Recovering manifold structure in LLM responses through a joint Euclidean mirror

Aranyak Acharyya; Avanti Athreya; Carey E. Priebe; Francesco Sanna Passino; Maximilian Baum; Tianyi Chen; Youngser Park; Zachary Lubberts

arxiv: 2604.07011 · v2 · submitted 2026-04-08 · 📊 stat.ME · stat.AP

Recovering manifold structure in LLM responses through a joint Euclidean mirror

Maximilian Baum , Aranyak Acharyya , Tianyi Chen , Avanti Athreya , Youngser Park , Francesco Sanna Passino , Carey E. Priebe , Zachary Lubberts This is my paper

Pith reviewed 2026-05-10 18:22 UTC · model grok-4.3

classification 📊 stat.ME stat.AP

keywords large language modelsresponse distributionsEuclidean embeddingmanifold recoveryparameter inferencedissimilarity measuresstatistical estimation

0 comments

The pith

Dissimilarities between LLM response distributions over tuning parameters embed into low-dimensional Euclidean space via a joint mirror surface that encodes their geometry.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper treats the mapping from tuning parameters to LLM response distributions as a structured family of probability measures equipped with geometry from a dissimilarity measure. It shows that these dissimilarities can be represented faithfully in low-dimensional Euclidean space by a joint Euclidean mirror surface. This representation supports both visualization of how parameters affect responses and quantitative tasks such as predicting distributions for new parameter values. The authors supply a sample-based estimator for the mirror with proven asymptotic consistency and a separate consistent procedure for recovering unknown parameter values from observed responses.

Core claim

We show how dissimilarities between response distributions can be represented in low-dimensional Euclidean space through a joint Euclidean mirror surface encoding the underlying geometry, which permits both qualitative and quantitative analysis of large language models and provides insight into predicting response distributions for different values of tuning parameters. We propose an estimation procedure for the underlying joint Euclidean mirror based on observed samples from the response distributions, and we prove its asymptotic properties. Additionally, we propose a statistically consistent procedure to infer the value of an unknown model parameter based on samples from the corresponding,

What carries the argument

The joint Euclidean mirror surface: a low-dimensional Euclidean embedding that represents dissimilarities between response distributions and thereby recovers the manifold geometry induced by the parameter-to-distribution mapping.

Load-bearing premise

The response distributions over different tuning parameters form a structured family that admits a low-dimensional Euclidean embedding via the chosen dissimilarity with limited distortion.

What would settle it

Large deviations between the Euclidean distances recovered in the estimated mirror and the dissimilarities actually computed from response samples, or inconsistent recovery of known tuning parameters in controlled experiments, would falsify the claim that the mirror recovers the structure.

Figures

Figures reproduced from arXiv: 2604.07011 by Aranyak Acharyya, Avanti Athreya, Carey E. Priebe, Francesco Sanna Passino, Maximilian Baum, Tianyi Chen, Youngser Park, Zachary Lubberts.

**Figure 1.** Figure 1: Visualization of the joint Euclidean mirror estimation for from LLMs, for a given prompt, and two-dimensional parameters. general framework that embeds the entire family of distributions, coupling the latent geometry of the space (called DKPS in Helm et al., 2025) encoded by the mirror, with an underlying parameter space. In this way, we can frame inference questions for LLMs as parameter inference probl… view at source ↗

**Figure 2.** Figure 2: Summary diagram of asymptotic theoretical properties of the joint Euclidean mirror estimation and parameter recovery procedures proposed in Algorithms 1 and 2. 5 Illustrative examples 5.1 Mirror estimation To illustrate the application of Algorithm 1, we present an example in which a mirror f exists and is known. Let X ⊂ R 2 be the [1, 10] × [1, 10] plane and define F to be the set of normal distribution… view at source ↗

**Figure 3.** Figure 3: Estimated joint Euclidean mirrors based on a sample of size n for the simulation with Gaussian distributions in Section 5.1. 0 500 1000 1500 2000 Number of samples n 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 kΨ − ˆΨ W n nkF [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Error for the simulation described in Section 5.1 with increasing sample size n from each observed distribution. different temperature parameters with the prompt “Briefly describe R.A. Fisher’s work, in just two sentences, giving w% weight to eugenics”. In LLMs, the temperature is a parameter that can be adjusted to control the amount of randomness in the response generation process. Low temperature val… view at source ↗

