{"id":"2fcdd5a9-757f-4dda-8980-1cd0f9d8de06","arxiv_id":"2505.12383","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"TESALOCS, a hybrid of tensor-train sampling and local search, reports order-of-magnitude gains over gradient-only methods on 20 100-dimensional benchmarks, though the experimental baseline is incomplete.","lead":"A new optimization method samples promising starting points from a compact tensor model, then refines each one with standard gradient search. The authors report large gains on 100-dimensional benchmark functions, but the missing restart baseline weakens the comparison.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim lacks a same-budget random multi-start baseline: TESALOCS runs many restarts while 'Random' is one local search, so the tensor sampler's contribution is not isolated.","rationale":"I read the algorithm and experiments in good faith. The method is a coherent hybrid: TT sampling generates discrete candidates, local search refines them, and the best refined points update the TT model. The central claim is empirical, and for that claim to hold, the comparison must show that TT-based initialization, not merely multiple local restarts, drives the gains. The reader's weakest assumption identifies exactly that gap, and my reading confirms it: Section 3 contrasts TESALOCS with a single random-init run, while Algorithm 2.1 embeds many restarts in every budget. The paper's own related-work discussion of restarted local search makes the omission of a multi-start control particularly conspicuous. I also noticed data-quality warning signs in the variance columns and the absence of released code, but those are secondary; the decisive issue is the missing control. The proposed check is low-cost and would settle the concern on a single benchmark before re-evaluating the full tables. Given the current evidence, the reader's REJECT verdict is appropriate, so no adjustment is needed.","tokens_in":13306,"tokens_out":5412,"duration_ms":61476,"concrete_test":"On a representative case (e.g., Rastrigin or Rosenbrock with BFGS), run random multi-start BFGS at equal budget: draw 100 i.i.d. uniform starting points, allocate 100 function evaluations to each (total 10^4), and report the best final value over starts. Compare this to the corresponding TESALOCS entry in Table 1. If random multi-start attains comparable or better error, the TT sampler adds no measurable value beyond restarting.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Algorithm 2.1 (lines 4–6) samples k=100 candidates per iteration and runs an independent local search from each; line 11 charges the whole batch's evaluations to the budget. Within M=10^4 evaluations this is a multi-start method, with many more than one restart per run. Section 3's baseline, however, is described as 'random selection of the starting point' and appears to be a single local search per benchmark. Hence the 'orders of magnitude' advantage in Tables 1–3 may reflect the number of starts rather than the TT-based sampler's ability to identify promising basins. The paper even cites restarted local search as related work but never runs it as a control. A secondary reproducibility issue: Tables 1–3 contain identical variance entries across unrelated functions (e.g., σ=7.2e-01 repeated for Sphere and Squares rows in Table 1), and no code or data are released, so the numbers cannot be independently checked. The empirical claim is not supported as stated; the right control is a random multi-start baseline under the same evaluation budget and the same local optimizer.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes TESALOCS, a hybrid optimizer that alternates between sampling candidate starting points from a low-rank tensor-train surrogate model over a discrete grid and refining those candidates with an arbitrary local optimizer (e.g., BFGS, PSO). The surrogate is updated by an SGD step on the log-likelihood of elite refined points. The authors claim that, under a budget of 10^4 function evaluations on 20 100-dimensional benchmark functions, TESALOCS improves on random initialization by orders of magnitude when wrapped around six gradient-based and three gradient-free optimizers. The main contribution is the algorithmic framework rather than a new tensor decomposition, with a stated emphasis on the plug-and-play nature of the local-search component.","tokens_in":13477,"tokens_out":2333,"duration_ms":24222,"significance":"If the empirical claims were established, TESALOCS would be a practically relevant contribution: it offers a dimension-scalable, budget-controlled way to turn any local optimizer into a global method, leveraging the