{"id":"a0f5904f-9993-45bb-8acc-79763fe4b39c","arxiv_id":"2505.07883","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A sign-flip constraint on one latent dimension of a VAE trained on LLM embeddings yields complementary event probabilities that sum to near one and track true probabilities on held-out dice events.","lead":"This paper trains a variational autoencoder on embeddings from Large Language Models, forcing one latent dimension to flip sign between an event and its complement. The recovered probabilities are more coherent than the models' stated judgments and remain similarly accurate on dice-roll questions.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The single sign-flip assumption (Eq. 3) is not tested outside the dice template; z1 could be a surface feature collinear with probability, and complement-embedding prediction accuracy is never reported.","rationale":"The central claim has two parts: recovered probabilities are more coherent than judged probabilities, and they align with true probabilities. Coherence is largely built into the training objective, since the model is trained to produce complement embeddings by flipping z1, so the remaining question is whether the flipped dimension actually encodes log-odds of Ptrue rather than a collinear surface feature. The paper's dice experiments are suggestive but not decisive: all prompts follow a rigid template, so lexical features such as the queried number or comparison type are perfectly confounded with probability. The strongest evidence would be generalization to events with different surface structure. The VAE prior does not identify the scale: with β=5 and an unexplained 'temperature=5' conversion, the mapping from z1 to probability is not derived from the axioms alone. The reader's identified weakest assumption is the same one; I agree with that diagnosis. The right verdict remains CONDITIONAL pending such a test, so no change to the reader's verdict is needed.","tokens_in":14555,"tokens_out":15165,"duration_ms":163760,"concrete_test":"Take the trained model and run it on a new set of complementary events with known probabilities that are paraphrases of the dice events (e.g., 'What is the chance of rolling a 5 on a 6-sided die?' vs. 'How likely is it to roll 5 on a normal six-sided die?'). If the recovered probabilities remain coherent and track the true probabilities, the z1 code is semantic; if coherence or accuracy degrades sharply, z1 is a template-specific surface feature.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is Eq. (3): p(¬e|z,e) ≈ p(¬e|T(z)) with T(z)=[-z1,z_{-1}], followed by the interpretation of z1 as log-odds in Eq. (6). The training objective never observes Ptrue; it only requires that flipping z1 lets the decoder produce the complement embedding. On the dice template, the only complement-relevant scalar is the event probability, so the VAE can satisfy this by loading probability into z1. But the same objective would be satisfied by any monotone odd feature (e.g., a 'not-ness' or specificity feature correlated with probability). Nothing in the LLM's geometry guarantees that the complement relation in embedding space is a single sign-flip, and the paper reports no measure of how well pθ(¬e|T(z)) predicts held-out complement embeddings. Because Ptrue is absent, the scale of z1 is fixed only by the VAE prior and reconstruction losses; the paper's ambiguous 'temperature=5' (Sec. 4) underscores that the σ(z1) mapping is not independently calibrated. Consequently, the reported dice results are consistent with the claim but do not establish that a single sign-flipped latent recovers calibrated probabilities outside this template.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an unsupervised variational-autoencoder method for recovering event probabilities from LLM embeddings. Given embeddings e and ¬e for complementary events, a VAE is trained to reconstruct e and, in a second step, to predict ¬e by sign-flipping the first latent variable (T(z)=[-z^(1), z^(-1)]). The first latent variable is interpreted as log odds and converted to a probability via the logistic function, so that the Gaussian prior plus the sign flip enforces P(A)+P(¬A)=1. On dice events (1,728 training and 480 held-out questions) using Gemma-2-9b-instruct embeddings, the recovered probabilities have test incoherence 0.038 versus 0.137 for raw judged probabilities, correlate with true probabilities at r=0.73, and have MSE statistically indistinguishable from judged probabilities. An ablation that removes the complement-prediction step yields worse coherence, and a linear probe trained on true probabilities fails to generalize to held-out events. A replication with Llama-3.1-8b-instruct is reported in Appendix I.","tokens_in":14794,"tokens_out":3818,"duration_ms":40765,"significance":"If the central claim survives additional scrutiny, this is a useful contribution to interpretability and uncertainty estimation for large language models: it shows that a coherence prior can be injected through a latent-space symmetry rather than by post-hoc normalization, and that the resulting latent variable is partially interpretable. The paper has real strengths: a held-out test set with known ground-truth probabilities, an ablation study, a linear-probe comparison, and a second-model replication. The main risk is that the