{"id":"65a4c35d-0da9-40d8-8439-b25942cfd681","arxiv_id":"2502.10235","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Adapters that map multivariate time series into a latent space let a frozen univariate foundation model produce probabilistic multivariate forecasts, improving MSE on most tested tasks.","lead":"AdaPTS adds a trainable encoder decoder layer around a frozen univariate time series foundation model so the model can handle multivariate inputs and return probabilistic forecasts. On four public benchmarks it beats the unadapted Moment model in five of eight settings, matches it in two, and loses on one.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 5/8 headline is an oracle-selection count: each task is scored by the best of several tuned adapter variants, with no pre-specified choice rule and no released code, so multiple testing can produce the result; a pre-registered single-adapter evaluation is needed.","rationale":"The reader's weakest assumption, Assumption 3.3, is real but not the most load-bearing for the central claim. The paper labels the linear-FM assumption 'for ease of derivation,' and the empirical headline about improving Moment in 5 of 8 tasks would stand or fall on Table 1 regardless of Proposition 3.4. In fact, Proposition 3.4 is even weaker than the reader suggests: for a linear FM, the adapter matrix Wφ cancels in the input-dependent term, so the theory only characterizes a rank-one bias adjustment, and the proof's assertion that the loss is convex 'from the inverse operation' is false in general. This makes the theory section unsound but secondary. The load-bearing risk is that the empirical 5/8 count is computed by taking the best of several adapter variants per task, with no pre-specified selection rule and no released code; under multiple testing, such a count can arise by chance. If a pre-registered single configuration reproduces the improvement count, the concern is resolved. I therefore keep the CONDITIONAL verdict: the idea is plausible and the table is informative, but the main empirical claim should be verified under a fixed selection protocol before acceptance.","tokens_in":18139,"tokens_out":11545,"duration_ms":131007,"concrete_test":"Before seeing any test labels, define a deterministic model-selection rule on the validation splits, such as always picking the adapter family with the lowest validation MSE, with ties broken by a fixed order. Apply that rule to each of the 8 tasks, then evaluate the chosen configuration on the held-out test split and count tasks where it beats the Moment baseline. Also recompute the count using only the single best-on-validation variant per task; if the 5/8 count relies on variants that are not best on validation, the summary is post hoc. If a pre-registered selection rule yields fewer than 5 improvements, the headline result should be revised.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Table 1 evaluates several adapter variants (PCA, LinearAE, dropoutLinearAE, LinearVAE, VAE) per task, each with hyperparameters tuned on the validation split via Ray Tune/HEBO. The text's summary counts a task as an AdaPTS improvement if any one of these variants beats the Moment baseline (5/8), as a match if the best variant ties (2/8), and as a degradation otherwise. This is an oracle-selection bound, not the performance of a single reproducible AdaPTS procedure: no rule is given for choosing the adapter family from validation data alone. With five learned families plus multiple hyperparameter settings, the chance that at least one noisy variant beats the baseline on a task is high, so the 5/8 count is weak evidence that the framework, as a decision procedure, reliably improves on Moment. The reproducibility statement says code will be released only after acceptance, so the selection procedure cannot currently be audited. Note also that the '8% improvement' claimed for ETTh1 H=96 in Section 5.1 is not what Table 1 shows (0.411 to 0.395 is about 4%), suggesting the narrative summary is not tightly checked against the tables. If the 5/8 count is an artifact of post hoc selection, the central empirical claim loses its support.