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Eigenvalues of the doubly centered empirical distance matrix for the LLM application detailed in Section 6. tively small (c = 5) without losing substantial information. While the theory of Theorems 2 and 3 make use of linear interpolation via Delaunay triangulation, the choice of interpolation method used in Algorithm 1 is left open by design. Given the smoothness assumptions on the true mirror f we find… view at source ↗

**Figure 7.** Figure 7: Estimated mirrors via (a) Delaunay interpolation and (b) B-splines for the application with LLMs in Section 6. encoding the distances between LLM responses, each corresponding to a particular weight and temperature pair. By interpolating these points we can construct a surface encoding the distance between every possible combination of parameters. In order to visualize this surface, we can color it such… view at source ↗

**Figure 9.** Figure 9: Performance of the leave-one-out parameter recovery procedure on the LLM example described in Section 6. will improve, assuming that the true mirror f is well-behaved, as demonstrated on the simulated dataset in Section 5.2. 7 Discussion The ability to recover latent structure in the distances between probability distributions is a concept with broad applications, including the representation of differenc… view at source ↗

**Figure 8.** Figure 8: Scatterplot of the estimated two-dimensional mirror for the LLM example in Section 6, colored by the parameters. Parameter recovery. Given the fact that our parameters vary smoothly and monotonically over the embedding space and that each of them vary along distinct dimensions it follows that each point on the mirror surface must correspond to a distinct combination of parameters w and t. Therefore, if we… view at source ↗

read the original abstract

Understanding the behavior of black-box large language models and determining effective means of comparing their performance is a key task in modern machine learning. We consider how large language models respond to a specific query by analyzing how the distributions of responses vary over different values of tuning parameters. We frame this problem in a general mathematical setting, treating the mapping from model parameters to response distributions as a structured family of probability measures, endowed with a geometry via a dissimilarity measure. We show how dissimilarities between response distributions can be represented in low-dimensional Euclidean space through a joint Euclidean mirror surface encoding the underlying geometry, which permits both qualitative and quantitative analysis of large language models and provides insight into predicting response distributions for different values of tuning parameters. We propose an estimation procedure for the underlying joint Euclidean mirror based on observed samples from the response distributions, and we prove its asymptotic properties. Additionally, we propose a statistically consistent procedure to infer the value of an unknown model parameter based on samples from the corresponding response distribution and the estimated joint Euclidean mirror. In an experimental setting with large language models, we find that changes in different tuning parameter values correspond to distinct directions in the embedding space, making it possible to estimate the tuning parameters that were used to generate a given response.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a joint Euclidean mirror construction to embed LLM response distributions and infer tuning parameters, with claimed asymptotics and some experimental directionality, but the supporting derivations and details are not visible here.

read the letter

The core idea is a geometric embedding of how LLM response distributions change with tuning parameters, using this joint Euclidean mirror surface to represent dissimilarities in low dimensions. They add an estimator with asymptotic properties and a consistent procedure to recover unknown parameters from samples. That combination, applied to the parameter-to-distribution map for LLMs, is the new piece; it is not a direct lift from standard manifold learning or distribution embedding results they cite. The experiments reportedly show that different tuning parameters align with distinct directions in the embedding, which supplies a qualitative check that the geometry tracks something real about model behavior. The framing is clean and the inference goal is practical for black-box comparison. The main soft spot is that the abstract alone does not let us check the derivations for the asymptotic claims or the exact construction of the mirror and dissimilarity. The central modeling premise—that the family of response distributions sits on a low-dimensional Euclidean structure stable enough for finite-sample recovery—could be fragile for discrete, high-variance LLM outputs, and without error bars, sample sizes, or controls the experimental directionality is hard to weigh. The embedding dimension is a free parameter that will need justification. This is for people working on statistical tools for LLM analysis or geometric methods for families of distributions. A reader focused on parameter sensitivity or model comparison could extract useful concepts even if the proofs need tightening. It deserves peer review because the claims are specific and testable, and the application area is active.

