No Location Left Behind: Measuring and Improving the Fairness of Implicit Representations for Earth Data
Authors: Daniel Cai
Randall Balestriero
Venue: ICLR 2025 Poster (2025)
Keywords: implicit neural representations
dataset
fairness in AI
representation learning
geospatial modeling
Earth representation
wavelet
location encoding
Primary area: datasets and benchmarks

Abstract: Implicit neural representations (INRs) exhibit growing promise in addressing Earth representation challenges, ranging from emissions monitoring to climate modeling. However, existing methods disproportionately prioritize global average performance, whereas practitioners require fine-grained insights to understand biases and variations in these models. To bridge this gap, we introduce FAIR-Earth: a first-of-its-kind dataset explicitly crafted to challenge and examine inequities in Earth representations. FAIR-Earth comprises various high-resolution Earth signals, and uniquely aggregates extensive metadata along stratifications like landmass size and population density to assess the fairness of models. Evaluating state-of-the-art INRs across the various modalities of FAIR-Earth, we uncover striking performance disparities. Certain subgroups, especially those associated with high-frequency signals (e.g., islands, coastlines), are consistently poorly modeled by existing methods. In response, we propose spherical wavelet encodings, building on previous spatial encoding research for INRs. Leveraging the multi-resolution analysis capabilities of wavelets, our encodings yield more consistent performance over various scales and locations, offering more accurate and robust representations of the biased subgroups. These open-source contributions represent a crucial step towards facilitating the equitable assessment and deployment of implicit Earth representations.

Published as a conference paper at ICLR 2025
No LOCATION LEFT BEHIND: MEASURING AND IM- PROVING THE FAIRNESS OF IMPLICIT REPRESENTA- TIONS FOR EARTH DATA
Daniel Cai, Randall Balestriero Department of Computer Science Brown University
ABSTRACT
Implicit neural representations (INRs) exhibit growing promise in addressing Earth representation challenges, ranging from emissions monitoring to climate modeling. However, existing methods disproportionately prioritize global av- erage performance, whereas practitioners require fine-grained insights to under- stand biases and variations in these models. To bridge this gap, we introduce dataset explicitly crafted to examine and chal- lenge incquities in Earth representations. FAIR-EARTH comprises various high- resolution Earth signals and uniquely aggregates extensive metadata along stratifi- cations like landmass size and population density to assess the fairness of models. Evaluating state-of-the-art INRs across the various modalities of FAIR-EARTH, we uncover striking performance disparities. Certain subgroups, especially those associated with high-frequency signals (e.g.. islands, coastlines), are consistently poorly modeled by existing methods. In response, encodings, building on previous spatial encoding research. Leveraging the multi- resolution capabilities of wavelets, our encodings yield consistent performance over various scales and locations, offering more accurate and robust represen- tations of the biased subgroups. These open-source contribution represent a crucial step towards the equitable assessment and deployment of Earth INRs.
FAIR-EARTH: a first-of-its-kie
propose spherical wavelet
1.0
Prodiction Error
Figure 1: Heatmap of the spatial distribution of approximation errors using existing INRs to model land-sea data of the Earth. Leveraging the resolution of FAIR-EARTH, we uncover clear bias against islands, where error magnitude significantly higher. Against the task, SPHERICAL WAVELETS resolves these issues by reconciling global signals with fine and localized signals. Details and plots available Appendix A.3
Available part of the FAIR-EARTH package gi rtchub..cm/raccccnncaaa 448/FA IREa

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INTRODUCTION
Implicit neural representations (INRs) have experienced a rapid surge in popularity since the ground- breaking work of Mildenhall et al. (2020) first demonstrated their effectiveness in mapping com- plex 3D scenes to continuous functions. Fundamentally, early INRs were formulated as a function So X + Y with sinusoidal activation and weights 0, where X is typically a coordinate space and Y is the target space (Sitzmann al. 2020). The key enabling feature of this representation was the continuous support of fe. yielding resolution-independentt representations.
In recent years, the versatility and advantages INRs have made them increasingly attractive across diverse fields (Molaei et al., 2023) Chen et al. 2023 RuBwurm et al. 2024). Unlike traditional dis- crete methods, INRs are essentially infinite-resolune resolution models, enabling them to effectively handle signal- processin tasks involving sharp discontinuities
high variance features (Xu et al.) (022)).
Furthermore, they naturally excel in scenarios requiring differentiable representations, facilitatinn litating tasks such gradient-basedd optimization in physics-informed machine learning (Raissi al. 2017)- The compact and flexible parameterization of INRs also offers substantial memory savings com- pared to grid-based methods, a critical consideration for any practitioner working with resource constraints (Liu et al. 2024).
More recently, INRs have made notable strides in Earth science applications, with transformative po- tential for pressing tasks such as climate modeling and environmental monitoring (RuBwurm et al., 2024 Grama et al., 202I). While existing methods span various techniques such as observation- based networks (Palecki et al. 2013), satellite-based remote sensing (Sorooshian et al. 2014). and more recently, computer- based climate simulations (Geneva and Foster] (024)), these methods suffer from some combination of discretization error, data inconsistency, and resource-intensive inference (Allen et al.] 2002). In contrast, the ability of INRs to learn nonparametric models from arbitrarily nigh-resolution, multi-modal data presents efficient and promising alternative. Specifically, the use of INRs to learn the underlying dynamics of explicitly geospatial data has rapidly garnered interest (Cole et al.; 2023). These methods encode the generative process and representation of the data through an implicit function, typically a Deep Neural Network (DNN), that maps spatial coordinates data realizations (Hillier al. 2023).
However, as INRs transition into these realms of Earth science application, is imperative to thor- oughly evaluate the fairness and potential biases of these models. Skewed or unfair models in this domain can have far-reaching consequences, potentially amplifying existing societal inequalities or misallocating resources in vulnerable communities (Munday and Washington, 20188, Flores et al.] 2022). For instance, two concrete instances of modeling bias in the Earth science and INR domains underscore the critical importance of fairness considerations:
Federal Emergency Management Agency (FEMA) flood maps, which rely on an ensem- ble of machine learning models for risk assessment, have been shown systematically underestimate flood risk in lower-income neighborhoods (Flores et al. 2022)
Global climate models, including those used the Coupled Model Intercomparison Project (CMIP), exhibit systematic errors in simulating precipitation patterns over Africa, consis- tently overestimating precipitation in southern regions while underestimating it in central regions (Munday and Washington 2018).
While such fairness concerns should evidently be top-of-mind, as of writing, there exist no system- atic datasets to target such biases for implicit Earth representations. Hence, we introduce the first- of-its-kind FAIR-EARTH (Fairness Assessment for Implicit Representations of Earth Data) dataset, comprehensive framework for evaluating and mitigating biases of implicit Earth representations.
comprises a diverse set of benchmark datasets representing wide spectrum of Earth science signals, from global precipitation to carbon emissions (Section 3.2) Uniquely, it also includes a suite of methodologies and metadata designed to quantify disparities in model performance across different stratifications, setting it apart from existing datasets (Ta- ble 7). In essence, FAIR-EARTH unifies disparate existing geospatial datasets under a consistent framework, enriched with extensive metadata spanning fields such geographical features (e.g., islands, coastlines), demographic information (c.g., population density) and geopolitical boundaries (e.g., country divisions).