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces AdaPTS, a framework of feature-space adapters that map multivariate time series into a latent space, apply a frozen univariate foundation model (Moment) per channel, and map predictions back to the original space. Several adapter families are proposed (linear autoencoder, dropout linear autoencoder, linear VAE, VAE, plus PCA as a baseline), together with a theoretical analysis for the linear-adapter/linear-FM case and experiments on four multivariate benchmarks (ETTh1, Illness, Weather, ExchangeRate). The main empirical claim is that AdaPTS improves Moment's MSE in 5 of 8 tasks, matches it in 2, and degrades in 1, while providing probabilistic outputs and reduced-dimensional representations.","tokens_in":18486,"tokens_out":12217,"duration_ms":114727,"significance":"If the claims are correct, AdaPTS would be a simple, modular way to extend univariate time-series foundation models to multivariate probabilistic forecasting without fine-tuning the FM, with potential computational savings from dimensionality reduction. The paper is clearly written, the problem is well motivated, and the idea of using invertible or encoder-decoder feature transformations is interesting. The strengths are the breadth of adapter variants and the effort to provide both theory and experiments. However, the theoretical result in Proposition 3.4 contains a serious mathematical flaw (the claimed closed-form solution is singular), and the empirical '5/8' headline rests on an oracle-selection protocol rather than a single reproducible decision procedure. As presented, the evidence does not yet support the central claims; the concept may be salvageable with substantive corrections.","major_comments":[{"comment":"The closed-form solution W* = (B^T A)^+ B^T B is singular for D > 1 whenever B = b_FM 1^T, because B^T B has rank one and therefore rank(W*) <= 1. This violates Assumption 3.2, which requires W_phi to be in GL(D), and contradicts the invertibility requirement in Definition 3.1. The proposition therefore does not solve the constrained optimization problem over invertible adapters. The lambda-regularized form in Remark 3.5 solves a different objective, so it does not repair the theoretical claim.","section":"§3.2 / Proposition 3.4 and Appendix A.1"},{"comment":"The proof's assertion that L(W_phi) is convex in W_phi is incorrect: the map W -> W^{-1} is not affine, and the squared Frobenius norm of A - B W^{-1} is not convex in W over GL(D). For example, in the scalar case f(w) = (a - b/w)^2 the second derivative is (6b^2 - 4abw)/w^4, which can be negative. Consequently, the stationary-point condition derived in the proof does not establish global optimality, and the 'global solution' wording of Proposition 3.4 is unsupported.","section":"Appendix A.1"},{"comment":"The summary 'AdaPTS improves the forecasting accuracy of Moment in 5 out of the 8 considered tasks' is an oracle-selection count: for each task the best-performing adapter among PCA, LinearAE, dropoutLinearAE, LinearVAE, and VAE is chosen post hoc, with no pre-specified rule for selecting the adapter family from the validation set alone. Because each family has its own tuned hyperparameters, the probability that at least one variant beats the baseline on a task by chance is high, so the 5/8 count does not describe the behavior of a single reproducible AdaPTS procedure. Please report the test performance of a validation-selected adapter (with the selection rule stated), or fix the adapter family across all tasks, and also correct the '8% improvement' claim for ETTh1 H=96, since Table 1 shows a change from 0.411 to 0.395, about 4%.","section":"§5.1 / Table 1"},{"comment":"The theory assumes a linear foundation model f_FM(X) = W_FM^T X + b_FM 1^T, but all experiments use Moment, a deep nonlinear transformer. The paper labels the assumption 'for ease of derivation' but does not provide a nonlinear analogue or an argument that the linear result transfers to the actual experimental setting. Appendix D.1 replaces the closed form with gradient-based optimization for Moment, but this is an empirical observation, not a theoretical guarantee. If the theory is meant only as intuition, that should be stated clearly; if it is claimed as a foundation, a nonlinear analysis or an explicit scope limitation is needed.","section":"Assumption 3.3"}],"minor_comments":[{"comment":"The notation f_FM(X) is used both for the channel-wise application of a univariate model to a multivariate input and for the matrix form in Assumption 3.3; the dimensions of X, Y, and the adapter outputs should be stated more carefully.","section":"§3.1 / Eq. (1)"},{"comment":"The '8% improvement' for ETTh1 H=96 is inconsistent with Table 1: the MSE changes from 0.411 to 0.395, which is approximately a 4% improvement. Please correct this number.","section":"§5.1"},{"comment":"The reliability diagram's caption does not explain the color or shading used for different prediction horizons, and the figure reports only the first feature of one dataset, which is a limited basis for the general calibration claim.","section":"Fig. 5"},{"comment":"The abstract states 'We release the code', while the reproducibility statement says the code 'will be released' after acceptance; these statements should be made consistent.","section":"Reproducibility statement"},{"comment":"There is a typo: 'mean squred error' should be 'mean squared error'.","section":"Appendix C.2"},{"comment":"The chain rule expression for the gradient with respect to W_phi has a