ARXIV:2603.28764 · AI RESEARCH TOOLS · SUBMITTED 31 MAR · 20:25 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

N Alex Cayco Gajic · Arthur Pellegrino · arXiv

A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Blocked on Code›Score2.0Evidence unverified

Opportunity summary

Pain A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Evidence 56 refs | 3 sources | 50% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their intrinsic…

METHOD

Full abstract

Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their intrinsic geometry, they may fail to capture subtle yet crucial distinctions between fundamentally different neural network solutions. Here, we introduce metric similarity analysis (MSA), a novel method which leverages tools from Riemannian geometry to compare the intrinsic geometry of neural representations under the manifold hypothesis. We show that MSA can be used to i) disentangle features of neural computations in deep networks with different learning regimes, ii) compare nonlinear dynamics, and iii) investigate diffusion models. Hence, we introduce a mathematically grounded and broadly applicable framework to understand the mechanisms behind neural computations by comparing their intrinsic geometries.

RESULT

ScienceToStartup currently rates this 2.0/10 on the public viability pass. We show that MSA can be used to i) disentangle features of neural computations in deep networks with different learning regimes, ii) compare nonlinear…

WHY NOW

AI Research Tools moved forward this cycle; last verified April 2026. Public score 2.0/10.

Continue into Read for claims, analysis, references, and neighboring papers.

Opportunity summary

Score2.0

PainA novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Evidence56 refs | 3 sources | 50% coverage

Blockerno shell-level blocker reported

Analysis summary

A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

ARXIV:2603.28764 · AI RESEARCH TOOLS · SUBMITTED 31 MAR · 20:25 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

N Alex Cayco Gajic · Arthur Pellegrino · arXiv

A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Blocked on Code›Score2.0Evidence unverified

Opportunity summary

Pain A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Evidence 56 refs | 3 sources | 50% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

METHOD

Full abstract

RESULT

WHY NOW

AI Research Tools moved forward this cycle; last verified April 2026. Public score 2.0/10.

Continue into Read for claims, analysis, references, and neighboring papers.

Opportunity summary

Score2.0

PainA novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Evidence56 refs | 3 sources | 50% coverage

Blockerno shell-level blocker reported

Analysis summary

A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

Paper Pack

10.48550/arXiv.2603.28764

Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Abstract

Source availability

PDF linked

The paper record includes a public PDF URL.

Extraction status

Parse run linked

A document parse run is attached to this paper.

Proof status

unverified

56 refs; 3 sources; 50% coverage.

What was readable

linkedon file20 anchors8 extracted54 indexednot indexed

Derived fallback: Estimated from adjacent evidence; not verified from source.

Viability

2.0

Time to MVP

MVP estimate missing

Commercial

No commercial flags on file

Export

Preparing verified analysis

lens / founder

PROBLEM

METHOD

RESULT

WHY NOW

AI Research Tools moved forward this cycle; last verified April 2026. Public score 2.0/10.

Claim map

Strong 8Mixed 0Weak 0

Evidencepartial
MSA distinguishes rich and lazy representations
Implicationpartial
Explicitly stated in the abstract as a key capability and demonstrated with specific experimental results comparing rich and lazy networks.
Verificationpartial
partial
Evidencepartial
MSA provides a principled means of comparing the intrinsic geometries of neural network representations
Implicationpartial
Directly stated as the core methodological contribution, with explicit contrast to extrinsic methods and evidence showing MSA's superior performance.
Verificationpartial
partial
Evidencepartial
it is invariant to the choice of coordinates on the manifold and to rotations in the neural network state space.
Implicationpartial
Explicitly stated as a mathematical property of MSA, though the full proof is referenced to a later section.
Verificationpartial
partial
Evidencepartial
MSA enables the comparison of nonlinear dynamics
Implicationpartial
Explicitly stated in the abstract and demonstrated with a specific application to dynamical systems models.
Verificationpartial
partial
Evidencepartial
MSA, in contrast, found zero similarity in these cases.
Implicationpartial
Directly stated as a key experimental result comparing MSA to baseline methods.
Verificationpartial
partial
Evidencepartial
its non-specificity enables comparison across model classes.
Implicationpartial
Directly stated as a property of MSA, though the evidence is more conceptual than experimental in the provided excerpt.
Verificationpartial
partial
Evidencepartial
SR is a pseudo-distance function on SPD matrices. This means that it satisfies i) separation: dSR(G, G) = 0, ii) symmetry: dSR(G, G′) = dSR(G′, G)and iii) the triangle inequality
Implicationpartial
Explicitly and formally stated as a mathematical property of the SR.
Verificationpartial
partial
Evidencepartial
investigate diffusion models.
Implicationpartial
Stated in the abstract as a capability, but no specific evidence or results from such an application are provided in the given excerpt.
Verificationpartial
partial

Constellation map

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Methods

Materials

PDF linkedDocument parse run

Markets

AI Research Tools

Competitors

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Competitive landscape

A novel mathematical framework for analyzing the intrinsic geometry of neural network representations to understand computational mechanisms.

