{"id":"ad2aa9a3-a5c0-4cfb-94f7-9eb3e957116f","arxiv_id":"2606.22524","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"The paper defines expectile entropy, divergence, and mutual information that can exhibit negative values and separate from classical Shannon quantities under risk-seeking or risk-averse regimes.","lead":"This paper replaces the expectation operator in information theory with expectiles to define risk-aware entropy, divergence, and mutual information. A smart generalist might read it to see how information measures could incorporate risk attitudes for safer AI and communication systems.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Operational correspondence of expectile quantities to risk-aware rates and endogenous regions not established","rationale":"The identified load-bearing spot matches the reader's weakest assumption exactly. Because the review was abstract-only and the full text is now referenced, the same unverified operational link remains the critical gap; no stronger internal inconsistency is visible from the given material.","tokens_in":1599,"tokens_out":306,"duration_ms":15811,"concrete_test":"In the multiuser section, extract the derivation of the endogenous rate region; verify whether it follows solely from the expectile mutual information definition or introduces separate game-theoretic elements (e.g., risk-adjusted utilities or equilibrium conditions). If the latter, recompute a simple two-user example with the pure expectile MI to check if the claimed region emerges without those elements.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that replacing E[·] with expectiles yields quantities that are operationally meaningful for risk in information exchange and that these directly induce endogenous rate regions in multiuser mean-field games without extra modeling. The abstract asserts new behaviors (negative divergence, separation from classical MI) and that rate regions become endogenous to risk-sensitivity indices, but this rests on the definitions alone. Standard information theory requires explicit achievability/converse arguments to link a functional to achievable rates; the substitution may preserve algebraic properties yet fail to correspond to any concrete risk-aware coding or game payoff without additional assumptions on utilities or constraints.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper develops a risk-aware information theory by replacing the expectation operator with expectiles to define expectile entropy, divergence, and mutual information. It claims these quantities exhibit behaviors impossible under Shannon theory, such as negative divergence under risk-seeking regimes and a fundamental separation from classical mutual information. In multiuser systems, the framework induces a mean-field game where achievable rate regions become endogenous to heterogeneous risk-sensitivity indices, concluding that Shannon information cannot quantify extreme risks in advanced machine intelligence.","tokens_in":1731,"tokens_out":474,"duration_ms":14957,"significance":"If the operational correspondence between the expectile quantities and risk-aware rates or game payoffs is rigorously established, the framework could provide a foundation for risk-sensitive communication, learning, and collective intelligence in autonomous systems. The substitution approach is conceptually direct, but its significance remains speculative without derivations linking the new functionals to concrete coding theorems or equilibrium analysis.","major_comments":[{"comment":"Abstract: the claim that expectile divergence can be negative (and that this is impossible under Shannon theory) is asserted without any explicit definition of the expectile divergence, derivation of its sign properties, or numerical example demonstrating the behavior while preserving other information-theoretic axioms.","section":"Abstract"},{"comment":"Abstract: the statement that 'achievable rate regions become endogenous to heterogeneous risk-sensitivity indices' in a mean-field-type game is not supported by any game formulation, utility functions, or achievability/converse arguments; the claim appears to follow directly from the substitution without additional modeling of constraints or payoffs.","section":"Abstract"},{"comment":"The manuscript provides no section containing proofs, achievability arguments, or numerical checks that the expectile-based quantities correspond to operational risk-aware rates or induce distinct rate regions beyond the classical case; standard information theory requires such arguments to establish operational meaning.","section":null}],"minor_comments":[{"comment":"The abstract introduces several new terms ('expectile entropy', 'expectile divergence', 'expectile mutual information') without immediate reference to their formal definitions or the value of the risk-sensitivity index used in examples.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments, which correctly identify gaps in explicit derivations and operational arguments. The manuscript introduces the framework conceptually through substitution and highlights emergent properties, but we acknowledge the need for additional detail to strengthen the presentation. We will revise accordingly.","responses":[{"response":"We agree the abstract is concise and omits these elements. The full manuscript defines expectile divergence via direct replacement of expectation by the expectile operator in the standard divergence expression. Sign properties (including negativity for risk-seeking parameters) follow from the asymmetric weighting in the expectile definition. We will add the explicit definition to the abstract, a short derivation of the sign, and a numerical example in the revision while verifying consistency with axioms in the risk-neutral limit.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the claim that expectile divergence can be negative (and that this is impossible under Shannon theory) is asserted without any explicit definition of the expectile divergence, derivation of its sign properties, or numerical example demonstrating the behavior while preserving other information-theoretic axioms."},{"response":"The claim is presented as a direct consequence of heterogeneous expectile-based mutual information in a multiuser setting, inducing endogenous rate regions in the mean-field limit. No explicit game with utilities or coding arguments is developed in the current text. We will add a short modeling subsection outlining the mean-field interaction and discuss how the substitution affects the effective payoffs, while noting that full equilibrium analysis remains future work.","revision_made":"partial","referee_comment":"[Abstract] Abstract: the statement that 'achievable rate regions become endogenous to heterogeneous risk-sensitivity indices' in a mean-field-type game is not supported by any game formulation, utility functions, or achievability/converse arguments; the claim appears to follow directly from the substitution without additional modeling of constraints or payoffs."