sign error: the correct expression is +2 W^{-T}(B^T A - B^T B W^{-1}) W^{-T}, not the negative. The stationary condition is unaffected, but the error should be fixed.","section":"Appendix A.1"},{"comment":"The main experiments use beta=0.5 and sigma=1.0 according to Table 3, while the ablation in Fig. 6 explores beta up to 4.0 and log sigma^2 up to 3.0; it would be helpful to state explicitly which hyperparameter values were used for each row of Table 1.","section":"Table 3 / Fig. 6"},{"comment":"The synthetic experiment appears to compute the loss on the same data used to derive W*; please specify whether the reported MSE is in-sample or on a held-out test set.","section":"§3.3"}],"recommendation":"major_revision","confidential_remarks":"The paper would benefit from a reviewer-visible code release before acceptance; the current policy of releasing code only after acceptance hampers reproducibility assessment, especially given the oracle-selection concern. The mathematical issues in Proposition 3.4 are substantive and should be fixed rather than merely acknowledged in a remark."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know about AdaPTS is that it packages a sensible idea — put a trainable invertible encoder–decoder around a frozen univariate foundation model and treat the latent space as stochastic to get probabilistic forecasts — and shows it can beat the plain per-channel Moment baseline on several tasks. That is genuinely useful for practitioners who want uncertainty estimates without fine-tuning a large model. The paper is also honest in places: it reports standard errors, includes ablations on latent dimension and β/σ, and admits the calibration is overconfident at longer horizons, which qualifies the abstract's uncertainty claim.\n\nThe new ingredient is the adapter family itself (linear AE, dropout LAE, linear VAE, VAE) applied to multivariate forecasting; the prior PCA adapters from the same group were for classification and RL. That framing is clear, and the appendix at least names the hyperparameters.\n\nNow the soft spots, in decreasing importance.\n\nFirst, the central empirical claim — \"improves on Moment in 5 of 8 tasks\" — is an oracle count. Each task is scored by the best of several adapter variants, each tuned with its own hyperparameters. There is no pre-specified rule for choosing the adapter family on validation data. With five families and HPO, some variant beating the baseline on a task is weak evidence that the framework as a decision procedure helps. The code is only released after acceptance, so the selection process cannot be audited. This is the main load-bearing weakness.\n\nSecond, the theory. Proposition 3.4 gives a closed-form optimal adapter under a linear-FM assumption, and the proof's convexity claim is shaky (the loss is convex in W_phi^{-1}, not W_phi; the gradient argument treats the inverse as the variable). The paper does not claim the result transfers to Moment, only labels it \"for ease of derivation,\" so it is a motivating example rather than a false claim. Fine, but then it shouldn't be presented as \"theoretical foundations of adapters.\" A short paragraph saying \"the linear case motivates the architecture; the nonlinear case is empirical\" would be more accurate.\n\nThird, the baselines. Only Moment with and without adapters, plus PCA. No comparison to other multivariate forecasting methods (iTransformer, PatchTST, etc.) or to established probabilistic baselines (DeepAR, etc.), so the practical gain is not benchmarked against the field.\n\nMinor: the \"8% improvement\" for ETTh1 H=96 is not what Table 1 shows (0.411 to 0.395 is ~4%). And in the MAE table, LinearAE on Illness H=24 lists 2.624±0.035, the same number as the MSE table, likely a copy-paste error.\n\nWho is this for? Researchers and engineers who want a cheap way to reuse a frozen univariate FM for multivariate probabilistic forecasting. The framework is simple and modular; if the code and a fixed selection rule appear in revision, the empirical claims could be verified.\n\nMy recommendation: send to peer review. The idea is useful, the authors are clear-eyed about limitations, and the flaws are fixable. A referee should push for a pre-specified adapter-selection rule, a release of code, a comparison against at least one strong multivariate baseline, and toning down the theory claims.","headline":"Useful adapter framework for multivariate forecasting with a frozen univariate FM, but the headline 5/8 result rests on best-of-many selection without a fixed rule, and the theory doesn't cover the actual nonlinear FM.","tokens_in":18955,"tokens_out":2393,"would_cite":false,"duration_ms":23631,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62M10","68T07","62F15"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that frozen univariate time-series foundation models can be