Segment

AI Research Tools

Adoption evidence

No public code link in the paper record yet

Commercial read

2.0/10 public viability

Direct

not classified

Adjacent

not classified

Substitute

not classified

Unknown

not classified

Buzz

No indexed public discussion is attached to 2603.28764 yet. That is a visibility signal, not a blank module: the monitor is watching the public channels below.

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References(54)

Emergent Riemannian geometry over learning discrete computations on continuous manifolds

2025Julian Brandon, Angus Chadwick et al.

InputDSA : Demixing then comparing recurrent and externally driven dynamics

2025Ann Huang, Mitchell Ostrow et al.

Discovering alternative solutions beyond the simplicity bias in recurrent neural networks

2025William Qian, Cengiz Pehlevan

Efficient Working Memory Maintenance via High-Dimensional Rotational Dynamics

2025L. Ritter, Angus Chadwick

Dynamical Archetype Analysis: Autonomous Computation

2025Ábel Ságodi, I. Park

Generalizable, real-time neural decoding with hybrid state-space models

2025Avery Hee-Woon Ryoo, Nanda H Krishna et al.

Feature Learning beyond the Lazy-Rich Dichotomy: Insights from Representational Geometry

2025Chi-Ning Chou, Hang Le et al.

A Review on Riemannian Metric Learning: Closer to You than You Imagine

2025Samuel Gruffaz, Josua Sassen

Unraveling the Geometry of Visual Relational Reasoning

2025Jiaqi Shang, Gabriel Kreiman et al.

Quantifying Differences in Neural Population Activity With Shape Metrics

2025Joao Barbosa, Amin Nejatbakhsh et al.

KoopSTD: Reliable Similarity Analysis between Dynamical Systems via Approximating Koopman Spectrum with Timescale Decoupling

2025Shimin Zhang, Ziyuan Ye et al.

What Representational Similarity Measures Imply about Decodable Information

2024Sarah E. Harvey, David Lipshutz et al.

Equivalence between representational similarity analysis, centered kernel alignment, and canonical correlations analysis

2024Alex H. Williams

DFORM: Diffeomorphic vector field alignment for assessing dynamics across learned models

2024Ruiqi Chen, Giacomo Vedovati et al.

Reconstructing computational system dynamics from neural data with recurrent neural networks

2023D. Durstewitz, G. Koppe et al.

Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry

2023Yong-Hyun Park, Mingi Kwon et al.

SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis

2023Dustin Podell, Zion English et al.

Beyond Geometry: Comparing the Temporal Structure of Computation in Neural Circuits with Dynamical Similarity Analysis

2023Mitchell Ostrow, Adam Eisen et al.

Similarity of Neural Network Models: A Survey of Functional and Representational Measures

2023M. Klabunde, Tobias Schumacher et al.

The training process of many deep networks explores the same low-dimensional manifold

2023J. Mao, Itay Griniasty et al.

Showing 20 of 54 references

CITED BY

No citing papers are indexed in the public S2S graph yet. This is an explicit zero-signal state, not a hidden lookup.

Foundation

Prior WorkRiemannGL: Riemannian Geometry Changes Graph Deep Learning

2.0

Prior WorkAligning the Unseen in Attributed Graphs: Interplay between Graph Geometry and Node Attributes Manifold

2.0

Prior WorkGauge-invariant representation holonomy

2.0

Prior WorkRiemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence

2.0

Prior WorkRevisiting the Platonic Representation Hypothesis: An Aristotelian View

2.0

Prior WorkManifold-Matching Autoencoders

2.0

Extension

Builds On ThisMeasuring the Representational Alignment of Neural Systems in Superposition

1.0

Builds On ThisRiemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering

0.0

Commercially relevant

Higher ViabilityHarnessing Data Asymmetry: Manifold Learning in the Finsler World

3.0

Higher ViabilityThe Geometry of Transfer: Unlocking Medical Vision Manifolds for Training-Free Model Ranking

5.0

Conflicting

none indexed

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Agent drawer

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Developer contracts, payload previews, evidence maps, and run controls stay here instead of the Read, Build, and Track workspace.

