RELISH: LLM REgression with a Latent Iterative State Head

Matthew Lease; Yiheng Su

REVIEW 3 major objections 3 minor 64 references

RELISH turns frozen LLM token features into accurate scalar predictions with a tiny iterative attention head, beating three standard families of text-regression methods.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-13 14:29 UTC pith:TPFJB7IL

load-bearing objection The supplied body is the wrong paper (QSP phase estimation, 2604.01205), so RELISH’s empirical claims cannot be audited from what we have. the 3 major comments →

arxiv 2604.01206 v2 pith:TPFJB7IL submitted 2026-04-01 cs.CL cs.LG

RELISH: LLM REgression with a Latent Iterative State Head

Yiheng Su , Matthew Lease This is my paper

classification cs.CL cs.LG

keywords text regressionlarge language modelsparameter-efficient learningcross-attention headfrozen backbonescalar predictionpredictive head

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that text regression with large language models should not treat numbers as text to decode or as many sampled generations to average. Instead, RELISH predicts a scalar directly from frozen LLM token representations by repeatedly refining a small learned latent state with cross-attention over those tokens, then mapping the final state with a linear regressor. Across six datasets, four backbones, and two training regimes, the method is claimed to outperform autoregressive decoding, regression-aware inference, and prior predictive heads while adding only about 3.4–3.7 million trainable parameters—roughly 0.01–0.04% overhead, far less than LoRA-style adapters that scale with model size. A sympathetic reader cares because it offers a path to strong numeric prediction from LLMs without expensive backbone fine-tuning or awkward number-as-text decoding.

Core claim

RELISH shows that iterative cross-attention refinement of a learned latent state over frozen LLM token representations, followed by a linear map, yields better text-regression accuracy than the main competing LLM regression families while remaining highly parameter-efficient on frozen backbones.

What carries the argument

The Latent Iterative State Head: a small learned latent vector is refined over multiple steps by cross-attending to frozen token-level LLM representations; the final state is mapped to a scalar by a linear regressor.

Load-bearing premise

The scalar target is already encoded well enough in frozen LLM token features that a small iterative attention head plus a linear map can recover accurate point estimates without training the backbone.

What would settle it

On the paper’s six datasets and four frozen backbones, check whether RELISH’s error is consistently lower than strong baselines from autoregressive decoding, regression-aware inference, and existing predictive heads at the stated ~3.4–3.7M trainable-parameter budget; if not, or if gains vanish when the backbone stays frozen, the central claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Text regression can treat the LLM as a frozen feature encoder and put almost all trainable capacity in a lightweight head.
Number-as-text decoding and multi-sample aggregation are not required for competitive scalar prediction from LLMs.
Parameter overhead for regression can stay roughly constant (~3–4M) rather than growing with backbone size as LoRA does.
The same head design is claimed to transfer across multiple datasets, backbones, and two LLM training regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If frozen features already carry the signal, similar iterative latent heads may help other continuous prediction tasks (ranking scores, risk, prices) without full fine-tuning.
Failure modes would concentrate where the target depends on information not linearly or attention-accessible in frozen last-layer tokens—e.g., rare numeric formats or deep multi-hop arithmetic.
A natural next test is whether deeper iteration or multi-layer latent states keep improving after the reported head size, or hit a plateau set by frozen representation quality.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

The supplied body is the wrong paper (QSP phase estimation, 2604.01205), so RELISH’s empirical claims cannot be audited from what we have.

read the letter

The one thing you need to know: we do not have the RELISH manuscript. The abstract is for arXiv 2604.01206 (LLM text regression with a latent iterative state head). The full text we were given is a different paper—programmable QSP-based quantum phase estimation (2604.01205). So this is not a review of RELISH’s methods, tables, or ablations; those are not present.

