For-Value: Forward-Only Data Valuation

• For-Value is a forward-only data valuation framework that quantifies a training sample's impact by measuring the increase in validation likelihood during training.
• It avoids expensive gradients, Hessians, and retraining by leveraging forward activations and token prediction errors for rapid influence scoring.
• Empirical results show that For-Value effectively identifies influential examples and detects mislabeled data, outperforming traditional methods on LLMs and VLMs.

Searching arXiv for the specified paper and closely related data-valuation work to ground the article in recent research. For-Value is a forward-only data valuation framework for pretrained LLMs and vision-LLMs that estimates how much an individual training example helps a target validation example without using gradients, Hessians, or retraining. In the framework’s own formulation, a training sample is valuable to a validation sample if it makes the model’s likelihood of the validation sample increase more during training. The method is designed for settings in which existing valuation methods are computationally prohibitive for billion-parameter models, and it uses only forward activations and token prediction errors to produce per-sample influence scores from a single forward pass (Deng et al., 13 Aug 2025).

1. Position of For-Value within data valuation

For-Value addresses a problem that is central to data valuation more broadly: the need to quantify the contribution of individual data points to downstream model behavior. In the data-market literature, data value is treated as context-dependent and conditional on the buyer’s existing holdings, task, and market structure rather than as a fixed intrinsic property of a dataset (Raskar et al., 2019). For-Value instantiates that general perspective at the level of fine-tuning examples for foundation models: the value of a training sample is defined relative to a particular validation sample and relative to the model’s current predictive state (Deng et al., 13 Aug 2025).

The paper identifies several classes of prior valuation methods as impractical for pretrained LLMs and VLMs. Hessian- and influence-function-style approaches rely on gradients, Hessian information, or Hessian inverses or approximations. Retraining- and Shapley-style approaches require repeated training runs, subset evaluations, or stored model states. TracIn-like approaches require many checkpoints and gradient storage across checkpoints. The framework is therefore motivated by a deployment regime in which one may lack access to full fine-tuned weights, gradients, or the compute budget needed for retraining or second-order estimation (Deng et al., 13 Aug 2025).

This positioning is significant because other task-specific valuation methods in adjacent settings also attempt to avoid expensive model execution. In vertical federated learning, FedValue defines a model-free valuation metric based on conditional mutual information rather than training a predictive model (Han et al., 2021). In privacy-sensitive data marketplaces, ZK-Value seeks verifiable Shapley-style data attribution without exposing raw data, but does so through a specialized zero-knowledge pipeline rather than a forward-only representation-based estimator (Wang et al., 5 May 2026). A plausible implication is that For-Value belongs to a broader trend in which valuation is made practical by exploiting task structure and representation geometry instead of direct retraining.

2. Formalization of influence and the core score

The paper defines data value as the rate of change of the validation log-likelihood during training,

$\frac{d}{dt}\ln \pi_{\theta(t)}(y_v\mid x_v).$

Under the paper’s unconstrained-feature assumption, pretrained LLMs and VLMs produce rich hidden embeddings that are mapped to logits by an unembedding matrix $W$. The analysis then decomposes influence into two parts: one term mediated by shared hidden representations and token predictions, and a second special case involving shared input or overlapping outputs and the token-unembedding layer. When training and validation inputs are distinct, the second term vanishes, leaving the framework’s main score (Deng et al., 13 Aug 2025).

The key influence score is a weighted sum over validation-token and training-token positions: $$\sum_{k=1}^{|y_v|} \sum_{k'=1}^{|y_i|} \alpha_{k,k'} \cdot \left\langle h_{x_v, y_{v,<k}},\, h_{x_i, y_{i,<k'}} \right\rangle$$ with

$$\alpha_{k,k'} = \left\langle e_{y_{v,k}} - \pi_{\theta}(\cdot \mid x_v, y_{v,<k}), \; e_{y_{i,k'}} - \pi_{\theta}(\cdot \mid x_i, y_{i,<k'}) \right\rangle.$$

In this expression, the hidden-state inner product captures hidden-representation alignment, while $\alpha_{k,k'}$ captures token-level prediction-error alignment. The framework therefore values a training sample not merely because it is semantically similar to a validation sample, but because the model processes the two examples through similar hidden states and exhibits similar prediction errors on them (Deng et al., 13 Aug 2025).