single sign-flip assumption is not directly validated, and the absolute calibration of the recovered probabilities depends on an unexplained temperature parameter. These are load-bearing issues rather than cosmetic ones, so the paper needs revision before the claims can be accepted at face value.","major_comments":[{"comment":"The reduction p(¬e|z,e) ≈ p(¬e|T(z)) with T(z)=[-z^(1), z^(-1)] is the load-bearing step of the method, but the paper provides no direct evidence that the decoder actually predicts held-out complementary embeddings through this single sign-flip. Because the dice template has essentially one probability-relevant scalar and many memorizable surface features (e.g., the word 'not' or numeric tokens), a latent z^(1) encoding any monotone confound correlated with probability would satisfy the training objective. Please report a quantitative measure of how well p_θ(¬e|T(z)) predicts held-out complementary embeddings, and test the sign-flip assumption on at least one non-dice domain or with templates that decorrelate surface features from probability.","section":"Section 3, Eq. (3)"},{"comment":"The scale of z^(1) is determined only by the VAE prior and reconstruction losses; converting z^(1) to a probability via the logistic function with 'temperature=5' introduces a free parameter that governs absolute probability calibration. Since the true probability is never observed during training, the reported MSE and correlation for P_recovered depend on this arbitrary scaling. Please justify the temperature value, report sensitivity to it, and either calibrate it on a validation split or derive it from the Gaussian prior and the trained decoder.","section":"Section 4, temperature parameter"},{"comment":"The abstract's claim that recovered probabilities 'align closely with the true probabilities' overstates the accuracy result: on the test set, P_recovered has MSE 0.1014, which is numerically worse than P_judged's 0.0927 and not statistically different (t(959)=-1.58, p=.12). Moreover, normalized P_judged has much lower incoherence (0.0021) than P_recovered (0.0383). The precise contribution is therefore improved coherence relative to raw P_judged, with accuracy comparable to direct judgments, not improved accuracy. Please reframe the claims accordingly and include normalized P_judged in the headline comparison.","section":"Section 4, Table 1 and Abstract"}],"minor_comments":[{"comment":"The 95% confidence interval for normalized P_judged on the test set is [-0.0020, 0.0062], but incoherence is a nonnegative quantity by definition (Eq. 8); this interval likely comes from a normal approximation and should be replaced with a bootstrap or other method that respects the nonnegative support.","section":"Table 1"},{"comment":"Please state explicitly whether 'temperature=5' divides z^(1) inside the sigmoid or scales the logit in Eq. (6); the current text says 'we applied the same value of 5 for temperature' without a formula, which makes the exact mapping ambiguous.","section":"Section 4, temperature description"},{"comment":"The reference to the Gemma team paper contains a typo ('none Gemma Team'); please correct this.","section":"References, [14]"},{"comment":"There is a typo in the text: 'P_judged from the Llamma model' should be 'Llama model'.","section":"Appendix I"},{"comment":"For layers 25 and earlier the correlations between recovered and true probabilities become strongly negative, but the paper does not comment on why this happens; a brief explanation or discussion would improve confidence in the method's stability across layers.","section":"Appendix F, Table 3"}],"recommendation":"major_revision","confidential_remarks":"The main concern is the unverified Eq. (3): if z1 is a surface confound rather than a probability feature, the central claim collapses. That said, the issue is empirically testable and the paper's scope is appropriately narrow (dice events with known ground truth). I recommend major revision rather than rejection, provided the authors add a direct test of complement-embedding prediction and address the calibration/framing issues."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is worth a look. It does something genuinely new: it trains a VAE on LLM embeddings with a sign-flip operation on one latent dimension, forcing the latent to behave like log-odds for complementary events. The twist is that true probabilities are never observed during training; coherence is enforced structurally. On dice events, the recovered probabilities are substantially more coherent than verbal judgments (incoherence 0.038 vs 0.137 on test) and track true probabilities about as well as direct judgments (r=0.73, MSE roughly 0.10). That is a legitimate proof of concept.\n\nI'll give credit where it's due: the framework is clean, the ablation (removing the complement-prediction step) shows Step 2 matters, and the linear probe baseline is a nice control—it nails the training set but falls apart out of sample, while the VAE generalizes. The latent interpretability checks (non-modified latents tracking rolls, sums, comparison type) are a nice bonus. And they replicated on Llama-3.1, though with weaker results.