What the abstract claims is clear and useful if true: a small head that iteratively refines a latent state by cross-attention over frozen token representations, then a linear map to a scalar. It reports consistent wins over three LLM-regression families (autoregressive decoding, regression-aware inference, existing predictive heads) on six datasets, four backbones, two regimes, with only ~3.4–3.7M trainable params (0.01–0.04% overhead) versus larger LoRA-style alternatives. That is a concrete systems claim—parameter-efficient continuous scoring without decoding numbers as text—and the GitHub link is the right kind of artifact to check later.

I cannot credit the math, the data, or the citation pattern for RELISH because they are not in the packet. The weakest assumption in the abstract (that frozen token features already carry the scalar target in a form recoverable by iterative cross-attention plus a linear head) is exactly the kind of claim that needs ablations, matched budgets, and fair baselines; we do not have them. Free parameters (latent dim, iteration count, etc.) are also unspecified here.

The quantum paper that was pasted instead is a separate, serious-looking piece of work on signal design for phase estimation; it is not a substitute for evaluating RELISH. Treating that body as evidence for the LLM claims would be inventing a review.

Who this is for: people who care about efficient continuous labels from frozen LLMs. Right now the abstract alone is not enough for a reading group or for citation. A serious editor would still send the real RELISH paper to referees if the full version matches the abstract’s scope—the claim is important enough for the subfield and not desk-reject material on its face—but with the wrong body in hand I would not accept or reject the work itself. Get the actual PDF or the repo before spending more time.

Referee Report

3 major / 3 minor

Summary. The submission is titled and abstracted as RELISH, a lightweight head for text regression that iteratively refines a learned latent state via cross-attention over frozen LLM token representations and maps the final state to a scalar with a linear regressor. The abstract claims consistent gains over three families of LLM regression methods (autoregressive decoding, regression-aware inference, and existing predictive heads) across six datasets, four LLM backbones, and two training regimes, with only ~3.4–3.7M trainable parameters (0.01–0.04% overhead) on frozen backbones—less than LoRA-based alternatives. The body supplied with the submission, however, is an entirely different manuscript: “Programmable Signal Design for Quantum Phase Estimation via Quantum Signal Processing” (arXiv:2604.01205, quant-ph), which develops QSP-based max–min signal design, a sensitivity-efficiency parameter κ, an iterative QSP-PE algorithm, and numerical comparisons to robust phase estimation. No RELISH architecture, equations, datasets, metrics, or ablations appear in the full text.

Significance. If the abstract’s claims for RELISH were supported by a matching manuscript—fair baselines, ablations of the iterative latent state, and reproducible parameter counts—the work would be of clear interest to the LLM regression and parameter-efficient adaptation communities: a frozen-backbone head with sub-0.05% overhead that beats both decoding-based and head-based families would be a useful practical contribution. That significance cannot be assessed from the materials provided, because the scientific content of the body is quantum phase estimation, not text regression. The QSP-PE paper itself is a coherent contribution in its own field, but it is not the paper under review as RELISH.

major comments (3)

Title/abstract vs. full text: The abstract and paper_id identify RELISH (cs.CL, LLM text regression). The full manuscript is instead Programmable Signal Design for Quantum Phase Estimation via QSP (arXiv:2604.01205). There is no description of a latent iterative state head, cross-attention over token representations, linear regressor, six datasets, four LLM backbones, or the three baseline families. The central empirical claim of the abstract is therefore completely unsupported by the body and cannot be refereed.
Unauditable architecture and efficiency claims: The abstract asserts ~3.4–3.7M trainable parameters (0.01–0.04% overhead) and superiority to LoRA (0.26–0.42%). The body contains no RELISH parameter table, latent dimension, iteration count, or training protocol on frozen LLMs. Without those sections, the parameter-efficiency and “consistently outperforms” claims are not checkable and cannot ground acceptance.
Missing experimental evidence for the strongest claim: No tables, metrics, statistical tests, or ablations for text regression appear. The numerical figures and theorems in the body (e.g., κ vs. RPE, Theorem 1 on Heisenberg scaling, Algorithms 1/S1/S2) address quantum phase estimation, not LLM regression. A load-bearing evaluation of RELISH is impossible from this package.

minor comments (3)

The abstract alone is clear and well written; if a correct RELISH manuscript is resubmitted, the abstract can largely stand with only standard tightening of claims to match tables.
Code link https://github.com/SamSoup/RELISH is cited in the abstract but cannot substitute for a matching methods/results section in the journal submission.
The attached QSP-PE manuscript has its own presentation issues (e.g., duplicate [42] notes, mixed figure encoding in Fig. 1 caption text) but those are irrelevant to a RELISH decision.