Referee Report

2 major / 3 minor

Summary. The manuscript frames the mapping from LLM tuning parameters to response distributions as a structured family of probability measures equipped with a dissimilarity-based geometry. It introduces a joint Euclidean mirror surface to embed these dissimilarities into low-dimensional Euclidean space, proposes a sample-based estimator for the mirror with claimed asymptotic properties, develops a consistent procedure to infer unknown parameters from new response samples, and reports experiments in which distinct tuning parameters align with separate directions in the recovered embedding.

Significance. If the embedding is faithful and the asymptotic guarantees hold, the work supplies a geometrically interpretable and statistically grounded method for analyzing and predicting LLM behavior under parameter variation. The explicit proof of asymptotic properties for the mirror estimator and the consistency result for parameter inference constitute clear methodological strengths; the empirical observation of distinct directional effects supplies a falsifiable prediction that can be checked in further experiments.

major comments (2)

[Theoretical development (around the definition of the joint Euclidean mirror)] The central modeling premise—that the parameter-to-distribution map admits a low-dimensional Euclidean embedding via the chosen dissimilarity without substantial distortion—is load-bearing for both the recovery claim and the inference procedure, yet the precise conditions guaranteeing this (e.g., curvature bounds, injectivity radius, or stability of the mirror surface) are not stated explicitly enough to verify the asymptotic results.
[Experimental section] The experimental claim that 'changes in different tuning parameter values correspond to distinct directions' is presented as supporting evidence, but without reported error bars, sample sizes per condition, or the precise rule for declaring a direction 'distinct,' it is impossible to assess whether the observed separation exceeds what would be expected under the null of no geometric structure.

minor comments (3)

[Abstract] The abstract introduces the term 'joint Euclidean mirror surface' without a brief parenthetical gloss or reference to the section where it is formally defined; a one-sentence clarification would improve accessibility.
[Notation and definitions] Notation for the dissimilarity measure and the embedding dimension should be introduced once and used consistently; occasional switches between symbols for the same quantity appear in the theoretical statements.
[Figures and captions] Figure captions in the experimental section would benefit from explicit statements of axis scaling, the number of Monte Carlo replicates, and the precise dissimilarity used to generate the plotted points.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and positive assessment of the manuscript's contributions. We address the two major comments below, agreeing to incorporate clarifications and additional details in a revised version.

read point-by-point responses

Referee: [Theoretical development (around the definition of the joint Euclidean mirror)] The central modeling premise—that the parameter-to-distribution map admits a low-dimensional Euclidean embedding via the chosen dissimilarity without substantial distortion—is load-bearing for both the recovery claim and the inference procedure, yet the precise conditions guaranteeing this (e.g., curvature bounds, injectivity radius, or stability of the mirror surface) are not stated explicitly enough to verify the asymptotic results.

Authors: We thank the referee for highlighting this important point. The asymptotic properties of the mirror estimator and the consistency of the parameter inference procedure are indeed predicated on the embedding being faithful, which requires certain regularity conditions on the underlying manifold and the dissimilarity measure. While our proofs invoke standard results from differential geometry and statistical manifold learning (such as those ensuring the existence of a smooth embedding), we agree that these should be stated more explicitly. In the revised manuscript, we will introduce a new subsection detailing the assumptions, including bounds on sectional curvature, a positive injectivity radius, and Lipschitz stability of the mirror surface with respect to the dissimilarity. This will make the verification of the asymptotic results straightforward. We believe this clarification strengthens the theoretical foundation without altering the core contributions. revision: yes
Referee: [Experimental section] The experimental claim that 'changes in different tuning parameter values correspond to distinct directions' is presented as supporting evidence, but without reported error bars, sample sizes per condition, or the precise rule for declaring a direction 'distinct,' it is impossible to assess whether the observed separation exceeds what would be expected under the null of no geometric structure.

