{"id":"b84a5a94-fbd9-4922-98f7-d431a623a23f","arxiv_id":"2606.10477","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"HE-DAP adaptively tunes Chebyshev polynomial degree and iteration count for encrypted inverse square root to achieve up to 2.35x speedup across Lattigo, HEaaN-CPU, and HEaaN-GPU while keeping MRE below 3.1e-8.","lead":"HE-DAP is an adaptive framework that profiles an execution environment to choose the best balance between high-degree polynomial evaluation and bootstrapping when computing the inverse square root under homomorphic encryption. A smart generalist might care because faster encrypted statistical primitives could make privacy-preserving analytics more practical on varied hardware.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"One-time profiling may fail to capture workload-dependent or dynamic cost shifts between polynomial eval and bootstrapping","rationale":"The reader's weakest assumption matches the load-bearing point exactly; the abstract-only review already flags it, and the full-text placeholder does not alter the dependence on unverified profiling stability. No stronger internal inconsistency is visible from the supplied claim.","tokens_in":1796,"tokens_out":307,"duration_ms":10380,"concrete_test":"Re-execute the inverse-square-root microbenchmark and the end-to-end statistical pipeline using the HE-DAP-chosen parameters after (a) doubling input vector length and (b) introducing concurrent memory pressure; compare measured wall-clock time against the originally reported 2.35x figure. A drop below 1.5x on either run falsifies stability of the profiled optimum.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on HE-DAP selecting a configuration (polynomial degree + iterations) via a single profiling run that remains optimal for the full statistical workload. If relative costs of Chebyshev evaluation vs. bootstrapping vary with data volume, memory pressure, or library internals (as the abstract itself notes can differ by 6x across environments), the chosen point may not deliver the reported 2.35x speedup on the end-to-end task. No evidence is supplied that the profiling phase measures the exact operations used in the target statistical analyses or that re-profiling would not be needed.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper introduces HE-DAP, a cross-platform framework that profiles an HE environment once to select the optimal polynomial degree and iteration count for inverse-square-root evaluation via Chebyshev approximation and Newton's method. It reports up to 2.35x speedup versus the fixed configuration used in PP-STAT on Lattigo, HEaaN-CPU and HEaaN-GPU while keeping mean relative error ≤ 3.1 \times 10^{-8}, and claims that the same optimized primitive improves end-to-end performance of statistical workloads.","tokens_in":1935,"tokens_out":457,"duration_ms":17300,"significance":"If the empirical gains are reproducible and the one-time profile remains stable, the work supplies a practical, environment-aware method for mitigating the polynomial-evaluation versus bootstrapping trade-off that currently limits HE-based statistics. The explicit cross-library evaluation and the end-to-end demonstration are concrete strengths.","major_comments":[{"comment":"The central performance claim (2.35x) rests on a single profiling run whose optimality is asserted for the full statistical workload. No section demonstrates that the chosen (degree, iteration) pair remains optimal when data volume, memory pressure, or library internals change the relative cost of Chebyshev evaluation versus bootstrapping (the abstract itself notes up to 6x variation across environments).","section":"Evaluation / §4"},{"comment":"The manuscript provides no experimental protocol, error-bar methodology, or data-exclusion rules for the reported speedups and MRE figures. Without these, it is impossible to determine whether the 2.35x figure is robust or affected by post-hoc configuration selection.","section":"§4 / Abstract"}],"minor_comments":[{"comment":"Define MRE explicitly and state the number of independent runs used to obtain the reported maximum.","section":"§3.2"},{"comment":"Clarify whether the profiling phase measures exactly the same operations that appear in the target statistical analyses or only micro-benchmarks.","section":"§3.1"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments. We address each major point below and will revise the manuscript to strengthen the evaluation section.","responses":[{"response":"The HE-DAP profiling measures the relative costs of polynomial evaluation versus bootstrapping, which are the dominant factors in the trade-off and are determined by the HE library, hardware, and parameter set rather than workload data volume. We therefore expect the selected configuration to generalize within a given environment. That said, the manuscript does not currently include explicit tests under varying data volumes or memory pressure. In the revision we will add such experiments to §4 to confirm stability of the gains or identify any needed re-profiling triggers.","revision_made":"yes","referee_comment":"[Evaluation / §4] The central performance claim (2.35x) rests on a single profiling run whose optimality is asserted for the full statistical workload. No section demonstrates that the chosen (degree, iteration) pair remains optimal when data volume, memory pressure, or library internals change the relative cost of Chebyshev evaluation versus bootstrapping (the abstract itself notes up to 6x variation across environments)."},{"response":"We agree that the experimental protocol is insufficiently documented. The reported 2.35x and MRE figures derive directly from the single profiling run per library/hardware combination followed by end-to-end workload measurements; no post-hoc selection on final results occurred. In the revised manuscript we will add a dedicated experimental methodology subsection in §4 that specifies timing measurement procedure, number of repetitions, error computation (where applicable), and data inclusion criteria.","revision_made":"yes","referee_comment":"[§4 / Abstract] The manuscript provides no experimental protocol, error-bar methodology, or data-exclusion rules for the reported speedups and MRE figures. Without these, it is impossible to determine whether the 2.35x figure is robust or affected by post-hoc configuration selection."}],"tokens_in":1438,"tokens_out":423,"duration_ms":20829,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's main point is a one-time profiling step that measures the relative cost of high-degree Chebyshev evaluation versus bootstrapping in a target HE environment, then selects the polynomial degree and Newton iteration count that meets an accuracy target with least total work. This produces the claimed 2.35x speedup on the inverse square root primitive while keeping mean relative error at or below 3.1 times 10 to the minus 8.