The paper repeatedly emphasizes that hidden-state similarity alone is insufficient. If the prediction-error term is removed by setting $\alpha$ to $1$, the score becomes effectively an embedding-similarity method equivalent to the Emb baseline, and performance drops substantially. This suggests that For-Value is best understood as representation similarity weighted by learning-signal compatibility, not as a nearest-neighbor heuristic in feature space (Deng et al., 13 Aug 2025).

For efficient computation, the score is rewritten in a matrix inner-product form that aggregates token-wise contributions before comparing training and validation summaries. This reformulation allows valuation to be performed from forward outputs only, with no backpropagation stage (Deng et al., 13 Aug 2025).

3. Forward-only computation and computational profile

The practical algorithm consists of a forward pass on the validation example to obtain hidden states and token probabilities, batched forward passes on training examples, construction of token prediction errors of the form $e-p$, restriction of the computation to the seen vocabulary or in-batch vocabulary rather than the full vocabulary, and computation of the final score via the matrix-inner-product form. The method is therefore “forward-only” in a literal sense: it does not require gradient computation at any stage (Deng et al., 13 Aug 2025).

The paper reports the following complexity profile for For-Value.

Quantity	Reported complexity
Training complexity	$0$
Computational complexity	$O(nd|\hat V|)$
Memory complexity	$W$0

Here, $W$1 is the number of training samples, $W$2 is the embedding dimension, and $W$3 is the in-batch vocabulary size. The paper notes that $W$4 is usually small, often under $W$5, which is one reason the method is practical at scale (Deng et al., 13 Aug 2025).

This computational profile contrasts sharply with other valuation paradigms. Classical data-market valuation frameworks emphasize absolute, relative, and conditional valuation modes but do not provide a single-pass estimator for model-scale influence (Raskar et al., 2019). In verifiable marketplace settings, ZK-Value achieves proof generation in seconds to minutes and verification under $W$6 s, but its concern is privacy-preserving certification of valuation rather than cheap influence estimation inside a model (Wang et al., 5 May 2026). For-Value instead targets the internal auditing problem for pretrained LLMs and VLMs, where the critical bottleneck is avoiding Hessians, gradients, and retraining (Deng et al., 13 Aug 2025).

4. Empirical behavior on LLMs and VLMs

The empirical evaluation covers both influential-data identification and mislabeled-data detection. For LLMs, the paper evaluates Qwen2.5-1.5B and Llama-2-13B-chat on sentence transformations, math word problems without reasoning, and math word problems with reasoning. For VLMs, it evaluates Qwen2.5-VL-3B-Instruct and Llama-3.2-11B-Vision on image-to-text subject generation and image-to-text style generation. Across these settings, For-Value is reported to match or outperform Hessian-free, DataInf, HyperINF, and Emb in identifying impactful fine-tuning examples (Deng et al., 13 Aug 2025).

The paper reports that For-Value remains strong on both the smaller and larger text models, achieves near-perfect or perfect scores on some math settings, and performs best or near-best on multimodal tasks. The style-generation setting is particularly notable because the baselines degrade more sharply there, while For-Value remains robust. The qualitative analysis further shows that the method retrieves semantically relevant training samples, samples with the same transformation type, samples with the same math reasoning pattern, and samples with the same visual subject or style, while assigning low influence to unrelated samples (Deng et al., 13 Aug 2025).