extended to probabilistic multivariate forecasting by wrapping them in trainable feature-space adapters, and shows the recipe works on the Moment model…","keywords":["time series forecasting","foundation models","adapters","multivariate time series","probabilistic forecasting","uncertainty quantification","variational inference","Monte Carlo dropout"],"falsifier":"Run the synthetic linear experiment of Section 3.3 with a known linear foundation model and channel-dependent biases so that $B$ has full rank, compute $W^*_\\varphi$ from Eq. (4), and verify it attains the global minimum of the loss and beats the identity adapter; if the pseudo-inverse stabilization changes the optimum, the claimed global optimality is not established. For the nonlinear setting, train AdaPTS with the encoder removed and only a linear decoder; if accuracy gains persist, the paper's feature-transformation explanation is not the operative mechanism.","tokens_in":17975,"feed_emoji":"📈","tokens_out":8788,"duration_ms":86750,"temperature":0.7,"pith_summary":"Pre-trained time-series foundation models are usually univariate: they ingest one channel at a time, so applying them to multi-channel data means either processing channels independently, which ignores cross-feature structure, or fine-tuning the whole model. AdaPTS proposes to insert a trainable feature-space transformation, called an adapter, before a frozen univariate foundation model and invert it after forecasting, so the multivariate problem is solved in a learned latent space with no change to the backbone. The paper reports that this procedure improves the forecasting accuracy of Moment on 5 of the 8 tasks tested, matches it on 2, and degrades on 1, while stochastic versions of the adapters add probabilistic predictions and uncertainty estimates. The contribution is a modular recipe: keep the foundation model frozen, learn only the adapter, and thereby reuse univariate foundation models for multivariate probabilistic forecasting.","feed_headline":"Adapters let univariate time-series models forecast multivariate data","feed_subtitle":"Frozen Moment, wrapped in trainable feature transforms, beats per-channel baselines on 5 of 8 benchmark tasks.","key_machinery":"The carrying object is the adapter, formally defined as an invertible feature-space transformation $\\varphi: \\mathbb{R}^D \\to \\mathbb{R}^{D'}$ applied before the foundation model and inverted after it, so that predictions are obtained as $\\mathrm{dec}(f_{FM}(\\mathrm{enc}(X)))$. The probabilistic extension makes the encoder stochastic: a VAE adapter maximizes the ELBO $\\mathbb{E}_{q_\\varphi(Z|X)}[\\log p_\\theta(Y|X, f_{FM}(Z))] - \\mathrm{KL}(q_\\varphi(Z|X) \\| p(Z))$, and a dropout linear autoencoder treats dropout as approximate variational inference over adapter weights. The foundation model's parameters are frozen throughout; only the encoder and decoder are trained.","core_discovery":"Under linearity assumptions—linear adapter and linear foundation model—the paper derives the closed-form optimal adapter $W^*_\\varphi = (B^\\top A)^+ B^\\top B$, where $A = Y - W_{FM}^\\top X$ and $B = b_{FM} 1^\\top$, and proves that it beats the identity adapter on the forecasting objective. For the actual nonlinear case, AdaPTS instantiates adapters as linear and deep autoencoders and as probabilistic variants (VAE and dropout linear autoencoder) trained with an ELBO-style objective, and the experiments show MSE improvements on ETTh1 with $H=96$, Illness with $H=24$ and $H=60$, and Weather with $H=96$, matched performance on ETTh1 with $H=192$ and ExchangeRate with $H=96$, and degradation on ExchangeRate with $H=192$. The paper also claims that the learned latent representations overlap much better between training and test windows than the raw features, which it links to robustness against distribution shift, and that the probabilistic adapters are reasonably calibrated at short horizons.","pith_inferences":["The paper's theory covers linear foundation models only; the proof of adapter optimality does not transfer unchanged to nonlinear Moment, so the explanation for the empirical gains in the real experiments remains an open question.","If the decoder is the main source of gain, then adapters might be replaceable by a lightweight learned mapping on the FM's output alone, which would be cheaper still; the paper does not test this.","Because calibration degrades as the horizon grows, a deployment of AdaPTS would likely need horizon-dependent likelihoods or post-hoc recalibration to avoid overconfident long-range forecasts.","The latent-space overlap result suggests a testable extension: adapters should help most on multivariate tasks with strong train/test distribution shift, and could be evaluated on cross-domain forecasting benchmarks."],"forward_implications":["Any frozen univariate time-series foundation