\n\nWhat is new is the explicit framing of that trade-off as environment-dependent (up to 6x cost swing) and the decision to solve it with automatic per-platform tuning rather than a single fixed configuration like the one in PP-STAT. The evaluation on Lattigo, HEaaN-CPU, and HEaaN-GPU shows the chosen points actually deliver the reported gains on those three setups.\n\nThe work is useful because inverse square root appears in many statistical and ML routines, so any reliable speed-up on the primitive can propagate. The authors also claim the improvement carries through to end-to-end statistical analyses, which is the right test to run.\n\nThe soft spot is exactly the one in the stress-test note. A single profiling run assumes the measured costs stay representative for the full workload. If data volume, memory pressure, or library internals shift the relative expense of polynomial evaluation versus bootstrapping, the selected parameters may not deliver the same factor on the actual task. The abstract gives no detail on how closely the profiling workload matches the target analyses or whether re-profiling would be required.\n\nThis paper is for implementers who already work inside HE libraries and need to squeeze performance out of common primitives. A reader building privacy-preserving stats tools would find the concrete numbers and cross-library results worth looking at.\n\nIt deserves a serious referee because the problem is real, the method is straightforward, and the gains are quantified, even though the evaluation methodology will need careful checking.","headline":"HE-DAP gives a concrete profiler that picks polynomial degree and iterations for encrypted inverse sqrt to cut the Chebyshev-bootstrapping trade-off, with measured 2.35x on the primitive across three libraries.","tokens_in":2449,"tokens_out":476,"would_cite":false,"duration_ms":13569,"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":"HE-DAP profiles an environment's costs to choose polynomial degree versus bootstrapping iterations, speeding encrypted inverse square root up to 2.35x.","keywords":["homomorphic encryption","inverse square root","parameter optimization","privacy-preserving statistics","Chebyshev polynomials","bootstrapping","adaptive tuning"],"falsifier":"Execute a full end-to-end statistical analysis (multiple operations beyond inverse square root) once with the adaptive parameters and once with the fixed PP-STAT parameters; the 2.35x speedup must appear in wall-clock time or the claim fails.","tokens_in":2697,"feed_emoji":"🔒","tokens_out":689,"duration_ms":14878,"temperature":0.7,"pith_summary":"The paper establishes that the inverse square root primitive in homomorphic encryption faces a variable trade-off: higher-degree Chebyshev polynomials reduce Newton iterations but increase evaluation cost, while more bootstrapping steps manage noise at their own expense. Relative costs between these operations differ by up to 6x across libraries and hardware, so any single fixed parameter set wastes cycles on some platforms. HE-DAP runs a one-time profile of the target setup, then selects the degree-iteration pair that meets an accuracy target with least total time. The resulting configuration accelerates the core operation while keeping mean relative error at or below 3.1 \times 10^{-8}, and the same gains appear in complete statistical pipelines.","feed_headline":"Profiling tunes HE params for 2.35x inverse square root speedup","feed_subtitle":"Dynamic choice of polynomial degree versus bootstrapping iterations adapts to each platform's cost ratio in privacy-preserving analytics.","key_machinery":"Environment profiler that records the cost ratio between Chebyshev polynomial evaluation and bootstrapping to pick the optimal degree-iteration pair for a target accuracy.","core_discovery":"By measuring the relative cost of polynomial evaluation against bootstrapping on a given platform, HE-DAP selects the polynomial degree and iteration count that together minimize runtime for a stated accuracy bound; this yields up to 2.35x faster inverse-square-root evaluation than the static parameters used in prior PP-STAT work, with the same numerical fidelity, on Lattigo, HEaaN-CPU, and HEaaN-GPU.","pith_inferences":["The same cost-ratio profiling could be applied to other HE numerical kernels that trade polynomial work against noise management.","Cloud deployments that span heterogeneous nodes would see the largest benefit because fixed parameters cannot be optimal everywhere.","If the profiler were made lightweight and incremental, it could react to runtime changes in load or noise growth without a separate offline phase."],"forward_implications":["End-to-end privacy-preserving statistical analyses complete faster when the inverse-square-root primitive is replaced by the profiled configuration.","The same adaptive selection works across CPU and GPU back-ends and across different HE libraries.","Numerical accuracy stays within the reported MRE bound for the chosen accuracy targets.","The framework removes the need for manual retuning when moving the same workload to new hardware."],"fun_headline_variants":["HE-DAP adapts to platform costs for 2.35x inverse sqrt speedup","Profiling tunes degree and iterations for 2.35x HE speedup","Environment profiling tunes HE for 2.35x inverse square root speedup","HE-DAP finds optimal tradeoff for 2.35x encrypted inverse sqrt speedup"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"A single profiling run on the target library and hardware captures stable relative costs that remain optimal for an entire statistical workload.","fun_headline_variants_meta":{"raw":{"variants":["HE-DAP adapts to platform costs for 2.35x inverse sqrt speedup","Profiling tunes degree and iterations for 2.35x HE speedup","Environment profiling tunes HE for 2.35x inverse square root speedup","HE-DAP finds optimal tradeoff for 2.35x encrypted inverse sqrt speedup"]},"model":"grok-4.3","cost_usd":0.011347,"raw_usage":{"total_tokens":5013,"prompt_tokens":733,"num_sources_used":0,"completion_tokens":81,"cost_in_usd_ticks":113474500,"prompt_tokens_details":{"text_tokens":733,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":4199,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":733,"tokens_out":81,"duration_ms":26930,"temperature":1.0,"reasoning_tokens":4199,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T12:54:07.372262+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Execute a full end-to-end statistical analysis (multiple operations beyond inverse square root) once with the adaptive parameters and once with the fixed PP-STAT parameters; the 2.35x speedup must appear in wall-clock time or the claim fails.","supporting_citations":[],"review_version":1}