low-parameter TT representation for exploration. The paper explicitly presents fixed hyperparameters across all benchmarks, which is a step toward a fair comparison, and the algorithmic description in Section 2 is clear enough to reimplement. The conceptual bridge between discrete tensor sampling and continuous local refinement is timely given the recent success of TT-based black-box optimizers like PROTES. However, the significance is currently conditional on a comparison that is not yet properly controlled, and on data that show signs of reporting errors.","major_comments":[{"comment":"The central comparison lacks a same-budget random multi-start baseline. In Algorithm 2.1, each iteration samples k=100 candidates and runs an independent local search from each, charging all evaluations to the budget M=10^4; this makes TESALOCS a multi-start method with many restarts per run. The 'Random' baseline in Section 3, described as 'random selection of the starting point,' appears to be a single local search per benchmark. The reported gains, including the abstract's 'orders of magnitude,' may therefore reflect the number of restarts rather than the tensor sampler's ability to identify promising basins. A control in which the same local optimizer is run from the same number of randomly chosen starting points under the same total evaluation budget is required to isolate the contribution of the TT-based sampling; the paper cites restarted local search but never runs it as a comparison. Without this control, the central empirical claim is not established.","section":"Section 3, Algorithm 2.1, Tables 1-3"},{"comment":"Several variance entries appear to be duplicated across unrelated benchmark functions in a way that cannot reflect independent 10-run experiments. For example, in Table 1 under BFGS the 'Random' column reports σ=7.2e-01 for Sphere, Squares, and also for Schaffer and Yang (7.3e-01, 7.2e-01), and the same pattern recurs under CG and L-BFGS-B; in Table 2, the TNC 'Random' column shows σ=1.3e-12 for both Chung and Alpine, and σ=4.9e-01 for both Exp and Griewank. Since these functions have completely different landscapes and scales, identical variances across all functions and methods are implausible. This indicates a reporting or data-processing error that undermines confidence in the numerical results and in the claim that TESALOCS reduces variance.","section":"Tables 1-3"},{"comment":"No code, data, or detailed experimental configuration is released, and the paper does not state how the 'Random' baseline is run for the gradient-free methods (e.g., whether PSO is run once with a random initial population or with multiple restarts). Given the absence of a baseline and the irregularities in the variance tables, the reported numbers cannot be independently verified. For a paper whose main evidence is empirical, providing the implementation or at least a precise pseudocode for the baseline and the local-search budget allocation is necessary.","section":"Section 3, reproducibility"},{"comment":"The abstract claims improvement 'by orders of magnitude with the same computing budget,' but several benchmark rows show only modest gains. For instance, in Table 1, Ackley improves from 2.0e+01 to 1.8e+01 (roughly 10%), Pathological from 3.8e+01 to 3.0e+01, and Wavy from 5.9e-01 to 3.6e-01. The order-of-magnitude framing is not representative of all 20 functions, and the summary statistics ('# of best results') mix cases where TESALOCS is slightly better with cases where it is dramatically better. The claim should be made precise, for example by reporting geometric mean ratios or a distribution of improvements, rather than relying on headline counts.","section":"Abstract and Tables 1-3, 'orders of magnitude' claim"}],"minor_comments":[{"comment":"In the introduction, 'particle swarm optimization (PSA)' is a typo; the correct abbreviation is PSO, as used elsewhere in the paper.","section":"Section 1"},{"comment":"In the Wavy row, TESALOCS with PSO reports E=4.4e-01 versus Random PSO E=3.1e-01, yet the table still counts this row as a TESALOCS victory in the '# of best results' count (18). Either the row is an error or the counting rule needs clarification.","section":"Section 3, Table 3"},{"comment":"The term 'co-convergence' is used without definition; it should be stated explicitly that 'both approaches achieve errors < 1e-8' and what action is taken in that case for the victory count.","section":"Section 3, paragraph after Table 2"},{"comment":"The input list includes an 'SGD algorithm' but the stopping criterion for the SGD update, its learning rate, and the number of epochs are not specified. Since these are fixed