model can be lifted to multivariate forecasting by learning an adapter at its input and output, without retraining the backbone.","Reducing the latent dimension below the number of observed channels can preserve or improve accuracy while lowering inference cost; on Illness the VAE adapter reaches its best MSE with only two latent components.","Deterministic foundation models can return predictive distributions by using a stochastic adapter, with calibration that the paper shows is reasonable at short horizons.","The decoder is the main source of accuracy gain in the deterministic linear adapter, so learning to invert the forecast back into the original feature space matters more than the encoder's compression.","The benefit is not universal: on ExchangeRate with $H=192$ every adapter variant degrades relative to the no-adapter baseline, so gains depend on dataset and horizon."],"supporting_citations":[{"why":"Provides Moment, the frozen univariate foundation model that all AdaPTS experiments wrap and evaluate against.","marker":"Goswami et al., 2024"},{"why":"Exemplifies pre-trained univariate time-series foundation models that output distributions, motivating the adaptation problem.","marker":"Ansari et al., 2024"},{"why":"Supplies the dropout-as-approximate-variational-inference interpretation used to turn deterministic adapters into probabilistic ones.","marker":"Gal & Ghahramani, 2016"},{"why":"Provides the VAE and ELBO objective that underpins the probabilistic VAE adapter.","marker":"Kingma & Welling, 2013"},{"why":"Gives the partially stochastic Bayesian neural network results cited to justify stochastic encoders for universal conditional density estimation.","marker":"Sharma et al., 2023"},{"why":"Precursor work using lightweight adapters for multivariate time-series classification with many features.","marker":"Feofanov et al., 2024"},{"why":"Introduces the PCA-based adapter for preserving channel interactions, used as a baseline and motivation in the paper.","marker":"Benechehab et al., 2025"},{"why":"Supplies the $\\beta$-VAE regularization used in the actual VAE adapter training objective.","marker":"Higgins et al., 2017"}],"fun_headline_variants":["Adapters turn univariate FMs into multivariate forecasters","Proven optimal adapters for linear multivariate forecasting","Trainable adapters give univariate models multivariate power","Univariate model, multivariate data: adapters bridge the gap"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a linear model of the foundation model faithfully represents the setting where adapters help, but the actual foundation model in every experiment, Moment, is a deep nonlinear transformer, so the closed-form optimality proof does not directly cover the regime it motivates.","fun_headline_variants_meta":{"raw":{"variants":["Adapters turn univariate FMs into multivariate forecasters","Proven optimal adapters for linear multivariate forecasting","Trainable adapters give univariate models multivariate power","Univariate model, multivariate data: adapters bridge the gap"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000417,"raw_usage":{"total_tokens":2157,"prompt_tokens":961,"completion_tokens":1196,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":577,"completion_tokens_details":{"reasoning_tokens":1131}},"tokens_in":577,"tokens_out":1196,"duration_ms":13239,"temperature":1.0,"reasoning_tokens":1131,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T18:51:07.784779+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the synthetic linear experiment of Section 3.3 with a known linear foundation model and channel-dependent biases so that $B$ has full rank, compute $W^*_\\varphi$ from Eq. (4), and verify it attains the global minimum of the loss and beats the identity adapter; if the pseudo-inverse stabilization changes the optimum, the claimed global optimality is not established. For the nonlinear setting, train AdaPTS with the encoder removed and only a linear decoder; if accuracy gains persist, the paper's feature-transformation explanation is not the operative mechanism.","supporting_citations":[{"cited_title":"Do B ayesian neural networks need to be fully stochastic? In Ruiz, F., Dy, J., and van de Meent, J.-W","cited_arxiv_id":null,"evidence_quote":"Gives the partially stochastic Bayesian neural network results cited to justify stochastic encoders for universal conditional density estimation."},{"cited_title":"User-friendly Foundation Model Adapters for Multivariate Time Series Classification","cited_arxiv_id":"2409.12264","evidence_quote":"Precursor work using lightweight adapters for multivariate time-series classification with many features."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the PCA-based adapter for preserving channel interactions, used as a baseline and motivation in the paper."}],"review_version":1}