Circularity Check

0 steps flagged

No circular derivation in RELISH: available claims are empirical outperformance and parameter counts, not results forced by definition or self-citation.

full rationale

Only the RELISH abstract is available for the claimed paper (arXiv:2604.01206); the supplied full manuscript body is a different work (QSP phase estimation, arXiv:2604.01205) and cannot be used as RELISH’s derivation chain. Within the RELISH abstract, the central claims are empirical—consistent gains over three LLM-regression families across six datasets, four backbones, and two regimes, plus a stated trainable-parameter overhead (~3.4–3.7M; 0.01–0.04%) versus LoRA. There is no equation that defines a quantity in terms of the quantity it purports to predict, no fitted parameter re-labeled as a first-principles prediction, no uniqueness theorem imported from overlapping authors, and no ansatz smuggled in via self-citation. The architecture description (iterative latent state refined by cross-attention over frozen token representations, then a linear map) is a design choice, not a circular identity. Circularity burden is therefore zero on the material that can be audited; missing method/tables is an evidence gap, not circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 1 invented entities

Abstract-only review of RELISH. Load-bearing premises are standard ML practice plus the architectural bet that frozen token features + iterative latent cross-attention suffice for scalar regression. No free parameters or invented physical entities appear in the abstract; training hyperparameters and dataset choices would be free parameters in a full paper but are not specified here.

free parameters (1)

Trainable head size / latent dimension and iteration count (unspecified)
Abstract reports ~3.4–3.7M trainable parameters but does not fix latent width, number of refinement steps, or other head hyperparameters that determine capacity and the reported overhead.

axioms (3)

domain assumption Frozen LLM token-level representations contain usable information for continuous targets without updating backbone weights.
Central to the frozen-backbone design claimed in the abstract.
ad hoc to paper Cross-attention iterative refinement of a latent state plus a linear map is an adequate inductive bias for text regression.
This is the paper’s architectural postulate; success is empirical, not derived from a theorem in the abstract.
domain assumption Standard supervised regression evaluation on the (unnamed in abstract detail) six datasets is a fair comparison across the three baseline families.
Outperformance claims rest on that experimental protocol, which is not inspectable here.

invented entities (1)

RELISH latent iterative state head no independent evidence
purpose: Map frozen LLM token representations to scalar predictions via iterative cross-attention state refinement and a linear regressor.
The named architecture is the paper’s main construct; independent evidence would be external replications or theory, not provided in the abstract.

pith-pipeline@v1.1.0-grok45 · 31217 in / 2528 out tokens · 25621 ms · 2026-07-13T14:29:34.555001+00:00 · methodology

0 comments

read the original abstract

We present RELISH (REgression with a Latent Iterative State Head), a novel, lightweight architecture designed for text regression with large language models. Rather than decoding numeric targets as text or aggregating multiple generated outputs, RELISH predicts scalar values directly from frozen LLM representations by iteratively refining a learned latent state through cross-attention over token-level representations, and then mapping the final state to a point estimate with a linear regressor. Across six datasets, four LLM backbones, and two LLM training regimes, RELISH consistently outperforms prior baselines from all three major LLM regression families, including autoregressive decoding, regression-aware inference, and existing predictive head methods. Despite these gains, RELISH remains highly parameter-efficient, requiring only $\sim$3.4-3.7M trainable parameters across frozen LLM backbones (only 0.01-0.04$\%$ additional overhead), far less than LoRA-based alternatives that grow with model size (0.26-0.42$\%$). Our code is available at https://github.com/SamSoup/RELISH.