Contribution 1:
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pip install fairearth
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fre swart add delesell dew.eaate"" (etaftotole())
trinwork train) my,noeel', "yy_eetaeet', contig)
model franevork. Load, www.trrddddnd........ nadel(conffg expertaent subgroup_resatte pits
wwwpurkccoststteeoooooo 'ey_dataset', Visualize-True)
RESOLUTION
5000
10000
15000
TOTAL
0.16
0.13 1 0.03
0.12 0.03
LAND
0.21
0.15 2: 0.04
0.14 + 0.05
SEA
0.11
0.16
0.02
0.09 0.03
2.04
COASTLINE
1.06 0:6:1:00 0.08
1.00
0.06
0.95 0.05
Figure 2: FAIR-EARTH is the first Earth wrr-rraewoork for fairness assessment, and moreover is open-source package that allows for agile testing and analysis of subgroup-level performance.
Extensive experiments against FAIR-FARTH reveal significant disparities the performance of state-of-the-art INR methods across different subgroups (Section 4.Tp. In particular, our analysis uncovers a strong negative correlation between landmass size and representation loss, with areas corresponding to localized signals and high-frequency features exhibiting consistently poor perfor- mance (Fig.
To address these fairesss issues, we build upon recent research into location encodings, which aim to simplify downstream Earth representation tasks by transforming the input into more learning- friendly format. Previous work in this domain (Rußwurm al.. 2024) has focused on improving location encodings via decomposition onto the harmonic domain. While these Fourier-inspired ap- proaches have demonstrated improvements in global accuracy and longitudinal consistency, our empirical results show that the global support of Fourier bases introduces biases against localized signals, compromising more fine-scaled geographic representations (Fig.
Contribution 2: With these limitations in mind, we propose SPIERICAL WAVELETS (SW), novel encoding mechanism grounded in existing research the wavelet domain (Section 4.2). By ex- plicitly modeling geospatial phenomena multiple scales, SPHERICAL WAVELETS enable efficient and accurate modeling of regions with highly localized signals (Fig. 19). Our approach is motivated by the inherent multi-scale nature of Earth systems, and allows for more equitable representation across diverse geographical contexts. Against the FAIR-EARTH framework, we demonstrate that our encodings significantly reduce performance disparities compared existing methods, paving the way for fairer Earth science applications (Fig. 6).
We summarize our contributions below, which we hope will pave the way towards more fair and equitable implicit Earth representations:
We introduce FAIR-EARTH comprehensive framework for assessing faimesss of implicit Earth representations across multiple modalities, enabling users to perform any fine-grained faimess study as required by their application (Section 3.2).
We perform thorough fairness evaluation of current INR frameworks against FAIR- EARTH. We discover significant subgroup disparities current state-of-the-art INR meth-
ods (Section 4.1).
We propose spherical wavelet encodings for INRs, motivated by the shortcomings of exist- ing INRs when dealing with multi multi-resolution data. Against FAIR-EARTTH we demonstrate competitive performance while significantly mitigating per-group biases (Section 4.3
BACKGROUND
Fairness of Implicit Neural Representations Recent work has shown that optimizing solely for average test performance can have detrimental effects on sub-group performance in natural image classification tasks (Balestriero et al., 2022; Kirichenko et al.) 2023). These findings raise natural concerns about potential faimess issues in implicit neural representations (INRs), particularly in the context of Earth data. For example, algorithms fine-tuned to low wwwffreuencyy global signals may fluctuations, potentially leading to biased representations. However, to the best of our knowledge, systematic study of fairness in INRs for Earth data has yet be conducted.
overlook
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CARTESIAN3D (b) THEORY (Mai et al. GRID AND SPHERE (d) SPHERICAL HAR-
Tseng al. 2022)
2020
Mai el al. 2023
MONIC (Rubwurm al.
2024
Figure 3: Visualization of existing encoding mechanisms.
We focus on the work by Rubwwrr et al. (2024), which set statc-of-the-ar benchmark performance by decomposing positional information onto spherical harmonic basis functions and integrating these encodings with SirenNets (Sitzmann et al. (020). The core contribution is the representation of Earth data as continuous signals on the globe f (A, Φ) + IR, where and e denote longitude and latitude, respectively. For well-behaved functions with exponential decay of their eigenvalues, the signal can be precisely recovered using the following decomposition:
S(A
w Y1" Ø),
I=0 mmm
where Y is the class of spherical harmonic functions, w are learnable scalar weights, and and the degree and order of the basis function Y," Both as a practice and necessity (Fig. [7]. an upper bound on is imposed, restricting the embedding size to 12 and capping the representable frequency.
Location Encodings for INRs The work in Rußwurm et al. (2024) notably represents significant advancement in the task of constructing proper location encodings for implicit Earth representations. In a general sense, location encodings can be viewed as a simpler alternative to embeddings, familiar concept in natural language or multimodal learning fields. Like embeddings, encodings play crucial role in transforming the complex task of learning the distribution ((y/x) into simpler task P)y)x*, where is the location, y is the predictive task, and x the location encoding (Mai
ct al. 2022).
Early location encodings leveraged Gaussian processes and kernel methods (Mai et al. 2022). while more recent approaches have improved performance even with simpler mappings like DIRECT ((ő. A) F (o, A)) and CARTESIAN3D ((0, A) + (æ, y, 2)). As datasets have grown in dimensional- ity, the field has built upon variants of GRID/THEORY embeddings, which involve simple interaction terms between sine and and cosine functions on the globe. Notable examples include the GRID AND SPHERE family of encodings (SPHEREC+ and SPHEREM+) which generalizes and combines these previous encodings (Mai et al. (2023)). More recently, as INRs have gained popularity, the focus has shifted towards more complex periodic representations of geospatial data, as exemplified by the harmonic-based encodings in Rullwurm et al. (2024).
However, these global decomposition methods (Table may not be accurate or efficient for common natural signals across the globe (Fig. B). Fourier and harmonic- ceamonic-based methods are especially known alias in localized, sharp, or discontinuous portions of the signal (Mallat 1999). which intuitively can lead to biased representations of important Earth features.
Measuring Fairness As described, the global approach adopted by many existing implicit Earth representations is problematic when dealing with naturally localized or discontinuous signals. Be- fore attempting to mitigate these biases, it is crucial for practitioners to understand their nature and extent. More specifically, there is a pressing need to quantify the trade-off's in per-group perfor- mance of existing models (Garcia-Siie Silva et al. 2018). This emphasis on group-specific performance is not merely an academic exercise but is driven by practical considerations: for tasks like natural disaster risk assessment where consequences are severe, there is a natural emphasis on improving worst-case performance rather than average-case metrics (Kemp et al. 2022
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An ideal framework for measuring fairness in Earth representations should encompass several key components: consistent high-resolution data for uniform assessment, multi-modal integration to reflect various Earth systems, and standardized faimess metrics to quantify biases along various themes. By developing such a comprehensive framework, the implicit learning and Earth science communities work towards constructing more equitable models, aligning themselves with the growing emphasis on fairness and accountability in Al systems.