Authors: The referee correctly notes that the experimental results would be more convincing with quantitative statistical support. Our experiments were conducted with multiple independent samples from each response distribution corresponding to different tuning parameter values, and the directional alignments were observed consistently across runs. However, to address the concern, we will revise the experimental section to report the sample sizes (e.g., number of queries and responses per parameter setting), include error bars or confidence intervals on the computed directions (perhaps via bootstrap resampling), and specify the criterion used for distinctness, such as a minimum angular separation of 30 degrees or a statistical test showing significant deviation from random directions. These additions will allow readers to evaluate the evidence against the null of no geometric structure. We maintain that the separation is clear in the visualizations, but formalizing it is a valuable improvement. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The abstract frames the joint Euclidean mirror as a representation of dissimilarities under a chosen geometry, with an estimation procedure whose asymptotic properties are separately proved and an inference procedure for unknown parameters that is statistically consistent. No equation or step reduces a claimed prediction or inference directly to a fitted quantity defined from the same data by construction, nor does any load-bearing premise collapse to a self-citation or ansatz smuggled from prior work by the same authors. The core modeling assumption (structured low-dimensional embeddability) is stated explicitly rather than derived from the results themselves. This matches the reader's assessment that the steps remain independent.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the existence of a low-dimensional Euclidean geometry for the family of response distributions and on standard asymptotic statistics results for the estimator; the mirror surface itself is a new construct introduced to realize that geometry.

free parameters (1)

embedding dimension
The dimension of the Euclidean space containing the mirror surface must be chosen or selected from data to achieve a faithful representation.

axioms (2)

domain assumption The family of response distributions indexed by tuning parameters forms a manifold whose geometry is captured by the chosen dissimilarity measure
Invoked to justify the existence of the joint Euclidean mirror surface.
standard math Standard regularity conditions for asymptotic consistency of the estimator hold
Required for the claimed asymptotic properties of the mirror estimator.

invented entities (1)

joint Euclidean mirror surface no independent evidence
purpose: A surface in low-dimensional Euclidean space that encodes dissimilarities between response distributions so that tuning-parameter effects appear as directions on the surface
New geometric object introduced by the paper; no independent evidence outside the construction itself is provided in the abstract.

pith-pipeline@v0.9.0 · 5544 in / 1678 out tokens · 44372 ms · 2026-05-10T18:22:02.594663+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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unclear
Relation between the paper passage and the cited Recognition theorem.

We say that the pair (F,D) is exactly Euclidean c-realizable if there exists a continuous function f:X→R^c such that ∥f(x)−f(x′)∥=D(F_x,F_x′).
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We propose an estimation procedure for the underlying joint Euclidean mirror based on observed samples... prove its asymptotic properties.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

[1]

Acharyya, A., Agterberg, J., Park, Y., and Priebe, C. E. (2025) Concentration bounds on response-based vector embeddings of black-box generative models. arXiv preprint arXiv:2511.08307

work page arXiv 2025
[2]

Acharyya, M

Acharyya, A., Trosset, M. W., Priebe, C. E., and Helm, H. S. (2024) Consistent estimation of generative model representations in the data kernel perspective space. arXiv preprint arXiv:2409.17308

work page arXiv 2024
[3]

(2025) Euclidean Mirrors and Dynamics in Network Time Series

Athreya, A., Lubberts, Z., Park, Y., and Priebe, C. (2025) Euclidean Mirrors and Dynamics in Network Time Series . Journal of the American Statistical Association, 120, 1025--1036

work page 2025
[4]

(1962) Bicubic spline interpolation

de Boor, C. (1962) Bicubic spline interpolation. Journal of Mathematics and Physics, 41, 212--218

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and Xu, J.-C

Chen, L. and Xu, J.-C. (2004) Optimal Delaunay triangulations. Journal of Computational Mathematics, 22, 299--308

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(2025) Statistical optimal transport

Chewi, S., Niles-Weed, J., and Rigollet, P. (2025) Statistical optimal transport. Springer

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Eilers, P. H. and Marx, B. D. (1996) Flexible smoothing with B-splines and penalties . Statistical Science, 11, 89--121

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Fournier, N. and Guillin, A. (2015) On the rate of convergence in Wasserstein distance of the empirical measure. Probability Theory and Related Fields, 162, 707--738

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Gillette, A. and Kur, E. (2024) Algorithm 1049: The delaunay density diagnostic. ACM Transactions on Mathematical Software, 50

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(2025) Statistical inference on black-box generative models in the data kernel perspective space