discussion (0)

Reference graph

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Kentaro Yamamoto, Yuta Kikuchi, David Amaro, Ben Criger, Silas Dilkes, Ciar´ an Ryan-Anderson, Andrew Tranter, Joan M. Dreiling, Dan Gresh, Cameron Foltz, Michael Mills, Steven A. Moses, Peter E. Siegfried, Maxwell D. Urmey, Justin J. Burau, Aaron Hankin, Do- minic Lucchetti, John P. Gaebler, Natalie C. Brown, Brian Neyenhuis, and David Mu˜ noz Ramo. Quan...

Pith/arXiv arXiv 2025
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Note1.https://github.com/dongsnaq/ QPE-Phase-Estimation. Supplementary Material for Programmable Signal Design for Quantum Phase Estimation via Quantum Signal Processing Zikang Jia,1 Suying Liu,2,3, and Yulong Dong4 1Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA 2Department of Computer Science, University of Maryland, College...

2026
[54]

1, are based on the Hadamard test

Hadamard-test-based quantum phase estimation and its signal representation Standard methods for quantum phase estimation (QPE), as illustrated by the circuit in Fig. 1, are based on the Hadamard test. In this construction, repeated queries to the Hamiltonian time-evolution operator are sandwiched between Hadamard gates acting on an ancilla qubit, up to an...
[55]

As a result, a constant gap from the optimal value is preserved due to the use of a fixed complementary signal pair

More importantly, the signal family itself is fixed throughout the iterative estimation process, so prior information from earlier stages is not used to adapt the signal. As a result, a constant gap from the optimal value is preserved due to the use of a fixed complementary signal pair. This naturally raises the question of whether one can replace this re...
[56]

The algorithm interleaves oracles to the Hamiltonian with a sequence of phase-modulation gates whose angles encode the desired transformation

Transformation functions of quantum signal processing based phase estimation (QSP-PE) QSP is a powerful quantum algorithmic primitive for performing universal function transformations of an input Hamiltonian [14, 23, 28]. The algorithm interleaves oracles to the Hamiltonian with a sequence of phase-modulation gates whose angles encode the desired transfor...
[57]

Signal class and problem formulation of QSP-PE As stated in Theorem 3, the corresponding signal class consists of cosine transforms with definite parity, given by bounded trigonometric polynomials. This can be equivalently written as follows Gd := ( g(θ) = dX k=0 ak cos(kθ) :a k = 0∀k̸≡d(mod 2),and|g(θ)| ≤1∀θ ) .(S11) The measurement probability is given ...
[58]

(S15) is formulated as a max-min optimization over the admissible signal class Fd

Structure of the optimal design problem The optimal design principle in Eq. (S15) is formulated as a max-min optimization over the admissible signal class Fd. Since any admissible signal is the square of a transformation functiong∈ G d, the derivative offadmits a special structure. We restate this optimality principle in the following definition. Definiti...
[59]

One can then enforce a uniformly lower bounded sensitivity by imposing inequality constraints on a dense set of sampled points inI

Relaxed optimization reformulation A brute-force way to tackle the optimal design principle in Theorem 5 is to parametrize the transformation function gby its Fourier coefficients. One can then enforce a uniformly lower bounded sensitivity by imposing inequality constraints on a dense set of sampled points inI. Since the signal functionfis given by the sq...
[60]

We demonstrate that the optimal signal is attained over a bounded confidence interval, as shown in Fig

Numerical results of optimal signal design In this section, we numerically evaluate the performance of optimal signals constructed via the design principle in Algorithm S1. We demonstrate that the optimal signal is attained over a bounded confidence interval, as shown in Fig. S1, within which the sensitivity efficiencyκimproves monotonically as the interv...
[61]