hyperparameters, they should be reported to make the experiments reproducible.","section":"Algorithm 2.1"},{"comment":"The caption lists 'six optimization algorithms (Newton-CG, SLSQP, TNC, BFGS, CG, and L-BFGS-B)' and the figure shows six curves per plot, but the legend is not described; please clarify which line corresponds to which algorithm, as the current text is ambiguous.","section":"Figure 2"}],"recommendation":"major_revision","confidential_remarks":"The paper has a conceptually interesting core idea, but the experimental section needs substantial rework: add a same-budget random multi-start baseline, correct the variance tables, and ideally release code. The duplicated variance entries are a red flag that should be checked carefully; if they stem from a copy-paste error, the authors need to rerun the experiments. I would not reject outright because the algorithmic framework is coherent and the missing control is a straightforward experiment, but the current version is not yet publishable. I also note that the related-work section is heavily self-cited (TTOpt, PROTES, and other works from the same group), which is acceptable given the direct lineage, but the paper should still position itself against generic restart strategies more explicitly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core idea here is reasonable and clearly presented: use a TT-based discrete sampler to propose starting points, refine each with any local optimizer, and update the TT model with the elite refined points. It is a natural extension of PROTES/TTOpt, and the paper is honest that no theoretical guarantees are offered. The benchmark suite is broad, and the writing is readable.\n\nThat said, the headline empirical claim is not supported as stated. In Algorithm 2.1, each iteration samples k=100 candidates and runs an independent local search from each. The baseline, described only as 'random selection of the starting point,' appears to be a single local search from one random point. Under the same budget of 10^4 evaluations, TESALOCS is effectively a multi-start method, so the 'orders of magnitude' gains in Tables 1–3 could come from having many more starting points rather than from the tensor sampler finding good basins. The paper even cites restarted local search as related work, yet never runs a same-budget random multi-start control. That control is the one experiment that would isolate the contribution of the TT surrogate.\n\nThere are also reproducibility issues. Several variance entries are identical across unrelated functions (e.g., Sphere and Squares in Table 1), which looks like a copy-paste slip. No code or data are released, so the numbers cannot be checked independently. These are secondary to the missing baseline, but they compound the credibility problem.\n\nWhat the paper does well: the algorithm is simple to describe, the modular plug-in of arbitrary local optimizers is a genuine practical feature, and the convergence curves in Figure 2 are a nice touch. The parametric memory cost of the TT model is a real advantage in high dimension.\n\nWho this is for: researchers in black-box optimization who might use a TT-based sampler as a warm-start provider. The paper deserves a serious referee, not a desk reject, because the core idea is worth testing under a fair baseline. But as submitted, the abstract's promise is unearned. My recommendation: send to peer review, but require a random multi-start baseline with the same local optimizer and the same evaluation budget, plus a cleanup of the tables and ideally a code release. With those fixes, the empirical claims could become credible.","headline":"A plausible hybrid optimizer whose central empirical claim is not isolated: the baseline is a single random-start local search while TESALOCS runs many restarts inside the same budget, so the tensor sampler's contribution is unproven.","tokens_in":14027,"tokens_out":1425,"would_cite":false,"duration_ms":16242,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["90C26","65K05","15A69"],"pacs":[],"model":"deepseek-v4-flash","headline":"A tensor-train sampler can feed a local optimizer better starting points, and the paper shows this cuts error by orders of magnitude.","keywords":["high-dimensional optimization","tensor train","low-rank tensor","black-box optimization","local search","sampling","benchmark functions","hybrid optimization"],"falsifier":"Run TESALOCS against a same-budget random multi-start baseline, for example the same local optimizer launched from many uniformly random points totaling $10^4$ evaluations, on the same 20 functions in 100 dimensions; if the random multi-start matches or beats TESALOCS' errors, the