Reasoning Shortcuts and Value Symmetries: What Symmetry Permits, Architecture Realizes, and Optimization Selects

• URL: http://arxiv.org/abs/2608.10420v1
• Date: Tue, 11 Aug 2026 03:10:20 GMT
• Title: Reasoning Shortcuts and Value Symmetries: What Symmetry Permits, Architecture Realizes, and Optimization Selects
• Abstract summary: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts.<n>A recent framework of Takemura, Inoue, and Nishino analyzes them through an automorphism group of value relabelings.<n>We first show that the framework's key definition, one shared permutation applied at every position, does not apply as stated to any of the four benchmarks it was evaluated on.
• Score: 10.012788934490084
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts. A recent framework of Takemura, Inoue, and Nishino analyzes them through an automorphism group of value relabelings and asks, as its central open question, when rules pin concepts down. We first show that the framework's key definition, one shared permutation applied at every position, does not apply as stated to any of the four heterogeneous benchmarks it was evaluated on, and that the most direct embedding, padding domains to a common size, produces confident false pathology: 90.91% of solution pairs reported unexplained on CLE4EVR, where every well-defined member of the hierarchy we introduce reports 0%, and the padded verdict's content rotates with configuration-file ordering. Re-measuring eleven rule families under fifteen pre-specified predictions (thirteen confirmed), unexplained-pair rates span 0% to 99.9999% and track provable structure: six theorems give sufficient conditions for transitivity and its failure, including a Free Slot Lemma certifying Kandinsky's pathology from syntax alone. For circuit-given rules, deciding symmetry-inertness of a coordinate is coNP-complete; nontrivial-automorphism existence is coNP-hard under randomized reductions, lies in $Σ_2^p$, is not $Σ_2^p$-complete unless PH collapses, and on monotone circuits is coNP-complete outright. In the Boolean case transitivity is classified exactly: automorphisms explain everything iff the solution set is an affine coset. Weakly supervised models place all 94 observed shortcuts at the one level the componentwise theory flags and none at the 48 it certifies transitive; twelve typed-ambiguous levels produce none, separating what symmetry permits from what optimization selects, and a dual-head control replicates the geography. All numbers trace to released artifacts.

Related papers

• Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks [7.541234468065092]
  A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit.<n>Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array.<n>We show this is a structural obstruction rather than an implementation slip.
  arXiv  Detail & Related papers  (2026-07-28T23:36:05Z)
• Frame-Dependent Traces and the Third-Particle Paradox [45.88028371034407]
  We show that the Paradox of the Third Particle arises when comparing subsystem descriptions across Quantum Reference Tracing perspectives.<n>We argue that our condition captures the Paradox content: rather than imposing consistency on the whole state space, we reproduce exactly the states on which it holds.
  arXiv  Detail & Related papers  (2026-07-23T18:00:01Z)
• Forgetting Is Not a Fix: Path Dependence in Sequential Engram Editing [35.76482964927589]
  We test the hypothesis that concept-specific memory traces become linear objects that can be extracted once and combined arithmetically.<n>We run that test on the authors' own reference implementation, at their reported best edit strength.<n>For unlearning-as-compliance: erasure certified today does not certify the artifact after its next edit.
  arXiv  Detail & Related papers  (2026-07-06T23:45:06Z)
• A homotopy-type-theoretic generalization of neurosymbolic inference [46.36639624013224]
  neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $$-structures.<n>We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind reasoning shortcuts.
  arXiv  Detail & Related papers  (2026-06-16T12:22:12Z)
• Stochastic Estimation of the Layer-wise Hessian Trace for Monitoring Neural-network Training [45.88028371034407]
  We present a parameter estimator of the trace of the diagonal blocks of the Hessian matrix of the empirical risk of a neural network.<n>The procedure combines the Hutchinson trace estimator with a single Hessian-vector product over the whole parameter vector.<n>We show that correctness under weight sharing requires the layer-wise Hessian to be assembled before the second differentiation.
  arXiv  Detail & Related papers  (2026-05-25T10:24:32Z)
• Distributional Energy-Based Models for Uncertainty-Aware Structured LLM Reasoning [40.342912574072024]
  Large Language Models produce structured outputs such as travel plans or code solutions.<n>Individual reasoning steps may appear correct while the output as a whole violates budgets, fails test cases, or contradicts earlier deductions.<n>We propose a learned quality scorer with deterministic analytical constraint penalties for verifying structured LLM outputs.
  arXiv  Detail & Related papers  (2026-05-15T17:08:27Z)
• Mechanized Foundations of Structural Governance: Machine-Checked Proofs for Governed Intelligence [0.0]
  We present five results in the theory of structural governance for cognitive workflow systems.<n>Three are in Coq 8.19 using the Interaction Trees library with mechanizedized coinduction; two are proved on paper with explicit reductions.<n>A sixth contribution connects the abstract model to the deployed runtime: the Verified Interpreter Specification.
  arXiv  Detail & Related papers  (2026-04-30T01:03:15Z)
• Exact Structural Abstraction and Tractability Limits [0.0]
  Exact correctness depends only on the induced classes $s sim_R simation' iff mathrmAdm_R(s)$.<n>Decision, search, approximation, statistical, randomized horizon, and distributional guarantees all reduce to this same quotient-recovery problem.
  arXiv  Detail & Related papers  (2026-04-08T17:59:47Z)
• The Attribution Impossibility: No Feature Ranking Is Faithful, Stable, and Complete Under Collinearity [0.0]
  No feature ranking can be simultaneously faithful, stable, and complete when features are collinear.<n>We prove this impossibility, quantify it for four model classes, resolve it via ensemble averaging (DASH), and machine-verify it with 305 Lean 4 theorems.<n>The design space theorem, diagnostics, and impossibility are mechanically verified in Lean 4 (305 theorems from 16 axioms, 0 sorry) -- to our knowledge, the first formally verified impossibility in explainable AI.
  arXiv  Detail & Related papers  (2026-04-08T10:11:45Z)
• DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks [45.3591788771536]
  We re-examine a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We show that the Karush-Kuhn-Tucker optimality conditions for the NOTEARS cannot be satisfied except in a trivial case. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.
  arXiv  Detail & Related papers  (2020-10-18T22:59:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.