ARXIV:2601.22510 · LLM TRAINING · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

arXiv

Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Blocked on Code›Score2.0Evidence unverified

Opportunity summary

Pain Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Evidence 0 refs | 0 sources | 17% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability. While recent work reveals the discrepancy between LLMs and humans in skill compositions, the learning dynamics of skill…

METHOD

Full abstract

Large language models (LLMs) often exhibit unexpected errors or unintended behavior, even at scale. While recent work reveals the discrepancy between LLMs and humans in skill compositions, the learning dynamics of skill compositions and the underlying cause of non-human behavior remain elusive. In this study, we investigate the mechanism of learning dynamics by training transformers on synthetic arithmetic tasks. Through extensive ablations and fine-grained diagnostic metrics, we discover that transformers do not reliably build skill compositions according to human-like sequential rules. Instead, they often acquire skills in reverse order or in parallel, which leads to unexpected mixing errors especially under distribution shifts--a phenomenon we refer to as shattered compositionality. To explain these behaviors, we provide evidence that correlational matching to the training data, rather than causal or procedural composition, shapes learning dynamics. We further show that shattered compositionality persists in modern LLMs and is not mitigated by pure model scaling or scratchpad-based reasoning. Our results reveal a fundamental mismatch between a model's learning behavior and desired skill compositions, with implications for reasoning reliability, out-of-distribution robustness, and alignment.

RESULT

ScienceToStartup currently rates this 2.0/10 on the public viability pass. We further show that shattered compositionality persists in modern LLMs and is not mitigated by pure model scaling or scratchpad-based reasoning.

WHY NOW

LLM Training 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

PainExploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Evidence0 refs | 0 sources | 17% coverage

Blockermissing authors

Analysis summary

Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

ARXIV:2601.22510 · LLM TRAINING · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

arXiv

Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Blocked on Code›Score2.0Evidence unverified

Opportunity summary

Pain Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Evidence 0 refs | 0 sources | 17% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

METHOD

Full abstract

RESULT

WHY NOW

LLM Training 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

PainExploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Evidence0 refs | 0 sources | 17% coverage

Blockermissing authors

Analysis summary

Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

Paper Pack

10.48550/arXiv.2601.22510

Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Abstract

Source availability

PDF linked

The paper record includes a public PDF URL.

Extraction status

Derived fallback

Read summaries are estimated from adjacent metadata, not verified extraction rows.

Proof status

unverified

0 refs; 0 sources; 17% coverage.

What was readable

linkedon filenot materializedderived fallback37 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

LLM Training moved forward this cycle; last verified April 2026. Public score 2.0/10.

Claim map

Abstract-backed public claims while anchored extraction refreshes.

Strong 0Mixed 0Weak 4

Evidencepartial
Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability. While recent work reveals the discrepancy between LLMs and humans in skill compositions, the learning dynamics of skill compositions and the underlying cause of non-human behavior remain elusive.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
Large language models (LLMs) often exhibit unexpected errors or unintended behavior, even at scale. While recent work reveals the discrepancy between LLMs and humans in skill compositions, the learning dynamics of skill compositions and the underlying cause of non-human behavior remain elusive.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
ScienceToStartup currently rates this 2.0/10 on the public viability pass. We further show that shattered compositionality persists in modern LLMs and is not mitigated by pure model scaling or scratchpad-based reasoning.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
LLM Training moved forward this cycle; last verified April 2026. Public score 2.0/10.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial

Constellation map

Paper-native neighborhood for concepts, methods, materials, markets, and competitors. Missing lanes stay labeled instead of disappearing behind commercialization gates.

Open full Signal Canvas

Concepts

not indexed

Methods

Materials

PDF linked

Markets

LLM Training

Competitors

not indexed

Competitive landscape

Exploring non-human-like learning dynamics in Transformers for arithmetic applications, uncovering challenges in model alignment and reliability.

Segment

LLM Training

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 2601.22510 yet. That is a visibility signal, not a blank module: the monitor is watching the public channels below.

Hacker News

Not indexed yet

Bluesky

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PDF

Preview the source document here, or use the hero PDF action for a new tab.