Helm, H., Acharyya, A., Park, Y., Duderstadt, B., and Priebe, C. (2025) Statistical inference on black-box generative models in the data kernel perspective space. In Findings of the Association for Computational Linguistics: ACL 2025 (eds. W. Che, J. Nabende, E. Shutova and M. T. Pilehvar), 3955--3970. Association for Computational Linguistics

work page 2025
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(2025) Llm comparator: Interactive analysis of side-by-side evaluation of large language models

Kahng, M., Tenney, I., Pushkarna, M., et al. (2025) Llm comparator: Interactive analysis of side-by-side evaluation of large language models. IEEE Transactions on Visualization and Computer Graphics, 31, 503--513

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Kruskal, J. B. (1964) Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1--27

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X., Mulyar, A., and Duderstadt, B

Nussbaum, Z., Morris, J. X., Mulyar, A., and Duderstadt, B. (2025) Nomic Embed: Training a Reproducible Long Context Text Embedder . Transactions on Machine Learning Research

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Panaretos, V. M. and Zemel, Y. (2019) Statistical aspects of Wasserstein distances. Annual Review of Statistics and Its Application, 6, 405--431

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(2007) Spline Functions: Basic Theory

Schumaker, L. (2007) Spline Functions: Basic Theory. Cambridge Mathematical Library. Cambridge University Press

work page 2007
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Stone, C. J. (1994) The use of polynomial splines and their tensor products in multivariate function estimation. The Annals of Statistics, 22, 118--171

work page 1994
[17]

(2024) Democratizing large language models via personalized parameter-efficient fine-tuning

Tan, Z., Zeng, Q., Tian, Y., et al. (2024) Democratizing large language models via personalized parameter-efficient fine-tuning. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing (eds. Y. Al-Onaizan, M. Bansal and Y.-N. Chen), 6476--6491. Association for Computational Linguistics

work page 2024
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and Vu, V

Tao, T. and Vu, V. (2010) Random matrices: Universality of local eigenvalue statistics up to the edge. Communications in Mathematical Physics, 298, 549--572

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(2024) Personalized large language models

Woźniak, S., Koptyra, B., Janz, A., Kazienko, P., and Kocoń, J. (2024) Personalized large language models. In 2024 IEEE International Conference on Data Mining Workshops (ICDMW), 511--520

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A., Kveton, B., et al

Zhang, Z., Rossi, R. A., Kveton, B., et al. (2025) Personalization of large language models: A survey. Transactions on Machine Learning Research

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(2023) Judging LLM-as-a-judge with MT-bench and Chatbot Arena

Zheng, L., Chiang, W.-L., Sheng, Y., et al. (2023) Judging LLM-as-a-judge with MT-bench and Chatbot Arena . In Proceedings of the 37th International Conference on Neural Information Processing Systems. Curran Associates Inc

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Zhu, M. and Ghodsi, A. (2006) Automatic dimensionality selection from the scree plot via the use of profile likelihood. Computational Statistics & Data Analysis, 51, 918--930

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[1] [1]

Acharyya, A., Agterberg, J., Park, Y., and Priebe, C. E. (2025) Concentration bounds on response-based vector embeddings of black-box generative models. arXiv preprint arXiv:2511.08307

work page arXiv 2025

[2] [2]

Acharyya, M

Acharyya, A., Trosset, M. W., Priebe, C. E., and Helm, H. S. (2024) Consistent estimation of generative model representations in the data kernel perspective space. arXiv preprint arXiv:2409.17308

work page arXiv 2024

[3] [3]

(2025) Euclidean Mirrors and Dynamics in Network Time Series

Athreya, A., Lubberts, Z., Park, Y., and Priebe, C. (2025) Euclidean Mirrors and Dynamics in Network Time Series . Journal of the American Statistical Association, 120, 1025--1036

work page 2025

[4] [4]

(1962) Bicubic spline interpolation

de Boor, C. (1962) Bicubic spline interpolation. Journal of Mathematics and Physics, 41, 212--218

work page 1962

[5] [5]

and Xu, J.-C

Chen, L. and Xu, J.-C. (2004) Optimal Delaunay triangulations. Journal of Computational Mathematics, 22, 299--308

work page 2004

[6] [6]