Run context

Paper: 2603.28764
Route: /paper/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds
Active tab: read
Artifact: geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds

Available agents

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Related-paper scout

API/MCP endpoints

REST paper pack API/api/v1/paper/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds/paper-pack
REST build passport API/api/v1/paper/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds/build-passport
REST OpenAPI/api/openapi.json
MCP descriptor/api/mcp
MCP resourcesciencetostartup://surfaces/paper-workspace

Tool contracts

paper_packbuild_passportopportunity_kernelforesightsource_proofevidence_state

Payload preview

Inspect payload

{
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Schema validation

paper-r2 contract: present
JSON-LD twin: SSR emitted
OpenAPI path parity: /api/openapi.json
MCP resource parity: paper-workspace

Job trace

queued: drawer opened by user action
running: inspect or copy payload
succeeded: payload available in SSR
failed: route errors appear in evidence cards

Evidence map

sources used: page freshness, source proof anchors, JSON-LD
missing sources: exposed by PaperPack and EvidenceState chips
derived fallbacks: marked unverified before handoff

Page Freshness

Canonical route, proof status, last verified, refs, sources, and coverage.

Page Freshness

Paper proof surface

Canonical route: /paper/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds

stale

Proof freshness: stale
Proof status: unverified
Display score: 2/10
Last proof check: 2026-03-31
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 56
Source count: 3
Coverage: 50%

This page is showing the last landed evidence receipt and score bundle because the latest proof data is outside the freshness window.

OpenAlex: pending — this preprint is not yet indexed by OpenAlex.

Agent Handoff

Endpoint list, payload shape, route context, and copyable handoff data.

Agent Handoff

Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

Canonical ID geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds | Route /paper/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds

REST example

curl https://sciencetostartup.com/api/v1/agent-handoff/paper/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds

MCP example

{
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}

source_context

{
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Buildability Receipt

Verdict, compute envelope, blockers, signature state, and receipt links.

Paper proof page receipt window

Not build-ready: Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

/buildability/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds

Ignoreblocked

Subject: Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

Verdict

Ignore

Verdict is Ignore because current viability and proof state do not clear the buildability gate.

Time to first demo

Insufficient data

No first-demo timestamp, owner estimate, or elapsed demo receipt is attached to this surface.

Compute envelope

Structured compute envelope

Insufficient data

No data, compute, hardware, memory, latency, dependency, or serving requirement receipt is attached.

Evidence ids

Receipt path

/buildability/geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds

Paper ref

geometry-aware-similarity-metrics-for-neural-representations-on-riemannian-and-statistical-manifolds

arXiv id

2603.28764

Freshness

Generated at

2026-03-31T20:25:09.773Z

Evidence freshness

stale

Last verification

2026-03-31T20:25:09.773Z

Sources

References

Coverage

50%

Hash state

Lineage hash

63e8a7ec17b8dbebc75d72cca19ba8f554fc72116b570ec83b314104c74eb3de

Canonical opportunity-kernel lineage hash.

Signature state

External signature

unsigned_external

No founder, registry, pilot, or production-adoption signature is attached to this receipt.

Verification

not_verified

Verification is blocked until an external signature is provided.

Blockers

Missing: repo_url
Missing: proof_status
Missing: distribution_readiness_scores
Unknown: distribution readiness has not been computed yet
Unknown: proof verification has not been recorded yet

56 refs / 3 sources / Verification pending

repo_url

proof_status

Missing proof, requirement, signature, approval, adoption, or telemetry fields are blockers and must not be inferred.

Open receipt API receipt Build Loop Signal Canvas Proof divergence Divergence API Brier outcomes API

Source Proof anchors

Visual citations from the paper document graph.

Source proof

Visual citation anchors from the paper document graph.

20 anchors

proof blockPage 282%

This equation captures one of the core mathematical components of the system. φ1 : Rnin →Rn1 and φ2 : Rnin →Rn2 by defining a

Page and bbox are available; crop image is pending.

proof blockPage 282%

This equation captures one of the core mathematical components of the system. a finite set of k inputs: M1 = [φ1(x1), ..., φ1(xk)] and

Page and bbox are available; crop image is pending.

proof blockPage 282%

This equation captures one of the core mathematical components of the system. M2 = [φ2(x1), ..., φ2(xk)] for xi ∈Rnin.

Page and bbox are available; crop image is pending.

JSON-LD twin

The application/ld+json payload rendered for agents.

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Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

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