The procedure iteratively refines a confidence interval forθestimation using optimized signals with bounded derivatives and resource-aware confidence updates

Iterative refinement scheme We consider an adaptive iterative estimator for a parameterθunder a resource schedule{(d k, mk)}k≥0, whered k is the query depth andm k is the number of measurement shots at stepk. The procedure iteratively refines a confidence interval forθestimation using optimized signals with bounded derivatives and resource-aware confidenc...
[62]

Therefore, estimating the unknown parameter by inverting the measurement outcome is 11 straightforward: we can recoverθby locating the intersection point on the signal curve

Classical post-processing One important feature of our designed signal function is that it has a uniformly lower-bounded derivative on the confidence interval. Therefore, estimating the unknown parameter by inverting the measurement outcome is 11 straightforward: we can recoverθby locating the intersection point on the signal curve. This is formally state...
[63]

As a result, the total quantum resource cost is dominated by the final step, which suggests the optimal Heisenberg-limited scaling

Heisenberg-limited quantum resource cost Recall that the depth schedule of our quantum algorithm is a geometric sequence. As a result, the total quantum resource cost is dominated by the final step, which suggests the optimal Heisenberg-limited scaling. In this subsection, we formally demonstrate that this adaptive framework attains this optimal scaling. ...
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As shown in Theorem 10, each post-processing step requires a total number of basic floating-point operations that scales linearly with the depth parameter

Classical computational cost of post-processing Thanks to the local monotonicity of the signal function, the classical post-processing can be carried out efficiently via bisection method. As shown in Theorem 10, each post-processing step requires a total number of basic floating-point operations that scales linearly with the depth parameter. Combining thi...

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(b) End-to-end signal programming framework

In contrast, QSP enables programmable signal transformations, allowing the signal to be tailored to a lo- cal confidence interval and achieving near-optimal sensitivity κ≈1. (b) End-to-end signal programming framework. Start- ing from a current estimate, the method designs an optimal signal by solving a max-min problem, implements it using a QSP circuit, ...

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By contrast, the versatility of QSP-based signals enables substantially larger uniform slope over the same interval, leading to higher sensitivity efficiency and improved constant factors in estimation precision. III. ALGORITHM AND PERFORMANCE GUARANTEE We develop an iterative phase estimation procedure based on progressive refinement of both the estimato...

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(c) Minimum derivative lower boundLas a function of query depthd, evaluated at three target phasesθ∈ {0.32,0.80,1.25} and shrinkage factorsζ∈ {1,2,5}

(b) Sensitivity efficiencyκas a function of shrinkage factorζ.κincreases monotonically withζ, and this improvement is uniform across all target phasesθ 0. (c) Minimum derivative lower boundLas a function of query depthd, evaluated at three target phasesθ∈ {0.32,0.80,1.25} and shrinkage factorsζ∈ {1,2,5}. For each combination ofθ andζ,Lis plotted againstda...

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(c) Optimized signal functionsf(θ) of QSP-PE (top) and RPE (bottom), with their corresponding Fourier mode decompositions shown at the lower right

At each depth, QSP-PE estimates are more tightly concentrated aroundθ ⋆, directly accounting for the lower MSE observed in (a). (c) Optimized signal functionsf(θ) of QSP-PE (top) and RPE (bottom), with their corresponding Fourier mode decompositions shown at the lower right. The QSP-PE signal achieves near-optimal sensitivity efficiencyκ= 0.915 and is con...

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2026

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1, are based on the Hadamard test

Hadamard-test-based quantum phase estimation and its signal representation Standard methods for quantum phase estimation (QPE), as illustrated by the circuit in Fig. 1, are based on the Hadamard test. In this construction, repeated queries to the Hamiltonian time-evolution operator are sandwiched between Hadamard gates acting on an ancilla qubit, up to an...

[55] [55]

As a result, a constant gap from the optimal value is preserved due to the use of a fixed complementary signal pair

More importantly, the signal family itself is fixed throughout the iterative estimation process, so prior information from earlier stages is not used to adapt the signal. As a result, a constant gap from the optimal value is preserved due to the use of a fixed complementary signal pair. This naturally raises the question of whether one can replace this re...