\n\nThe soft spots are mostly about how much I trust the load-bearing assumption. Equation (3) asserts that the entire complement relationship lives in a single latent that flips sign. On dice-templated prompts, any feature collinear with probability—like the number 5 or the word 'not'—could satisfy that objective. The paper never reports how well the decoder actually predicts held-out complement embeddings, which is the direct test of whether the sign-flip is doing real work. That gap should be filled.\n\nOther issues are smaller but real. The temperature/beta business is muddy: Eq. (6) is the plain logistic transform, yet the text says temperature=5 with no formula. That needs clarification. The strongest baseline—joint prompting with reasoning—only appears in an appendix, and it beats recovered probabilities on accuracy (MSE 0.07 vs 0.10) while being coherent. It should be in the main table. No code or data, and the test set is 480 dice events. So 'align closely' is true only for this narrow domain.\n\nNet: this is a solid conference paper candidate. The idea is novel and the experiments back the claim within their scope. What's missing is evidence that the single sign-flip assumption generalizes and a clean write-up of the conversion step. I'd send it to peer review; a good referee can push for those fixes without needing a rewrite.\n\nRecommended action: accept for review with the expectation of major revisions.","headline":"A clever proof-of-concept for extracting coherent probabilities from LLM embeddings via a sign-flip VAE, held back by an under-tested single-latent assumption and some reporting ambiguities.","tokens_in":15319,"tokens_out":3107,"would_cite":true,"duration_ms":30366,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A sign-flipped latent variable recovers event probabilities from LLM embeddings that add to one.","keywords":["event probabilities","LLM embeddings","coherence","variational autoencoder","log-odds representation","axiomatic constraints","complementary events","dice probability calibration"],"falsifier":"Construct a held-out set where complements are phrased without the word 'not' (for dice, 'rolling a 1, 2, 3, 4, or 5' versus 'rolling a 6') or use lexically unrelated complement pairs; then check whether the sign-flipped latent still recovers the true probabilities. If correlation with true probabilities drops toward zero while the text-judged probabilities stay accurate, the recovered latent was tracking the surface marker, not probability.","tokens_in":14319,"feed_emoji":"🎲","tokens_out":6132,"duration_ms":57236,"temperature":0.7,"pith_summary":"This paper asks whether coherent probabilities can be recovered from LLM embeddings even when the probabilities the model writes in text violate basic axioms. It claims yes: training a two-step variational autoencoder on embeddings of events and their complements, with complements generated by flipping the sign of one latent variable, makes probability emerge as log-odds in that dimension. Without ever being shown true probabilities, the recovered probabilities on held-out dice questions satisfy the complement rule far better than the model's text judgments and track the true probabilities. The broader point is that embedding space contains probability information that the model's own verbal responses do not faithfully report.","feed_headline":"Sign-flip latent recovers dice odds that sum to one","feed_subtitle":"A variational autoencoder reads hidden embeddings for dice events and beats the model's own text judgments on coherence.","key_machinery":"The load-bearing object is the first latent variable $z^{(1)}$ of a $\\beta$-weighted variational autoencoder ($\\beta$-VAE) trained directly on LLM embeddings. In Step 1 the VAE reconstructs embeddings from a ten-dimensional Gaussian latent space; in Step 2 it generates the complement embedding by applying $T(z)=[-z^{(1)}, z^{(-1)}]$ to the sampled latent vector. The centered isotropic Gaussian prior supplies the axiom: in log-odds space (i.e., $\\log(P/(1-P))$) the additive rule for complements is that log-odds sum to zero, so the sign-flip transformation combined with the logistic function $P=e^{z_1}/(1+e^{z_1})$ turns the latent operation into the probability-theoretic constraint.","core_discovery":"The central discovery is that enforcing the complement rule in latent space is enough to recover coherent probability estimates. In the trained encoder-decoder, the first latent variable $z^{(1)}$ behaves as log-odds: the complement embedding is generated by $T(z)=[-z^{(1)}, z^{(-1)}]$, and the centered Gaussian prior makes the log-odds of complementary events sum to zero; converting with $P=e^{z_1}/(1+e^{z_1})$ then enforces $P(A)+P(\\neg A)=1$. On a held-out test set of 480 dice events, probabilities recovered from Gemma-2-9b-instruct embeddings have incoherence 0.0383 versus 0.1366 for text judgments, correlate with true probabilities at $r=0.7328$, and reach MSE=0.1014. The same procedure improves coherence for Llama-3.1-8b-instruct, although with lower accuracy, suggesting that recovered quality tracks the model's underlying capability.","pith_inferences":["Editorial inference: if the one-dimensional log-odds encoding generalises beyond dice, the same sign-flip constraint could be applied to any paired event embeddings, effectively giving a coherence regulariser for downstream decision systems; the paper only demonstrates dice events.","Editorial inference: the Gemma versus Llama comparison suggests a testable