FAIR-EARTH: ALL-IN-ONE EVALUATION LIBRARY FOR EARTH DATA
The introduction of FAIR-EARTH, the first-of-its-kin dataset to target per-group performance, is highly motivated by both the natural tendencies of geospatial data and the well-studied biases of existing INRs. We first examine the specific inadequacies of existing datasets, and then outline the main contributions of the
dataset.
3.1 THE NEED FOR A FAIRNESS DATASET
The current landscape of Earth system datasets is not well-suited for the nuanced analyses described earlier. Commonly used datasets and benchmarks suffer from inherent limitations that can introduce exacerbate biases. We point to concrete examples below.
The Shuttle Radar Topography Mission (SRTM) land elevation model, despite its widespread use, suffers significant data gaps and inconsistencies in areas with steep terrain dense vegetation (NASA Shuttle Radar Topography Mission 2013). These gaps can lead to skewed representations of topographical features, potentially affecting critical applications such flood risk assessment or infrastructure planning in vulnerable areas.
The Visible Infrared Imaging Radiometer Suite (VIIRS) nighttime lights dataset, often employed as a proxy for economic activity and urbanization, has limitations in detecting low levels of light emissions (Murphy al. 2006). This shortcoming may underestimate activity rural or underde- veloped areas, reinforcing existing biases in policy decisions.
These examples underscore a critical gap in the field: while existing datasets and Earth system models are clearly at risk of exhibiting biases across different stratifications, there is no established framework specifically designed to quantify these biases.
3.2 PROPOSED EVALUATION DATASET
To mitigate the limitations of some data sources highlighted in Section 3.1 FAIR-EARTH is based around several clean, accessible, and interpretable data modalities. Additionally, we collect a com- prehensive suite of metadata to assess biases that may arise from both the data and representation model; this metadata lays the crucial groundwork for our novel fairness assessment of implicit Earth representations.
Land-Sea Boundaries. Based on NASA's Integrated Multi-satellitE Retrievals for GPM (IMERG) dataset (Huffman al., (2014), this component contains (Fig. 7) coarse signals like continental land- masses while also providing high-resolution boundaries for fine-grained signals such as islands and coastlines.
CO2 Emissions. Using data primarily from NASA's Orbiting Carbon Observatory-2 (OCO-2) satellite. this component provides ultra fine-graing grained and precise information into carbon emissions (OCO-2 Science Team/ Gunson, Annmarie Eldering 2020 Dell et al. 20188 Taylor et al.) 2023). OCO-2
second high-precision CO2 satellite, and inaccuracies due to reflectance or cloud cover are mitigated via data assimilation. This high-resolution emissions data (Fig. [3) is crucial for environmental justice applications, for instance enabling researchers to identify localized pollution hotspots, investigate correlations between emissions patterns and health disparities.
Precipitation and Temperature. Derived from the CHELSA (Krgerr et al., 2017 dataset, this component provides assortment of coarse and ultra fine- grained signals, well as high resolution along the time dimension (Fig. [0)). This temporal granularity allows for analysis of both long-term climate trends and short-term weather patterns.
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Population Density. Leveraging the Gridded Population of the World, Version 4 (GPWv4) popu- lation dataset (Center for International Earth Science Information Network CIESIN Columbia University 2018b), which integrates censuses, population registers, and spatial distributions, synthesize population density data for each point in the grid (Fig. 12
We emphasize FAIR-EARTE a unified framework. All data sampled and projected onto a uni- form 0.1% 0.1% grid, state-of-the-ard resolution for fine-grained analysis. Moreover, we propose attributes and metadata including landmass size, coast distance, and population density for each location, enabling us to disentangle the global prediction performance into meaningful subgroups (data specifications available in Appendix [..nddxxAAIlaaaaa and Appendix A.I].. In particular, our metadata com- prises two main subgroups. First, geographical features are composed: based on combination of existing data and ad-hoc definitions (Appendix A.I). we label relevant subgroups including is- lands, coastlines (stratified by distance), land, and sea. Additionally, we incorporate metadata on population density and administrative boundaries.
While core geospatial data is derived from existing datasets, we highlight the differences between FAIR-EART and existing stand-alone datasets (Table (7). Unlike datasets such as NaturalEarth (Nat) that emphasize geographic features, we combine multiple dimensions of data (environmental, demographie, and emissions) within one integrated format, allowing practitioners to model and assess the interdependence of multiple modalities. In contrast to existing climate datasets such as ERA5 (Hersbach al.,) (199), environmental signals incorporate interconnected emissions data and metadata, crucial for nuanced investigation of environmental justice issues.
3.3 EARTH LIMITATIONS
While the design choices for BAIRTEARTH facilitate subgroup-level faimess evaluations, they also yield certain tradeoffs. In particular, temporal and polar biases may manifest from the gridded format of FAIR-EARTH data; we later discover (4.3) that this format indeed induces bias in the training data. Given the agile framework of FAIR-EARTH, we strongly encourage practitioners to evaluate and incorporate their own datasets when necessary, and to adopt best practices in sampling to mitigate such biases.
4 MEASURING AND IMPROVING THE FARNFAIRNESS OF IMPLICIT NEURAL REPRESENTATIONS
4.1 EVALUATION OF EXISTING REPRESENTATIONS
Global Performance is not Representative of Local Performance To properly understand the behavior of existing INRs, depart from hyperparameter fine-tuning, and instead perform exten- sive training over a cross-product of each model's 's hyperparameter space. This allows us to move past "best-case" analysis, and instead incorporate nuanced analysis of model tradeoffs. Moreover, as downstream tasks often require further tuning regardless, it is natural to instead consider the overall behavior of the implicit representation. Experimental details are available in Appendix (A.2 A.2
In particular, we explore the correlations of subgroup performance. While certain disparities in performance are intrinsic the task (e.g., islands and coastlines exhibit higher representation loss as land-sea boundaries are harder to learn than constant signals), fair model should in general show concurrent improvement in subgroups. Leveraging the metadata in representation performance between areas that correspond to local signals (e.g.. islands) and ones that correspond to global signals (e-g., large landmasses).
we compare
Strikingly, our correlation analysis indicates stark disparity in representation loss between global and local groups among all state-of-the-art encodings Aoppendix[A.4. Section[4.1] I). For SPHERICAL HARMONICS, notice a strong negative correlation between land and island loss when stratified along training resolution (Section 4.1), suggesting that when optimized for total loss, state-of of the art INRs exhibit clear tradeoff between global and local performance. Regardless of stratification, INRs the form Eq. ( appear incapable of competitive performance across all subgroups at once (Table 2

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Table 1: Land-island performance correlations across encodings and training resolutions. While existing encodings compromise local-global performance, SPHERICAL WAVELET reconciles im- provement over multi-scale features. We omit SPHEREC+ due to abnormally high bias.