[56] [56]

The algorithm interleaves oracles to the Hamiltonian with a sequence of phase-modulation gates whose angles encode the desired transformation

Transformation functions of quantum signal processing based phase estimation (QSP-PE) QSP is a powerful quantum algorithmic primitive for performing universal function transformations of an input Hamiltonian [14, 23, 28]. The algorithm interleaves oracles to the Hamiltonian with a sequence of phase-modulation gates whose angles encode the desired transfor...

[57] [57]

Signal class and problem formulation of QSP-PE As stated in Theorem 3, the corresponding signal class consists of cosine transforms with definite parity, given by bounded trigonometric polynomials. This can be equivalently written as follows Gd := ( g(θ) = dX k=0 ak cos(kθ) :a k = 0∀k̸≡d(mod 2),and|g(θ)| ≤1∀θ ) .(S11) The measurement probability is given ...

[58] [58]

(S15) is formulated as a max-min optimization over the admissible signal class Fd

Structure of the optimal design problem The optimal design principle in Eq. (S15) is formulated as a max-min optimization over the admissible signal class Fd. Since any admissible signal is the square of a transformation functiong∈ G d, the derivative offadmits a special structure. We restate this optimality principle in the following definition. Definiti...

[59] [59]

One can then enforce a uniformly lower bounded sensitivity by imposing inequality constraints on a dense set of sampled points inI

Relaxed optimization reformulation A brute-force way to tackle the optimal design principle in Theorem 5 is to parametrize the transformation function gby its Fourier coefficients. One can then enforce a uniformly lower bounded sensitivity by imposing inequality constraints on a dense set of sampled points inI. Since the signal functionfis given by the sq...

[60] [60]

We demonstrate that the optimal signal is attained over a bounded confidence interval, as shown in Fig

Numerical results of optimal signal design In this section, we numerically evaluate the performance of optimal signals constructed via the design principle in Algorithm S1. We demonstrate that the optimal signal is attained over a bounded confidence interval, as shown in Fig. S1, within which the sensitivity efficiencyκimproves monotonically as the interv...

[61] [61]

The procedure iteratively refines a confidence interval forθestimation using optimized signals with bounded derivatives and resource-aware confidence updates

Iterative refinement scheme We consider an adaptive iterative estimator for a parameterθunder a resource schedule{(d k, mk)}k≥0, whered k is the query depth andm k is the number of measurement shots at stepk. The procedure iteratively refines a confidence interval forθestimation using optimized signals with bounded derivatives and resource-aware confidenc...

[62] [62]

Therefore, estimating the unknown parameter by inverting the measurement outcome is 11 straightforward: we can recoverθby locating the intersection point on the signal curve

Classical post-processing One important feature of our designed signal function is that it has a uniformly lower-bounded derivative on the confidence interval. Therefore, estimating the unknown parameter by inverting the measurement outcome is 11 straightforward: we can recoverθby locating the intersection point on the signal curve. This is formally state...

[63] [63]

As a result, the total quantum resource cost is dominated by the final step, which suggests the optimal Heisenberg-limited scaling

Heisenberg-limited quantum resource cost Recall that the depth schedule of our quantum algorithm is a geometric sequence. As a result, the total quantum resource cost is dominated by the final step, which suggests the optimal Heisenberg-limited scaling. In this subsection, we formally demonstrate that this adaptive framework attains this optimal scaling. ...

[64] [64]

As shown in Theorem 10, each post-processing step requires a total number of basic floating-point operations that scales linearly with the depth parameter

Classical computational cost of post-processing Thanks to the local monotonicity of the signal function, the classical post-processing can be carried out efficiently via bisection method. As shown in Theorem 10, each post-processing step requires a total number of basic floating-point operations that scales linearly with the depth parameter. Combining thi...