},{"response":"We agree the manuscript contains no such section; the contribution is the axiomatic substitution and the resulting qualitative distinctions rather than operational coding theorems. In revision we will add a dedicated section with numerical checks illustrating distinct regions and a discussion of potential operational interpretations, while clarifying that full achievability/converse results lie beyond the present scope.","revision_made":"yes","referee_comment":"[—] The manuscript provides no section containing proofs, achievability arguments, or numerical checks that the expectile-based quantities correspond to operational risk-aware rates or induce distinct rate regions beyond the classical case; standard information theory requires such arguments to establish operational meaning."}],"tokens_in":1259,"tokens_out":549,"duration_ms":30139,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this work replaces the expectation operator with expectiles to define new versions of entropy, divergence, and mutual information, then claims these produce behaviors like negative divergence and make rate regions in mean-field games depend directly on risk-sensitivity parameters.\n\nWhat is new is the explicit construction of these expectile quantities and the suggestion that they induce a mean-field game structure for information exchange where heterogeneous risk indices shape the achievable sets. The abstract does a reasonable job flagging that classical Shannon measures are risk-neutral and that extreme risks matter for applications like safe autonomous systems.\n\nThe soft spots sit in the missing links. The abstract asserts fundamental separation from classical mutual information and endogenous rate regions, yet offers no achievability arguments, converses, or even simple numerical checks. Standard information theory requires explicit coding theorems to tie a functional to operational rates; here the substitution alone is treated as sufficient. That leaves the operational correspondence unestablished and raises the possibility that the claimed properties are mostly algebraic consequences of the definition rather than independent results.\n\nThis is aimed at people working on risk-sensitive extensions in networks or multi-agent systems. A reader wanting concrete theorems or validated examples will come away short. It still deserves a serious referee because the direction touches relevant territory in risk-aware communication and the framework could be sharpened with the right technical steps.\n\nI would send it to peer review with the expectation that the authors supply the missing derivations and show how the new quantities actually map to coding or equilibrium payoffs.","headline":"The paper defines expectile entropy, divergence, and mutual information but provides no derivations showing these correspond to actual rates or endogenous game regions.","tokens_in":2244,"tokens_out":374,"would_cite":false,"duration_ms":18800,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"By replacing expectation with expectiles, information theory captures risk attitudes with possible negative mutual information.","keywords":["risk-aware information theory","expectiles","expectile entropy","mutual information","mean-field game","risk sensitivity"],"falsifier":"An empirical demonstration that expectile-based mutual information remains nonnegative in all risk regimes or that rate regions in a multiuser game do not depend on risk sensitivities.","tokens_in":2466,"feed_emoji":"","tokens_out":585,"duration_ms":27427,"temperature":0.7,"pith_summary":"The paper replaces the expectation operator in Shannon's definitions with expectiles to create expectile entropy, divergence, and mutual information. These new measures can take negative values and separate from classical mutual information in ways that reflect risk-seeking or risk-averse behaviors. In multiuser communication, this leads to game-theoretic rate regions that depend on each user's risk-sensitivity index rather than being universal. A reader would care because standard information theory assumes risk neutrality, which may fail for systems where extreme outcomes dominate decisions in machine learning and autonomous control.","feed_headline":"Expectiles make mutual information risk-aware and possibly negative","feed_subtitle":"Rate regions in multiuser games then depend on each participant's risk-sensitivity index.","key_machinery":"Expectile entropy, divergence, and mutual information obtained by replacing the expectation operator with expectiles.","core_discovery":"We develop a risk-aware information theory by replacing expectation with expectiles, introducing expectile entropy, divergence, and mutual information. These quantities exhibit behaviors impossible under Shannon's risk-neutral framework, including negative divergence under risk-seeking regimes and a fundamental separation from classical mutual information. In multiuser systems, the framework naturally induces a mean-field-type game theory of information exchange, where achievable rate regions become endogenous to heterogeneous risk-sensitivity indices. Our results reveal that Shannon information alone cannot quantify the extreme risks driving advanced machine intelligence.","pith_inferences":["Risk-sensitive information measures could inform the design of algorithms for collective intelligence in uncertain environments.","The endogenous rate regions suggest new ways to model negotiation in information exchange among heterogeneous agents.","This method might connect to risk measures used in finance and operations research for broader decision-making applications."],"forward_implications":["Expectile divergence can be negative under risk-seeking regimes.","Achievable rate regions become endogenous to the risk-sensitivity indices of the users.","The framework supports risk-aware communication, learning, and safe autonomous systems.","Shannon information cannot quantify extreme risks in advanced machine intelligence."],"fun_headline_variants":["Expectiles replace expectation in information theory","Negative divergence arises with risk-seeking expectiles","Expectile mutual information separates from Shannon version","Risk indices determine multiuser rate regions in games","Shannon info misses extreme risks in machine systems"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"That replacing the expectation operator with expectiles produces quantities that meaningfully capture risk in information exchange and induce endogenous rate regions without additional assumptions.","fun_headline_variants_meta":{"raw":{"variants":["Expectiles replace expectation in information theory","Negative divergence arises with risk-seeking expectiles","Expectile mutual information separates from Shannon version","Risk indices determine multiuser rate regions in games","Shannon info misses extreme risks in machine systems"]},"model":"grok-4.3","cost_usd":0.002792,"raw_usage":{"total_tokens":1502,"prompt_tokens":555,"num_sources_used":0,"completion_tokens":64,"cost_in_usd_ticks":27924500,"prompt_tokens_details":{"text_tokens":555,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":883,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":555,"tokens_out":64,"duration_ms":6589,"temperature":1.0,"reasoning_tokens":883,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T09:39:26.499418+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An empirical demonstration that expectile-based mutual information remains nonnegative in all risk regimes or that rate regions in a multiuser game do not depend on risk sensitivities.","supporting_citations":[],"review_version":1}