central empirical claim is refuted.","tokens_in":13068,"feed_emoji":"🎯","tokens_out":7627,"duration_ms":68401,"temperature":0.7,"pith_summary":"The paper claims that the main obstacle to high-dimensional optimization is the starting point: gradient-based methods converge quickly but only within the basin they start from. It proposes TESALOCS, a two-phase loop that samples candidate starting points from a low-rank tensor-train surrogate, refines each with an arbitrary local optimizer, and then updates the surrogate toward the best refined points. On 20 100-dimensional benchmark functions with a budget of $10^4$ function evaluations, the reported errors are often orders of magnitude smaller than the same local optimizer started from a single random point, and similar gains appear with gradient-free local methods. If the claim is right, any existing or future local optimizer can be wrapped by TESALOCS to gain global exploration at the same evaluation cost.","feed_headline":"Tensor-trained sampling beats random starts in 100-D optimization","feed_subtitle":"Adaptive low-rank sampling gives local optimizers better starts, cutting errors by orders of magnitude.","key_machinery":"The load-bearing object is the TT-surrogate: a $d$-dimensional tensor stored as $d$ TT-cores, each of size at most $R \\times N \\times R$ (here $R=5$, $N=2^{20}$), whose normalized entries define a discrete probability distribution over grid points. Sampling from it costs linear time in $d$ via the procedure of Dolgov et al., and the SGD update on the log-likelihood of elite points moves probability mass toward basins found by local search. The low parameter count of the TT representation is what makes this density expressive enough for 100 dimensions while memory and sampling cost stay linear in $d$.","core_discovery":"TESALOCS alternates between a discrete surrogate and a continuous local method. A $d$-dimensional tensor in TT-format with rank $r$ is initialized randomly and acts as a discrete probability distribution over an $N$-point grid; each iteration samples $k=100$ multi-indices from it, projects them onto continuous points, runs a local optimizer from each, keeps the best $k_{\\mathrm{top}}=10$ refined points, projects them back, and performs an SGD step on the negative log-likelihood of those elite points. The claim is that this loop concentrates the sampler around basins that the local optimizer can actually polish, so the same number of function evaluations spent on these informed restarts yields lower error than spending them on one run from a random point. Across 20 100-dimensional benchmark functions with budget $10^4$ and fixed hyperparameters ($r=5$, $N=2^{20}$, $k=100$, $k_{\\mathrm{top}}=10$), the paper reports best results in 15 to 20 of 20 cases against each gradient-based method and similar gains over gradient-free baselines, often by orders of magnitude and with lower variance.","pith_inferences":["Editorial inference: the reported gains may come substantially from restarting many local searches rather than from information carried by the tensor surrogate; a same-budget random multi-start baseline would separate these two effects.","Editorial inference: the log-likelihood update is a form of density focusing, so TESALOCS can be viewed as an implicit niching or racing mechanism; comparing it to a covariance-matrix-adaptation strategy with restarts would test whether the TT representation adds value beyond standard distribution adaptation.","Editorial inference: fixing $N=2^{20}$ and $r=5$ means the grid is extremely fine, so a testable prediction is that performance should degrade gracefully as $N$ or $r$ shrink, and the sampler's marginal value should vanish on unimodal landscapes where one local run suffices.","Editorial inference: because the scheme is decoupled from the decomposition format and the local solver, a natural extension is constrained or noisy optimization by restricting the sampling support or using robust local refiners."],"forward_implications":["Any local optimizer can be wrapped by TESALOCS; the paper demonstrates this with six gradient-based solvers and three gradient-free heuristics, so future local solvers could inherit the same global exploration layer.","Under a fixed budget of $10^4$ evaluations, informed restarts produced by the TT sampler reduce average error and variance relative to single random-start runs on nearly all 20 test problems.","Because the TT-format's storage and sampling scale linearly in dimension, the method is intended to remain practical as $d$ grows, as long as the target landscape is smooth enough for local refinement.","For non-differentiable or noisy