For mislabeled-data detection, the paper uses a dog-vs-cat VLM question-answering setup with $W$7 labels intentionally flipped. It reports that For-Value substantially improves AUC over the best baseline on Qwen-VL-3B, achieves very high Recall, and matches near-perfect detection performance on the larger Llama-3.2-11B model. These results support the framework’s use for noise auditing and mislabeled-data detection in multimodal fine-tuning corpora (Deng et al., 13 Aug 2025).

The broader significance is that the method appears to preserve valuation quality while changing the computation regime from backward-pass-intensive to forward-only. This resembles a more general “for-value” design principle found in other domains: in unit commitment, for example, forecasts optimized for downstream operating cost can outperform forecasts optimized for RMSE, because the target is decision quality rather than a convenient proxy (Ghazanfariharandi et al., 17 Mar 2025). A plausible implication is that For-Value similarly optimizes the valuation surrogate around actual learning influence rather than around tractable but weaker proxies such as raw embedding similarity.

5. Relation to adjacent valuation frameworks

For-Value is specific to pretrained LLMs and VLMs, but it can be understood by contrast with several adjacent notions of value. In AI data markets, valuation has been framed as a combination of intrinsic factors such as relevance and uniqueness and extrinsic factors such as supply, demand, liquidity, and governance constraints. That literature also stresses conditional valuation: the worth of new data depends on what is already possessed (Raskar et al., 2019). For-Value specializes this conditional logic to foundation-model fine-tuning, where the “already possessed” object is the model’s learned representation and predictive state.

In vertical federated learning, FedValue uses MShapley-CMI, a master-conditioned Shapley formulation in which a data party’s contribution is quantified by conditional mutual information with respect to the task party’s existing features. It is model-free and task-specific, but it is designed for distributed feature holders rather than for token-level influence inside a pretrained generative model (Han et al., 2021). In data marketplaces, ZK-Value addresses an orthogonal problem: how to make Shapley-based valuation publicly verifiable while preserving privacy, using LSH-Shapley, bucket histograms, super-oracle batching, and sparsity skipping (Wang et al., 5 May 2026).

These contrasts clarify what For-Value is not. It is not a marketplace-pricing mechanism, not a Shapley approximation over coalitions, and not a privacy-preserving proof system. It is instead a single-pass influence estimator that exploits the hidden representations already produced by foundation models (Deng et al., 13 Aug 2025). This suggests that “value” in For-Value is closer to conditional learning utility than to price, payout allocation, or governance-mediated market worth.

6. Scope, assumptions, and interpretation

The framework’s theory depends on an unconstrained-features assumption, under which pretrained models produce expressive hidden embeddings independent of architecture details, logits are obtained through an unembedding matrix $W$8, and teacher-forcing training dynamics can be decomposed in terms of hidden states and error vectors. Under the additional assumption that training and valuation inputs are distinct, the theoretically relevant influence is captured by the weighted representation-alignment score described above (Deng et al., 13 Aug 2025).

The paper therefore presents For-Value as an approximation to how training examples change validation likelihood under gradient descent, not as an exact retraining-based causal estimate. Its reported strengths are accuracy, interpretability, and speed in settings where gradients, Hessians, or retraining are infeasible. Its intended applications are fine-tuning data selection, influential-example retrieval, mislabeled-data detection, and scalable auditing of LLM and VLM training corpora (Deng et al., 13 Aug 2025).

Within the broader research landscape, this places For-Value among methods that redefine value in operational rather than purely statistical terms. In manufacturing, value has likewise been treated as a multi-criteria performance notion rather than as a single monetary quantity (Mauchand et al., 2012). In personalized search, consultation value is explicitly distinguished from semantic similarity by incorporating scenario scope, posterior action value, and time decay (Qin et al., 17 Jun 2025). For-Value extends a comparable distinction to model auditing: similarity alone is not value; value emerges when representation alignment is coupled with aligned prediction errors and hence with aligned learning signal (Deng et al., 13 Aug 2025).