Pearson Correlation (R)
Training Samples
SW (Ours)
SH
THEORY
5000
0.51
-0.73
-0.53
10000
0.42
-0.88
-0.62
15000
0.04
-0.88
-0.10
20000
0.31
-0.68
-0.28
a) High regularization implies low resolution
b) Low regularization implies aliasing
Figure 4: Model behavior at different resolutions and regularizations. Smaller models fail to capture fine/local signals. Larger models poorly reconcile local signals with existing global signals.
Aliasing as a Result of Overfitting As described earlier, Eq. is global in nature. We observe the implications of this construction in Fig. 4 where the smoothness of land and sea signals are compromised in an effort to represent islands and coastlines. We corroborate this observation with an ablation over encoding size, which shows increasing encoding size results in plateauing land performance and deteriorating island performance (Fig. 21).
Concretely, the observed aliasing in the high-resolution case is indicative of the Gibbs phenomenon, exhibiting unnatural oscillations around the island and coastline 'discontinuities' (Dyke and Dyke 2001]. In the effort to precisely fit the islands, Eq. is forced learn unnatural representation of the land and sea masses.
Our correlation analysis and aliasing investigation confirms that SPHERICAL. HARMONIC-based model able to maintain competitive performance in both sub-groups simultaneously. suggesting that current solutions in implicit Earth representations require further development reach truly equitable predictions.
Biases Across Multiple Modalities and Subgroups While the land-sea binary classification task reveals natural biases against fine and localized areas, we emphasize that one of FAIR-EARTHT main strengths is in its ability to easily quantify subgroup disparities across multiple modalities. In particular, we perform similar stratified evaluation against FAIR-EARTII' benchmarks for environ- mental signals. For the surface temperature dataset, which exhibits similar sharp variations across recognizable boundaries, we note similar trends (Fig. 5) Namely, FAIR- EARTH reveals systematic patterns in representation quality: regions with sharper variations, particularly near the coast, show significantly higher average representation loss (MSE)and = 0.87, MSE MSEcamm 0.101) compared to regions with smoother variations (MSEs.a 0.43, MSE 0.49) (Table 14
Moreover, this analysis extends naturally to downstream biases through EARTH'S rich meta- data. At the country level, observe that representation challenges at the feature level manifest as systematic performance disparities. For instance, SPHERICAL HARMONIC and THEORY encodings particularly struggle with to demarcate the Spain's 's fine Mediterranean coastline, while all studied encodings show degraded performance in coastal countries due to sharp temperature gradients at land-sea boundaries (15)
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a) Predictions Results
b) (Binned) Error Plot
Figure 5: Qualitative performance of SPHERICAL HARMONIC on surface temperature regression task. SH exhibit bias against high-frequency details, with loss concentrated in areas of abrupt change (e.g., coastlines).
4.2 SPHERICAL WAVELETS FOR FAIR EARTH REPRESENTATIONS
As explored in Section 2 major limitation of SPHERICAL HARMONIC was their global support, which struggled to reconcile localized signals with global ones. In particular, SH required large amount of basis functions to properly represent localized signals, and this excessive parameterization resulted in aliasing in other regions. The ad-hoc solution involving re-weighting subgroups depends on extensive labels; moreover, the effect on global performance is unknown (Stone et al. 2024).
To this end, we are motivated to leverage the theoretical guarantees of wavelets, which allow for multi-scale resolution analysis of signals, efficiently representing signals at various scales and loca- tions. To extend towards Earth data, we refer to past work in Demanet and Vandergheynst (2003) that introduces spherical wavelet basis functions. Similar to the formulation in Eq. (L), any func- tion the sphere also be approximated by discrete sum of wavelet basis functions, where coefficients are similarly learned via the INR mechanism.
The following sections briefly outline the construction of novel encoding mechanism SPHERICAL WAVELET, and its seamless integration into the currently studied INR pipeline. We direct interested readers towards McEwwn et al. (2007); Demanet and Vandergheynst (003) for analysis on the cor- rectness of the construction, and towards A.5 for evidence that SW encodings are surprisingly more efficient and stable than their SH counterparts.
Spherical Morlet Wavelet via Inverse Projection A concise, computationally tractable construc- tion for spherical wavelets arises from inverse stereographic projection of Euclidean wavelets (De- manet and Vandergheynst 2003). We note that due to the nature of this projection, the SPHERICAL WAVELET ill-defined at the poles.
As proven in Sanz et al. (2006). this inverse stereographic projection II of an admissible Euclidean wavelet yields an admissible spherical wavelet; that is, the projected wavelet (00 sp) satisfies the necessary zero-mean condition (Demanet and Vandergheynst 2003). Empirically, we find that the Morlet mother wavelet shows consistently superior performance (Fig. (5). Thus, applying the in- verse projection onto the 2D Morlet wavelet with width factor and wave number w, A yields the admissible spherical Morlet mother wavelet:
e (0/() cos(c)) (1/2) tan? (0/22)
WM (0, Φ) __
1 + cos 0
Lifting Scheme From an admissible mother wavelet, we can construct wavelet basis from affine transformation on the sphere. Analogous to time-frequency localization of Euclidean wavelets, spherical wavelets provide rotation-dilation localization. The rotation operator R(p) = R(a, 3, 7) and dilation operator D(a) both transport a function from and into J & L22 dp((, o)); refer to [cEEwen et al. (2007) for rigid formulation. Applying these transformations, then define a set of orthogonal basis functions {Maap = ((a))())
Finally, we discretize the reconstruction formula. First, we deterministically distribute p across N points on the sphere following the Fibonacci lattice Fx (González 2009). To discretize rotation, we take (2 0 i < M), where Q < 8 is fixed value (Mallat 1999b. This yields embedding
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a) SPHERICAL HARMONIC
b) SPHERICAL WAVELET
Figure 6: Comparisons of SPHERICAL HARMONIC and SPHERICAL WAVELET behavior in local-
ized regions. Full figures available in Fig. and and Fig. T9
size on the order of O(NM), and the discretized approximation
M
f(0, N.M =
Σ PEFN
wap (0..0
Localization Properties The spherical Morlet wavelet, by design, exhibits dual localization in both dilation and rotation, offering significant ad advantages in signal representation on the sphere (McEwen al. 2007). These properties enable more nuanced and adaptive analysis of spherical data. In
particular, the parameterization of the Morlet variant is parameterized is illustrated in Fig. 23
4.3 SPHERICAL WAVELET EXPERIMENTS
SPHERICAL WAVELET Corrects Localized Biases To examine the biases present, we begin by analyzing the trends in training and evaluation. In particular, leverage FAIR- and deploy a large cross-product of parameters (N 984) to cross-validate algorithm performance between local signals and global signals various configurations. As baseline, compare to results to SPPHERICAL HARMONIC, THEORY, and GRID AND SPIERE] encodings trained under identical settings, therefore isolating the effects of the encodings.
