSoDa and \(b\) the 46 large\-scale regression tasks from OSSL\. For each regression task, the RMSE of every configuration is expressed as the relative difference to the RMSE of the best\-performing configuration on that task \(x\-axis\)\. Lines show the percentage of regression tasks \(y\-axis\) on which a configuration falls within a given relative RMSE difference of the best model\. Lines toward the upper left indicate configurations that perform at or near the best achievable RMSE on most tasks\.Figure[A1](https://arxiv.org/html/2608.00608#A1.F1)visualizes the relative performance of all 14 model and dimensionality reduction configurations\. For each regression task, the RMSE of every configuration is expressed as its relative difference to the RMSE of the best\-performing configuration on that task\. Each line then shows the proportion of regression tasks on which a configuration stays within a given relative RMSE difference to the best model\.

On the field\-scale LimeSoDa datasets, PLS TabPFN showed the smallest mean relative gap to the best achievable RMSE \(5\.80%\), stayed within 10% of the best achievable RMSE on approximately 80% of the regression tasks, and within 20% on all but one of the 39 tasks\. TabPFN on full spectra reached a comparable median gap \(5\.21% compared to 5\.29% for PLS TabPFN\) but a wider spread, with a mean gap of 8\.18%\. PLS Cubist, the strongest classical baseline, showed a mean gap of 10\.53% and remained within 10% of the best model on approximately half \(48\.7%\) of the tasks\. On field\-scale data, the TabPFN variants thus not only ranked best, but also stayed consistently close to the best achievable RMSE, whereas even the strongest classical baseline was behind by a clear additional margin\.

On the OSSL, the separation between the best configurations and the remaining models was even more pronounced\. PLS TabPFN was the best configuration on nearly half of all tasks \(45\.7%\), with a median relative gap of only 0\.11% and an RMSE within 1% of the best on 71\.7% of tasks\. PCA TabPFN followed closely\. TabPFN on full spectra showed a higher mean gap \(10\.63%\) but still achieved RMSE within 10% of the best on 73\.9% of tasks, more often than any configuration outside the TabPFN family\. PLS Cubist remained competitive, with a mean gap of 8\.74% and results within 20% of the best achievable RMSE on nearly all tasks \(95\.7%\), yet achieved results close to the best achievable RMSE far less frequently than the TabPFN variants\. CNN and CNN ensemble visibly benefited from the larger training sizes, with CNN ensemble achieving a mean gap of 16\.21% and results within 20% of the best RMSE on 65\.2% of tasks, while PLSR fell far behind with a mean relative gap of 55\.03%, in contrast to its field\-scale results\.

## Appendix BHyperparameter optimization and training details

Table B1:Hyperparameter search spaces\. Curly brackets denote integer or categorical sampling\. Square brackets denote continuous uniform sampling\. Subscript “log” indicates log\-uniform sampling\.AlgorithmParameterLimeSoDaOSSLPCA / PLS / PLSRn\_components\{2,…,64\}\\\{2,\\dots,64\\\}\{2,…,200\}\\\{2,\\dots,200\\\}Random Forestmax\_depth\{3,…,30\}\\\{3,\\dots,30\\\}\{3,…,30\}\\\{3,\\dots,30\\\}min\_samples\_split\{2,…,10\}\\\{2,\\dots,10\\\}\{2,…,128\}\\\{2,\\dots,128\\\}min\_samples\_leaf\{1,…,10\}\\\{1,\\dots,10\\\}\{1,…,64\}\\\{1,\\dots,64\\\}max\_features\[0\.6,1\.0\]\[0\.6,\\,1\.0\]\[0\.6,1\.0\]\[0\.6,\\,1\.0\]max\_samples—\[0\.6,1\.0\]\[0\.6,\\,1\.0\]Cubistn\_committees\{1,…,20\}\\\{1,\\dots,20\\\}\{1,…,20\}†\\\{1,\\dots,20\\\}^\{\\dagger\}neighbors\{1,…,7\}\\\{1,\\dots,7\\\}\{1,…,7\}‡\\\{1,\\dots,7\\\}^\{\\ddagger\}CNNstart\_filters\{8,16,24,32\}\\\{8,16,24,32\\\}\{16,24,32,48,64\}\\\{16,24,32,48,64\\\}dropout\[0\.0,0\.3\]\[0\.0,\\,0\.3\]\[0\.0,0\.3\]\[0\.0,\\,0\.3\]learning\_rate\[10−4,5×10−3\]log\[10^\{\-4\},\\,5\{\\times\}10^\{\-3\}\]\_\{\\log\}\[10−4,5×10−3\]log\[10^\{\-4\},\\,5\{\\times\}10^\{\-3\}\]\_\{\\log\}weight\_decay\[10−6,10−2\]log\[10^\{\-6\},\\,10^\{\-2\}\]\_\{\\log\}\[10−6,10−2\]log\[10^\{\-6\},\\,10^\{\-2\}\]\_\{\\log\}batch\_size\{4,8,16,32\}\\\{4,8,16,32\\\}300300†\{1,5,10,15,20\}\\\{1,5,10,15,20\\\}when trained on full spectra\.‡\{1,3,5,7\}\\\{1,3,5,7\\\}when trained on full spectra\.Table[B1](https://arxiv.org/html/2608.00608#A2.T1)reports the hyperparameter search spaces for each model and dataset group\. When PCA or PLS was employed as a dimensionality reduction step, the number of retained components was optimized jointly with the model\-specific hyperparameters\. Bayesian optimization used 100 TPE trials with 20 random startup trials and multivariate kernel fitting\. For Cubist trained on full spectra on the OSSL datasets, exhaustive grid search over the listed parameter combinations was used instead of TPE due to high computational demands\. Random Forest was trained with 1,000 trees in all configurations\. The CNN implementation followed the reference implementation ofhuang2025usingand was trained using the Adam optimizer for up to 500 epochs, with early stopping \(patience of 60 epochs\) and learning rate reduction on plateau \(patience of 50 epochs\)\. For the CNN ensemble, 16 models were trained independently with different random initializations and batch ordering using the same optimized hyperparameters, and their predictions were averaged\. TabPFN required no model\-specific hyperparameter optimization\.

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