diagnostic—use the VAE's recovered coherence as a proxy for the model's internal probabilistic calibration, independent of its text outputs.","Editorial inference: because $z^{(1)}$ appears to encode log-odds, intervening on it (e.g., flipping its sign while decoding) might change judged probabilities for complements, providing a causal route the paper does not test.","Editorial inference: the main risk is that $z^{(1)}$ captures the surface word 'not' rather than probability; a direct test is to use complements expressed without 'not' or with unrelated wording, and if the recovered probabilities collapse, the claim of probability encoding fails."],"forward_implications":["Coherent probabilities can be extracted from embeddings without true labels, opening an unsupervised route to calibrating LLM uncertainty in dice-like decision problems.","The method splits the latent space into interpretable dimensions: the modified latent tracks true probability, while others encode prompt features such as number of rolls, sum-versus-single-roll, and comparison type.","Recovery quality is tied to the source model: Gemma's recovered probabilities beat its own text judgments on coherence and match them on accuracy, while Llama's recovered probabilities improve coherence but remain less accurate, implying the internal representation's quality limits the method.","The ablation implies that predicting complement embeddings (Step 2) is necessary; without it a standard beta-VAE does not single out a probability-specialised latent variable, and the recovered probabilities are less coherent and less accurate.","A linear probe trained on true probabilities excels on training events but fails on held-out events, so the axiomatic unsupervised method generalises where supervised probing does not."],"supporting_citations":[{"why":"Documents the incoherence of LLM text-judged probabilities for complementary events, which is the baseline problem the paper aims to fix.","marker":"[41]"},{"why":"Provides the variational autoencoder objective and reparameterization trick used to learn the latent embeddings and derive the variational bounds.","marker":"[23]"},{"why":"Supplies the beta-VAE weighting of the KL term used to strengthen the centered Gaussian prior that encodes the additive rule.","marker":"[18]"},{"why":"Introduces Gemma-2-9b-instruct, the open-weight model whose embeddings and text judgments are used in the main experiments.","marker":"[14]"},{"why":"Introduces Llama-3.1-8b-instruct, used to replicate the recovery procedure and to show that recovered accuracy depends on the source model's coherence.","marker":"[11]"}],"fun_headline_variants":["Latent log-odds enforce probability axioms","VAE recovers coherent dice odds from LLM embeddings","Enforcing complement rule in latent space fixes LLM probabilities","Hidden embeddings yield coherent probabilities for LLMs","Axiomatic constraints in latent space recover true event odds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire method rests on the assumption that all probability-relevant information in an embedding is concentrated in a single latent dimension that flips sign when the event is complemented, and that this dimension is truly log-odds rather than a surface feature such as the word 'not'.","fun_headline_variants_meta":{"raw":{"variants":["Latent log-odds enforce probability axioms","VAE recovers coherent dice odds from LLM embeddings","Enforcing complement rule in latent space fixes LLM probabilities","Hidden embeddings yield coherent probabilities for LLMs","Axiomatic constraints in latent space recover true event odds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00025,"raw_usage":{"total_tokens":1555,"prompt_tokens":947,"completion_tokens":608,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":563,"completion_tokens_details":{"reasoning_tokens":533}},"tokens_in":563,"tokens_out":608,"duration_ms":5790,"temperature":1.0,"reasoning_tokens":533,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:35:13.436858+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a held-out set where complements are phrased without the word 'not' (for dice, 'rolling a 1, 2, 3, 4, or 5' versus 'rolling a 6') or use lexically unrelated complement pairs; then check whether the sign-flipped latent still recovers the true probabilities. If correlation with true probabilities drops toward zero while the text-judged probabilities stay accurate, the recovered latent was tracking the surface marker, not probability.","supporting_citations":[{"cited_title":"Incoherent probability judgments in large language models","cited_arxiv_id":null,"evidence_quote":"Documents the incoherence of LLM text-judged probabilities for complementary events, which is the baseline problem the paper aims to fix."},{"cited_title":"Kingma and Max Welling","cited_arxiv_id":null,"evidence_quote":"Provides the variational autoencoder objective and reparameterization trick used to learn the latent embeddings and derive the variational bounds."},{"cited_title":"beta-V AE: Learning basic visual concepts with a constrained variational framework.International Conference on Learning Representations, 3, 2017","cited_arxiv_id":null,"evidence_quote":"Supplies the beta-VAE weighting of the KL term used to strengthen the centered Gaussian prior that encodes the additive rule."}],"review_version":1}