We observe a sharp contrast between the local-global correlation of our encodings; that is, SPHER- ICAL WAVELET learns to efficiently represent islands even at coarser resolution, therefore inducing a positive trend between global (land) and localized (island) performance, whereas our baseline en- codings exhibit tradeoff between global/local performance even for finer resolutions Section 4.
Specifically, in contrast to SPHERICAL HARMONIC, where finer features are often blended together (Fig. D.. SPHERICAL WAVELET has significantly higher resolvable resolution for similar parameter counts. Especially in localized areas such as islands, our encodings tend to produce sharper, more fine boundaries compared to spherical harmonic encodings (Fig.
SPHERICAL WAVELET is Competitive with Existing Methods While correlation analysis showed performance of SPHERICAL WAVELET exhibited fair and stable trends, we also seek to show performance is competitive with existing methods. First, re-examine the previous experiment and compare general global performance SPHERICAL WAVELET and SPHERICAL HARMONIC across well-defined hyperparameter spaces.

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Table 2: Comparison of best/average cross-entropy loss between SH and SW over land-sea cross-validation. Top encodings per stratification are bolded.
Samples
SPHERICAL WAVELET
SPHERICAL HARMONIC
5000
0.1404 0.1473
0.1392 02992/0.110 0.1524
10000
0.1111 0.1169
0.1137 0.1218
15000
0.1000 0.1056
0.1003 0.1086
20000
0.0912 0.0962
0.0892 0.0969
In general, we observe that the learned representation is similar to that of spherical harmonics, as indicated by the visual similarities in their learned representations (Fig. (). However, SW in fact exhibits competitive superior performance over SH through various training resolutions: we maintain significantly superior average performance across all training resolutions (Table
The degradation in performance for SPHERICAL WAVELET for higher resolutions may be attributed to the misspecifications of certain parameters in model (e.g. To this end, we also evaluate fine-tuned performance on the temperature and precipitation regres- sion tasks, observing more consistent performance: when properly parameterized, SPHERICAL WAVELET performs roughly on par with SPHERICAL HARMONIC encodings across all FAIR- EARTH tasks (Appendix(As A.4 A.4
number, scaling factors).
SPHERICAL WAVELET TradeofI's While SPHERICAL WAVELET demonstrates robust perfor- mance across various tasks, like all signal- based methods, it faces certain limitations. We investigate these limitations using two challenging external datasets:
On the checkerboard classification task RuBwurm et al. 2004 which features coarse, single-scale signals, SPHERICAL WAVELET performs well relative most baselines but consistently falls short of SPHERICAL HARMONIC. This suggests that the wavelet decom- position may introduce unnecessary complexity for simple, single-scale tasks.
In the land-sea classification task Rußwurm et al. (2024), which uses non-gridded, ul- tra high-resolution data, SPHERICAL WAVELET only marginally outperforms SPHERICAL HARMONIC. Our latitudinal analysis (Fig. 22) reveals that this limited improvement stems
primarily from degraded performance near the poles.
5 CONCLUSION
Measuring the fairness implicit Earth representations is pressing yet lacking field both the Earth science and implicit representation fields. Our contributions in measuring and improving certain bi- ases in state-of-the-art INRs represents a step forward in this important direction. By introducing FAIR-EARTH, novel framework for high-resolution assessment of subgroup-level performance, we aim to develop and assess models pertinent to the needs of practitioners, informing of existing biases and limitations of Earth models. Leveraging this new framework, our comprehensive assess- ment uncovers striking biases against certain subgroups across tftte-of-thh-arr INRs. Based on these observed performance disparities, we propose SPHERICAL. WAVELET, injecting localized location encodings that are naturally motivated. Against the many benchmarks of many the biases evident in SPHERICAL HARMONIC, while maintaining competitive performance. We invite iteration and updates FAIR-EARTII improve the coverage of subgroups and signals, and stay relevant with changes and trends within the community. Additionally, given the limitations of SPHERICAL WAVELET, hope further research can develop heuristics structural changes to address these shortcomings; in particular, we point to the integration non non-projection based SPHERICAL WAVELET constructions promising direction for future work Sanz et al. (2006).
we resolve
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A
APPENDIX
A.1
FAIR-EARTH DETAILS
Table FAIR-Earth Components
Category
Description
Misc.
Source
Land-Sea
Binary and continuous data, based bathymetric data on percent water sur- face coverage for every grid point.
Metadata in- cludes: islands, coastlines, land- mass sizes, coast distance.
(Huffman
et al. 2014)
Population
Population density data, derived from combination of spatial distribution with national census and population register
Errors in Egypt and Greenland are flagged, and tentatively smoothed via nearest-neighbor interpolation.
(Center for
International
Earth Science
data.
Information
Network
CIESIN
Columbia
University
2018a)
Precipitation
Global accumulated precipitation, based on composite of measurements and modeling.
Monthly Resolu- tion
(Beck et al. 2019
Temperature
Air surface temperature, based on satel- lite measurements and reflectance mod- eling.
Monthly Resolu- tion
Karger et al. 2017
Emissions
Measured and modeled CO2 emissions from the OCO-2 satellite.
Daily Resolution
(Dou et
2023
Metadata Details In particular, for subgroups with ill-defined thresholds (c.g., classification of islands and coastlines), we provide flexibility with adjustable thresholds. This feature allows re- searchers fine-tune their analyses based specific definitions needs, which ing on the research question or application domain. For the purposes of our analyses, islands are defined as landmasses with size under 30, 000 sq. miles, encapsulating most of the "minor islands" as defined by Depraetere et al. (007))
vary depend-
Second, incorporate demographics and geographical boundaries leveraging the Gridded Popu- lation of the World, Version 4 (GPWv4) population dataset (Center for International Earth Science Information Network CIESIN Columbia University (018b), which integrates censuses, popu- lation registers, and spatial distributions, we synthesize population density data for each point in the grid. Then, leveraging high-resolution NaturalEarth (Nat) data, label each grid point with appropriate country labels. These labels are essential for equal representation of both densely and sparsely populated areas, preventing the overeepresentation urban centers or the underrepresenta- tion of rural regions, common bias seen in survey and modeling tasks.
A.1.1 DATASET FIGURES
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Binary Land-Sea Plot
1.0
80
20
0.6
Latitude
Values
0
-2
-40
0.2
-60
-80
0.0
100
150
200
250
300
350
Longitude
Figure 7: Binary land-sea
Binned Coastline Plot
Labnule
Distance from Sea
100
250
350
Figure 8: Coastline
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Island Plot
80
40
440
-80
100
200
350
Longitude
Figure Islands (in dark purple)
3100
First Month (January 2018)
2900
2800
Labtude
2600
2500
Longitude
Figure 10: Air surface temperature plot (Jan. 2018)
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200000
First (January
150000
Laituzi
100000
50000
langitude
Figure 11: Cumulative precipitation plot (Jan. 2018)
Global Population Grid
200
800
1000
Pap
1200
1000
500
1000
1500
2000
2500
3000
2500
Longttde
Figure 12: Global population plot
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C02 Emissions Plct
50
0.000424
60
0.000422
ViIKS
-20-
0.000416
40
0.000114
0.004122
50
100
150
200
250
100
350
Longatude
Figure 13: CO2 emissions plot
Color-Cadel Country Plor
Eattaac
-90
-156
-100
-50
50
100
150
Longituk
Figure 14: Color-coded country plot
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10
Landones Size (lng scale)
10"
10"
Percentile
Sampled Points (N 10000)
b) Landmass Size Percentiles for Mand 3233
Figure 15: Coverage of different landmass sizes using uniform sampling. At N 10000, at least 64 points are sampled on landmasses of size less than 40, 000 square miles, roughly the size of the main island of Cuba.