References(37)

Reference metadata pending (f29cd5cab35c06518b9fab95168c11ab55ae2170)

Reference metadata pending (1eab09d29fa9e7ff08e8c82166b9faf4463e84d5)

Reference metadata pending (18be8449f3b4a26dfe8728c04fde77192d4509f7)

Reference metadata pending (2baab1e5fa4a61dc8aec35b903470748195f86f5)

Reference metadata pending (b2ab456c7638b0a0fc7f2ad0ba27e7d4a9b26797)

Reference metadata pending (8ec3406abcff76929a54060429bf207066228c89)

Reference metadata pending (512439b94b682534d8afc3c7c6809fee087a19b1)

Reference metadata pending (48e669c2679b9acf7beb8abdb789167d61ceca49)

Reference metadata pending (a5af3507ca363f3c84f16388502970ffb3188aef)

Reference metadata pending (05506581cade1a8ef6372616cec20b81a3d5c366)

Reference metadata pending (eb30f72c86a2da3c2a628244d6496a2cb6b78c71)

Reference metadata pending (da5d2425cdef713b105ceb92cd86e9528aa079d5)

Reference metadata pending (c923bb61ab5ef5e99809571ccc0395b2802f2807)

Reference metadata pending (92dea316d45c50d5077b4ff65a04bd9fb2eabd79)

Reference metadata pending (be897bb00435f9189bd0305f1b9522d6de0177f8)

Reference metadata pending (00c4d56adbebdb45658c27961113536afa91b138)

Reference metadata pending (c2f048c4523877dd55227aedbd19b6e095703e2d)

Reference metadata pending (f86fb205cd4d85478e65304fc38bdf1e4bed2440)

Reference metadata pending (297211bc86653d9ebbe694a75141c9a1c6c11e69)

Reference metadata pending (17a6116e5bbd8b87082cbb2e795885567300c483)

Showing 20 of 37 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 WorkTransformers converge to invariant algorithmic cores

2.0

Prior WorkTransformers Can Learn Rules They've Never Seen: Proof of Computation Beyond Interpolation

2.0

Prior WorkHumans and transformer LMs: Abstraction drives language learning

2.0

Extension

Builds On ThisGrounding Before Generalizing: How AI Differs from Humans in Causal Transfer

0.0

Commercially relevant

Higher ViabilityNumerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models

7.0

Higher ViabilityFrom Early Encoding to Late Suppression: Interpreting LLMs on Character Counting Tasks

4.0

Higher ViabilityLow-Dimensional Execution Manifolds in Transformer Learning Dynamics: Evidence from Modular Arithmetic Tasks

4.0

Higher ViabilityModel Collapse as Cultural Evolution

3.0

Higher ViabilityEvolutionary Task Discovery: Advancing Reasoning Frontiers via Skill Composition and Complexity Scaling

7.0

Conflicting

Competing ApproachDynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology

1.0

Related Resources

Owned Distribution

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Agent drawer

5 surfaces preserved for agents. Humans can ignore.

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

Run context

Paper: 2601.22510
Route: /paper/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic
Active tab: read
Artifact: shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic

Available agents

Read extractor
Build planner
Track monitor
Competitive mapper
Related-paper scout

API/MCP endpoints

REST paper pack API/api/v1/paper/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic/paper-pack
REST build passport API/api/v1/paper/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic/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/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic

stale

Proof freshness: stale
Proof status: unverified
Display score: 2/10
Last proof check: 2026-04-02
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 0
Source count: 0
Coverage: 17%

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

Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

Canonical ID shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic | Route /paper/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic

REST example

curl https://sciencetostartup.com/api/v1/agent-handoff/paper/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic

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: Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

/buildability/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic

Ignoreblocked

Subject: Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

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/shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic

Paper ref

shattered-compositionality-counterintuitive-learning-dynamics-of-transformers-for-arithmetic

arXiv id

2601.22510

Freshness

Generated at

2026-04-02T02:30:40.136Z

Evidence freshness

stale

Last verification

2026-04-02T02:30:40.136Z

Sources

References

Coverage

17%

Hash state

Lineage hash

146bf06299f08cbea7f82bfcbd6196857f31c5405550f7f39009ae666b17a853

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

Verification pending / evidence receipt incomplete

repo_url

references

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.

JSON-LD twin

The application/ld+json payload rendered for agents.

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Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

Shattered Compositionality: Counterintuitive Learning Dynamics of Transformers for Arithmetic

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Brief

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Translational engineer

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