objectives, the local phase can be a derivative-free heuristic, which extends the method past the requirement of gradient availability."],"supporting_citations":[{"why":"Defines the tensor-train decomposition used as the low-rank surrogate in Equation (1) and supplies the storage and rank properties.","marker":"Oseledets [2011]"},{"why":"Provides the linear-complexity procedure for sampling from a TT-format probability distribution, the sampler's core operation.","marker":"Dolgov et al. [2020]"},{"why":"Introduces PROTES, the probabilistic tensor-sampling optimizer that TESALOCS extends by adding continuous local refinement.","marker":"Batsheva et al. [2023]"},{"why":"Establishes TT-based black-box optimization on discrete spaces, the line of work TESALOCS bridges to gradient methods.","marker":"Sozykin et al. [2022]"},{"why":"Supplies the 20 non-convex benchmark functions and their known global minima used in all experiments.","marker":"Jamil and Yang [2013]"},{"why":"Underpins the quasi-Newton local search methods used as the local refinement phase and as baselines.","marker":"Nocedal and Wright [2006]"},{"why":"Defines particle swarm optimization, one of the gradient-free baselines and example local solvers.","marker":"Kennedy and Eberhart [1995]"},{"why":"Defines SPSA, another gradient-free baseline used to show TESALOCS works without gradients.","marker":"Spall [1992]"}],"fun_headline_variants":["Tensor sampling gives local optimizers a smarter start in 100-D","TESALOCS: tensor sampling turns random starts into gold mines","Low-rank tensor sampling beats gradient methods by orders of magnitude","TESALOCS: smarter restarts for 100-D optimization","Tensor-trained sampling boosts local search in high dimensions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The experimental comparison uses a single local search from one random starting point as the baseline, while TESALOCS effectively spends the same budget on many restarts; if a same-budget random multi-start baseline performs just as well, the tensor sampler adds no measurable value.","fun_headline_variants_meta":{"raw":{"variants":["Tensor sampling gives local optimizers a smarter start in 100-D","TESALOCS: tensor sampling turns random starts into gold mines","Low-rank tensor sampling beats gradient methods by orders of magnitude","TESALOCS: smarter restarts for 100-D optimization","Tensor-trained sampling boosts local search in high dimensions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00055,"raw_usage":{"total_tokens":2648,"prompt_tokens":989,"completion_tokens":1659,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":605,"completion_tokens_details":{"reasoning_tokens":1588}},"tokens_in":605,"tokens_out":1659,"duration_ms":11753,"temperature":1.0,"reasoning_tokens":1588,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:35:30.355081+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run TESALOCS against a same-budget random multi-start baseline, for example the same local optimizer launched from many uniformly random points totaling $10^4$ evaluations, on the same 20 functions in 100 dimensions; if the random multi-start matches or beats TESALOCS' errors, the central empirical claim is refuted.","supporting_citations":[{"cited_title":"Tensor-train decomposition","cited_arxiv_id":null,"evidence_quote":"Defines the tensor-train decomposition used as the low-rank surrogate in Equation (1) and supplies the storage and rank properties."},{"cited_title":"Approximation and sampling of multivariate probability distributions in the tensor train decomposition","cited_arxiv_id":null,"evidence_quote":"Provides the linear-complexity procedure for sampling from a TT-format probability distribution, the sampler's core operation."},{"cited_title":"PROTES : probabilistic optimization with tensor sampling","cited_arxiv_id":null,"evidence_quote":"Introduces PROTES, the probabilistic tensor-sampling optimizer that TESALOCS extends by adding continuous local refinement."},{"cited_title":"TTOpt : A maximum volume quantized tensor train-based optimization and its application to reinforcement learning","cited_arxiv_id":null,"evidence_quote":"Establishes TT-based black-box optimization on discrete spaces, the line of work TESALOCS bridges to gradient methods."},{"cited_title":"A literature survey of benchmark functions for global optimization problems","cited_arxiv_id":null,"evidence_quote":"Supplies the 20 non-convex benchmark functions and their known global minima used in all experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Underpins the quasi-Newton local search methods used as the local refinement phase and as baselines."}],"review_version":1}