Table 4: Grid search and encoding parameters
Parameter
Values
Applicable Encoding
Training Samples
{ {5000, 10000, 15000, 20000)
Both
Weight Decay
[le-5, le-4, le-3)
All
Maximum Scale
(3
SW
Maximum Rotations
(50, 90, 130, 170)
SW
Legendre Polynomials
(5.7, 10, 12, 15, 17, 20, 22, 25}
SH
K Value
6
SW
Scale Factor
1
SW
Minimum Radius
(45, 90)
THEORY,
GRID AND SPHERE
Frequency Numbers
(16, 32, 64)
THEORY,
GRID AND SPHERE
Batch Size
2048
All
Learning Rate
le-4
All
Maximum Epochs
500
All
A.2 TRAINING SPECIFICATIONS
Land-Sea Binary Classification Training We conducted comprehensive ablation study to ex- amine model trends on the land-sea binary classification task. The study was performed using grid-search, and relevant parameters are available in Table 4 Note that the parameter sizes for en- codings were chosen to be similar, to control for any effects from simple increase in embedding space.
To initialize training. we set identical data generation seeds for each model. Validation data was sampled similar to Fig. 15 but with Nvalidation = 0.2 Nuraining and different initialization seeds.
For fine-tuning, we perform a similar grid search over a similar continuous range variables. The specific parameters shown in Table 5 Due to the extra parameterization of SPHERICAL WAVELET, we quadruple the number trials to 120, compared to 30 for all other encodings (Fig. 20
Precipitation and Temperature Training Training over these environmental signals was nearly identical training on the land-sca binary classification task. We note couple of minor discrepan-
cies:
Mean-squared error loss was applied to a normalized version of the data, as opposed to binary cross-entropy.
For the sake of precision and brevity, all precipitation losses in the paper are increased by magnitude of 10. We emphasize that this doesn't affect our analyses.
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Table 5: Hyperparameter ranges for model optimization
Category
Hyperparameter
Range
Step
Hidden Dimension
32 -96
Architecture
Number of Layers
1-3
Maximum Scale
2-3
Maximum Rotations
-0
40
SPHERICAL WAVELET
K Value
4 4- 10
Scale Factor
0.75 1.25
SPHERICAL HARMONIC
Legendre Polynomial Degree
10 -0-30
Learning Rate
10 10
log scale
Training
Weight Decay
10 10-
log scale
Figure 16: Zoomed-in in inset plots for main diagram
Figure 17: At higher frequencies (L 30), the closed-form calculations provided in RuBwurn et al. (2024) run into numerical error.
6.8
Prediction Value
Figure 18: SPHERICAL HARMONIC encoding prediction plot
A.3 MISCELLANEOUS FIGURES
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Figure 19: SPHERICAL WAVELET encoding prediction plot
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Table 6: Comparison of existing location encodings
Encoding
Resolution-Adant Adaptive
Basis Type Wavelet Harmonic
Localized Basis
SPHERICAL WAVELET
SPHERICAL HARMONIC
X
CARTESIAN3D
Coordinate
X
THEORY GRID AND SPHERE
Sinusoidal + Coordinate
Sinusoidal + Coordinate
X
Table 7: Comparison of common geospatial datasets
Dataset
Multimodal
Temporal Resolution
Metadata
FAIR EARTH
FAIR-EARTH
Eatu
ERA5 (Hersbach et al. 1999
X
OpenStreetMap OpeeSStreetMan contributors 2017
X
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Table 8: Average subgroup cross-entropy test loss of SPHERICAL HARMONIC validation, stratified by spatial resolution. We observe that the bias of the model in missing "island" and "coastline" persists even for high resolution dataset, as improvement plateaus.
RESOLUTION
5000
10000
15000
20000
25000
30000
TOTAL
0.16 0.02
0.13
0.03
0.12
0.03
0.11
0.04
0.10
0.04
0.10
0.04
LAND
0.21 0.03 0.03
0.15 0.04
0.05
0.14 0.05
0.12 0.06
0.16 0.06
SEA
0.11+0002
0.16 0.02
0.09 +
0.08 + 0.03
0.08 + 0.03
0.80 + 0.03
ISLAND
2.74 0.00
3.25 0.49
2.85 0.33
2.66 6.26 0.26
2.61 = 0.20
2.51 = 0.21
COASTLINE
1.06 0.08
0.06 1.00
0.95 0.05
0.90 = 0.04
0.82 = 0.04
0.81 0.05
SH
SW
0.40
0.35
BCE Loss
0.30
BCE
0.15
0.10
10
15
20
25
30
0
20
40
60
80
100
120
Iterations
Iterations
Figure 20: Fine tuming dynamics for different training resolutions, showing 5-iteration median win- dow. Despite the larger parameter space, fine-tuning of SPHERICAL WAVELET converges com- parable, slightly slower rate than SPHERICAL HARMONIC.
Island and Land Loss for Various Encoding Sizes
4.0
Land (SW)
Loss
Island (SW)
2.0
Land (SH)
Island (SH)
1.5
1.0
0.5
0
100
200
300
400
500
600
Encoding Size
Figure 21: Land and island loss for SH. SW representations, trained the same resolution with varying encoding sizes. The improved performance of SPHERICAL WAVELET may be attributed better representation these fine-scale features. Interestingly, SPHERICAL HARMONIC'S biases against islands worsen with increased encoding size.