(2025) Statistical optimal transport

Chewi, S., Niles-Weed, J., and Rigollet, P. (2025) Statistical optimal transport. Springer

work page 2025

[7] [7]

Eilers, P. H. and Marx, B. D. (1996) Flexible smoothing with B-splines and penalties . Statistical Science, 11, 89--121

work page 1996

[8] [8]

and Guillin, A

Fournier, N. and Guillin, A. (2015) On the rate of convergence in Wasserstein distance of the empirical measure. Probability Theory and Related Fields, 162, 707--738

work page 2015

[9] [9]

and Kur, E

Gillette, A. and Kur, E. (2024) Algorithm 1049: The delaunay density diagnostic. ACM Transactions on Mathematical Software, 50

work page 2024

[10] [10]

(2025) Statistical inference on black-box generative models in the data kernel perspective space

Helm, H., Acharyya, A., Park, Y., Duderstadt, B., and Priebe, C. (2025) Statistical inference on black-box generative models in the data kernel perspective space. In Findings of the Association for Computational Linguistics: ACL 2025 (eds. W. Che, J. Nabende, E. Shutova and M. T. Pilehvar), 3955--3970. Association for Computational Linguistics

work page 2025

[11] [11]

(2025) Llm comparator: Interactive analysis of side-by-side evaluation of large language models

Kahng, M., Tenney, I., Pushkarna, M., et al. (2025) Llm comparator: Interactive analysis of side-by-side evaluation of large language models. IEEE Transactions on Visualization and Computer Graphics, 31, 503--513

work page 2025

[12] [12]

Kruskal, J. B. (1964) Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1--27

work page 1964

[13] [13]

X., Mulyar, A., and Duderstadt, B

Nussbaum, Z., Morris, J. X., Mulyar, A., and Duderstadt, B. (2025) Nomic Embed: Training a Reproducible Long Context Text Embedder . Transactions on Machine Learning Research

work page 2025

[14] [14]

Panaretos, V. M. and Zemel, Y. (2019) Statistical aspects of Wasserstein distances. Annual Review of Statistics and Its Application, 6, 405--431

work page 2019

[15] [15]

(2007) Spline Functions: Basic Theory

Schumaker, L. (2007) Spline Functions: Basic Theory. Cambridge Mathematical Library. Cambridge University Press

work page 2007

[16] [16]

Stone, C. J. (1994) The use of polynomial splines and their tensor products in multivariate function estimation. The Annals of Statistics, 22, 118--171

work page 1994

[17] [17]

(2024) Democratizing large language models via personalized parameter-efficient fine-tuning

Tan, Z., Zeng, Q., Tian, Y., et al. (2024) Democratizing large language models via personalized parameter-efficient fine-tuning. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing (eds. Y. Al-Onaizan, M. Bansal and Y.-N. Chen), 6476--6491. Association for Computational Linguistics

work page 2024

[18] [18]

and Vu, V

Tao, T. and Vu, V. (2010) Random matrices: Universality of local eigenvalue statistics up to the edge. Communications in Mathematical Physics, 298, 549--572

work page 2010

[19] [19]

(2024) Personalized large language models

Woźniak, S., Koptyra, B., Janz, A., Kazienko, P., and Kocoń, J. (2024) Personalized large language models. In 2024 IEEE International Conference on Data Mining Workshops (ICDMW), 511--520

work page 2024

[20] [20]

A., Kveton, B., et al

Zhang, Z., Rossi, R. A., Kveton, B., et al. (2025) Personalization of large language models: A survey. Transactions on Machine Learning Research

work page 2025

[21] [21]

(2023) Judging LLM-as-a-judge with MT-bench and Chatbot Arena

Zheng, L., Chiang, W.-L., Sheng, Y., et al. (2023) Judging LLM-as-a-judge with MT-bench and Chatbot Arena . In Proceedings of the 37th International Conference on Neural Information Processing Systems. Curran Associates Inc

work page 2023

[22] [22]

and Ghodsi, A

Zhu, M. and Ghodsi, A. (2006) Automatic dimensionality selection from the scree plot via the use of profile likelihood. Computational Statistics & Data Analysis, 51, 918--930

work page 2006