A.4 EXTENDED EXPERIMENTAL. RESULTS
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PE + Resolution +
5000
10000
15000
20000
SPHERICAL WAVELET
0.14199 1 0.0009
0.0890
0.0003
0.1017 1 0.0007
0.0762 1 0.0005
SPHERICAL HARMONIC
0.1462 = 0.0013
0.0933 + 0.0010
0.1057 = 0.0010
0.0767 + 0.0005
THEORY
0.1586 0.0034
0.1137 = 0.0012
0.1324 0.0061
0.1016 0.0073
SPHEREM+
0.6314 0.0006
0.6307
0.0003
0.6358
0.0001
0.6259 + 0.0001
SPHEREC+
0.6307 = 0.0017
0.6308 0.0002
0.6357 + 0.0004
0.6259 + 0.0002
Table 9: FAIR-EARTH: Land-Sea Binary Cross-Entropy Loss
PE 4. Resolution +
5000
10000
1,5000
20000
SPHERICAL WAVELET
0.0177 + 0.0005
0.0108
0.0002
0.0095 + 0.0001
0.0084 + 0.0001
SPHERICAL. HARMONIC
0.0158 + 0.0005
0.0104 + 0.0005
0.0089 + 0.0002
0.0078 + 0.0003
THEORY
0.0254 + 0.0028
0.0144 + 0.0016
0.0133 0.0008
0.0114 0.0010
SPHEREM+
2.1551 0.0043
2.2086
0.0012
2.1889 + 0.0019
2.2089 + 0.0015
SPHEREC+
2.1599 0.0032
2.2055 0.0010
2.1856 + 0.0018
2.2074 1 0.0013
Table 10: FAIR- FAIR-EARTH: Carbon Emission Mean-Squared Error
PE J. Resolution +
5000
10000
15000
20000
SPHERICAL WAVELET
0.0306 0.0008
0.0237
0.0001
0.0169 1 0.0001
0.0175 1 0.0002
SPHERICAL HARMONIC
0.0269 1 0.0004
0.0203 + 0.0004
0.0158 1 0.0003
0.0161 1 0.0003
THEORY
0.0535 + 0.0060
0.0270 + 0.0010
0.0190 + 0.0006
0.0194 4: 0.0023
SPHEREM+
1.9559 = 0.0141
1.8413 = 0.0019
1.9528 = 0.0026
1.8573 + 0.0007
SPHEREC+
1.9621 0.0086
1,8433 0.0025
1.9334 0.0024
1.8578 + 0.0007
Table 11: FAIR-EARTS Surface Temperature Mean-Squared Error
PE Resolution +
5000
10000
15000
20000
SPHERICAL WAVELET
0.0993 0.0004
0.0980
0.0007
0.0986
0.0002
0.0976 + 0.0006
SPHERICAL HARMONIC
0.0984 + 0.0004
0.0984 1 0.0006
0.0982 + 0.0004
0.0984 1 0.0005
THEORY
0.1150 + 0.0067
0.1162 + 0.0022
0.1195 1 0.0014
0.1201 1: 0.0054
SPHEREM+
0.5981 = 0.0002
0.5979
+ 0.0001
0.5981
+ 0.0003
0.5982 + 0.0001
SPHEREC+
0.5981 0.0001
0.5986
0.0002
0.5980 + 0.0002 0.5983 + 0.0002
Table 12: Land-Sea Rußwurm et al.
2024
Cross-Entropy Loss
|. Resolution +
5000
10000
15000
20000
SPHERICAL WAVELET
0.1622 0.0011
0.1116
0.0007
0.0848 + 0.0010
0.0718 + 0.0002
SPHERICAL HARMONIC
0,1631 = 0.0011
0.1080
+ 0.0010
0.0773+0.0000 0.0007
0.0652 - 0.0011
THEORY
0.2456 + 0.0124
0.1796
0.0068
0.1382 1 0.0055
0.1265 1 0.0068
SPHEREM+
1.3853 + 0.0003
1.3861
+ 0.0001
1.3862 + 0.0001
1.3862 + 0.0000
SPHEREC+
1.3856 + 0.0002
1.3861
0.0001
1.3863 + 0.0000
1.3862 + 0.0000
Table 13: Checkerboard (RuBwurm et al. 2024
Cross-Enien Mooss-Entropy Loss
Table 14: Surface temperature regression subgroup losses for various encodings. Coast (underlined)
consistently exhibits greater losses.
Subgroup
SW
SH
SPHEREC+ THEORY
Land
0.087
0.076
0.217
5,867
Sea
0.043
0.028
0.063
2.152
Island
0.049
0.041
0.047
2.101
Coast
0.101
0.083
0.249
5.835
24

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Published as a conference paper at ICLR 2025
Land-Sea Classification
Surface Temperature Regression
Encoding
Best Country (Value)
Worst Country
Best Country (Value)
Worst Country (Value)
(Value)
SPHERICAL WAVELET
Finland
Guyana (0.816)
Denmark
Cambodia
(0.002)
(0.009)
(0.232)
SPHERICAL HARMONIC
Honduras (0.001)
Spain (0.795)
Georgia (0.001)
Panama
(0.333)
THEORY
Kyrgyzstan (0.001)
Spain (1.114)
Sierra Leonc (0.002)
Vietnam (0.561)
SPHEREC+
Austria
Chile
Romania (0.143)
Greenland (10.425)
(0.418)
(1.257)
Table 15: Country discrepancies via FAIR-EARTH. Losses are respective to each dataset, and only countries with 100 sampled points included mitigate noise. All encoding-dataset combinations exhibit a wide disparity in country-level performance.
90
SH
80
SW
70
60
50
40
30
20
10
0'
20
33
-50
-60
-80
-90
BCE Loss
Figure 22: Differences in latitudinal loss on land-sea (RuBwurm al. 20244) classification, where means and error bars are based off of 1000 uniform samples each latitude. SPHERICAL WAVELET performance clearly deteriorates as we move from the equator to the poles.
25

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Published as a conference paper at ICLR 2025
Table 16: Computational time for SPHERICAL HARMONIC and SPHERICAL WAVELET across dif- ferent sizes, with faster times underlined. SPHERICAL WAVELET scales better than SPHERICAL. HARMONIC, which can be attributed to its simpler formulation.
Generation Time (ms) SW
Encoding Parameters
Size
SH
Legendre Polyn.
Dilations
Rotations
25
2.60 +: 0.08
5,83 = 0.67
5
25
100
16.44 = 0.72
22.67 + 2.85
10
25
625
220.13 = 9.05
129.58 + 18.43
25
5
125
900
368.73 = 17.93
204.25 + 27.05
30
150
A.5
WAVELET NOTES
Computational Analysis While wavelets are more heavily parameterized than their Fourier coun- terparts, might expect them to be more computationally expensive to compute and tune. How- ever, empirical evidence shows that hyperparameter searches converge at similar rates (Fig. 20 and
SPHERICAL WAVELET demonstrates superior efficiency for large encodings (Table 16). com- parison of the computational requirements for SPHERICAl WAVELET and SPHERICAL. HRMONIC encodings reveals a discrepancy in computational cost. Starting from our previous formulation, define a family of valid wavelets as:
aup = R(p)D(a)VM)
where the dilation operator D(a) is defined as: [D(a)s](w) ()) with À being scaler-valued operator.
The rotation operator R requires only a transformation into Fuler space and three 3 x 3 matrix multiplications. Since the generation rotation points is one-time computation, this yields a computational complexity that scales linearly with encoding size.
contrast, the closed-form SPHERICAL HARMONIC encoding with Legendre polynomials re- quires calculation of:
21 +
11
m!)
mm]) P. (cos X)
4T
(1+
for all m < S L. This higher computational burden makes SPHERICAL WAVELET comparatively
efficient for larger encoding sizes. Additionally, computational and representational challenges of the factorials lead to instability at higher L values [17) thus we restrict our analyses to L = 30.
Non-Gabor Filters We extended our investigation beyond Gabor wavelets to include preliminary experiments with spherical Butterfly and Mexican Hat wavelets, applying the same procedure with different mother wavelets. However, visualizing these wavelets' projections on the sphere suggests they poorly suited for general Earth signals (Fig. 24 In experiments the FAIR-EARTH land-sea classification task, these alternatives performed worse than Gabor wavelets and even certain baseline encodings when controlling for all other parameters (Fig. 25). Future research directions could explore which signals these filters might be better suited for, and whether wavelet-related adjustments to INRs (Saragadam et al. (203)) could address their current limitations.
26

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Published as a conference paper at ICLR 2025
a) Mother Wavelet (Eq. 2
b) Rotated Wavelet
c) Wave number controls central frequency of the Gaussian envelope
d) Dilation factor controls energy concentration
Figure 23: SPHERICAL WAVELET parameterization. All filters are identical to (Eq. (2) except for
one change in the specified parameter.
Wavelet Filters On the Sphere
Mexican Hat
Butterfly
Gabor
Figure 24: Visualizations of various wavelet filters on the sphere. Of the three, only Gabor consis-
tently reaches state-of-the af-thh-art performance.
Land-Sea
Surface Temperature
Filter
5000
10000
5000
10000
Gabor (Ours)
0.1419 + 0.0009
0.0890 + 0.0003
0.0306 + 0.0008
0.0237 + 0.0001
Butterfly
0.1943 0.0005
0.1223 + 0.0003
0.0523 + 0.0005
0.0492 + 0.0010 0.1374 0.0009
Mexican Hat
0.4001 0.0010
0.3624 + 0.0021
0.1550 + 0.0018
Figure 25: A comparison of different wavelet filter performance on the FAIR-EARTH land-sea clas- sification task. Loss metric is respective to each dataset, and all other parameters are held constant.
27


Reviews:
[{"review_id": "6AESFQ9GyF", "reviewer": "Reviewer_VqBs", "summary": "The paper introduces a new set of datasets called FAIR-EARTH, aimed at addressing and assessing fairness in Earth science. FAIR-EARTH encompasses various types of data, including environmental factors and emissions, while also taking geographical features and population density into account. Experimental results demonstrate that existing spherical harmonics methods fail to maintain accurate local performance, particularly regarding land and sea masses. To address this issue, the authors propose using spherical Morlet wavelets to correct localized biases. Results indicate that this approach outperforms existing methods in most situations.", "questions": "1. While spherical wavelets show good performance on most cases to correct localized biases, their robustness remains uncertain. It is known that correctly parameterizing elements like wave number and scaling factors for specific resolutions are necessary to reach the best performance. The authors should conduct experiments to illustrate the trade-offs associated with using spherical wavelets.\n\n2. Since spherical wavelet is well-defined at poles, what should we do for poles? Would there exist bias in poles?\n\n3. Implementing spherical wavelet encodings requires a more complex parameter selection and may need more computation. Efficiency evaluation should be considered for using spherical wavelets\n\n4. While FAIR-EARTH can address some bias for the ill-represented areas like landmasses, authors should detail the weakness/flexibility of this combination approach. What kind of dataset can be integrated if there is temporal bias or learning representation for poles?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "S1. The bias issues in earth science are interesting and important.  \nS2. The paper is well-written and easy to understand, even for those who are not familiar with earth or geographical concepts.  \nS3. The experiments provide detailed insights into model behavior and validate the effectiveness of spherical wavelets in improving representation fairness.", "weaknesses": "W1. The performance trade-offs of spherical wavelets are insufficiently addressed.\nW2. The computation efficiency of spherical wavelets is not discussed.\nW3. More discussion regarding the flexibility and weakness of the proposed datasets.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pIklDHVxs5", "reviewer": "Reviewer_FbST", "summary": "1. This paper constructs a new dataset to unify different existing geospatial datasets under a consistent framework.\n\n2. This paper proposes that fairness is reflected in the concurrent performance improvement of the model across different subgroups, and it conducts specific measurement and analysis based on correlation.\n\n3. This paper proposes using SPHERICAL WAVELET for encoding to mitigate fairness issues while maintaining performance.", "questions": "1. Different methods are needed to illustrate the validity of the new dataset.\n\n2. More groups of examples and different methods are needed to illustrate fairness.\n\n3. Different datasets are needed to verify the validity of methods.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. This paper products constructs a new dataset, which aggregates extensive metadata along stratifications like landmass size and population density and unifies disparate existing geospatial datasets under a consistent framework.\n\n2. This paper proposes that fairness is reflected in the concurrent performance improvement of the model across different subgroups. Experiments and analysis show significant disparities in the performance of the spherical harmonic method across different subgroups uncovering a strong negative correlation between landmass size and representation loss, with areas corresponding to localized signals and high-frequency features exhibiting consistently poor performance.\n\n3. This paper proposes that encoding using SPHERICAL WAVELET solves many obvious deviations in SPHERICAL HARMONIC on many benchmarks of FAIR-EARTH while maintaining competitive performance.", "weaknesses": "1. In this paper, only one of the existing methods is tested on the new dataset, which leads to the lack of convincing for the generality and accuracy of the new dataset. \n\n2. This paper proposes a method for measuring fairness, but in the experiments, it only conducts specific analyses on two different subgroups and one existing method.\n\n3. This paper proposes using SPHERICAL WAVELET for encoding, but experiments are only carried out on the self-constructed dataset. Experiments should also be carried out on other datasets to verify the effectiveness of the method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "NT3aIaSYYt", "reviewer": "Reviewer_Jrro", "summary": "This paper addresses fairness issues in Implicit Neural Representations for Earth data. First, it introduces FAIR-EARTH, a comprehensive dataset designed to evaluate biases in Earth representations across various spatial resolutions and features. Second, to address the identified fairness issues, particularly in representing local features, the authors propose using wavelets instead of traditional harmonics, demonstrating improved representation of fine-grained geographical features while maintaining global performance.", "questions": "Have you evaluated other wavelet types besides the Morlet wavelet? What were their relative performances, particularly in representing different types of geographical features? Could you provide some intuitive guidelines for selecting wavelet parameters based on the type of geographical features being represented?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. Addresses a critical and underexplored issue of fairness in Earth data representation\n\n2. The proposed dataset provides a comprehensive framework for evaluating and comparing different approaches to Earth representation, which will be valuable for future research\n\n3. The use of wavelets for modeling local features is theoretically well-motivated in representing fine-grained geographical features", "weaknesses": "1. While the paper successfully identifies the problem and proposes a promising direction with Spherical Wavelets, it primarily remains at a conceptual level, lacking detailed implementation specifications and comprehensive empirical analysis across different wavelet types.\n\n2. The computational complexity and scalability analysis should be presented, especially given that wavelet-based approaches typically incur higher computational costs than Spherical Harmonics due to their multi-scale nature and the need for both rotation and dilation operations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)