Iterative Vectors: In-Context Gradient Steering without Backpropagation

We thank the reviewer for their feedback and the opportunity to reflect. We believe the concerns raised warrant clarification to ensure a balanced perspective.

Claim 1

1. We do not intend to assert that "gradient simulation" is, in itself, a novel concept. We respectfully request the reviewer to consider the following points. Reviewer u1JW observed that "while activation steering has been explored in various contexts, its application to ICL appears novel." Additionally, Reviewer qbmE summarized that "the novelty of IVs lies in their ability to work within the activation space of language models to refine meta-gradients without backpropagation, offering a scalable solution to enhance language model performance."
2. We do not present the theory from Dai et al. [1] as our own contribution (stated in Lines 58, 68, and 78). Rather, we use it as inspiration and a foundation for developing our method (see Line 71).
3. A comprehensive and equitable evaluation framework, which represents one of our key contributions, is absent in both FV and TV. These studies utilize diverse designs for extraction rationale, hyperparameter selection, and editing strategies. It is essential to quantify these elements fairly while maintaining flexibility within a new, unified framework. Establishing such an evaluation framework is a significant undertaking and cannot be accomplished merely by "rewriting the formalism."
4. The reviewer observed that Dai et al. have already validated their theories concerning gradient simulation. As established by the derivation of IV in our work, our approach builds upon their concept of meta-gradients, which is tautological to our claim being "grounded in the idea of meta-gradients". As IV aligns with and builds upon this foundation, replicating such validated theoretical groundwork would be a duplication rather than a meaningful contribution to the field. Our focus is on demonstrating that IV’s effectiveness in practical settings does not hinge on replicating idealized or approximated scenarios, e.g., unnormalized attention approximation employed in Dai et al. It is important to highlight that strict adherence to simulation-based validation risks conflating theoretical approximations with the robustness of our method in real-world deployments. Our framework’s success in tackling complex tasks—validated empirically—underscores that IV’s utility transcends the need for such simulations.

Claim 2

On real-world tasks, FV shows only marginal improvements and requires an excessive amount of time (up to 20x longer), making it impractical. TV performs inadequately, failing 50% of the models on average. In contrast, IV consistently excels in performance, efficiency, and scalability. Please refer to our response to Reviewer u1JW for details.

Weaknesses

1. It is common practice to assume the theoretical foundation established in previous work to be valid, and our experimentation partly serves to further validate these hypotheses. Given that IV and the two baselines belong to the same family of methods—namely, activation vectors—one would naturally expect similarities in form. In Appendix E, we have thoroughly distinguished how IV differs from the methodologies introduced by Todd et al. [2] and Hendel et al. [3] in terms of theoretical support, extraction and editing processes, scaling efficacy, and other aspects. We are perplexed by the reviewer's comment, particularly given their claim to have read Appendix E, and we find it difficult to understand why the new insights we provided have been overlooked.
2. Please refer to the discussion of Claim 1 above.
3. With all due respect, we cannot concur with this assessment. The fact that the iterative updates and batched extraction incorporate an averaging operator does not render them "similar" to basic averaging, nor does it diminish their novelty and significance as part of our method. First, they naturally derive from the gradient simulation, and second, they play a crucial role in the dynamics of our method, validated through ablative studies (Section 4.5 and Figure 3). This is not observed in Todd et al., where the activation of certain attention heads is merely averaged without being reintegrated into the model for refinement, thus completely lacking the iterative and batched update elements.
4. Our analysis of scaling in Sections 4.3 (IVs Scale with In-Context Demonstrations) and 4.4 (IVs Improve with Increased Extraction Episodes) is not intended as a novel contribution or exploration. Instead, it serves as part of our validation process to rigorously assess the robustness and consistency of our method, as indicated by the section titles. The similarity in the validation process is not a weakness; rather, it demonstrates alignment with established methods [4].

We hope this clarification underscores the methodological and empirical significance of our contributions to enhancing LM capabilities.

We are delighted that the reviewer described our method as "conceptually simple" and "useful for practical use." We are committed to improving clarity in line with their suggestions.

We will condense Section 3.1 and utilize the space to introduce the verbalizer, while relocating some of the discussion on hyperparameters to the main body of the manuscript in the final version. We appreciate the suggestion to incorporate some examples in relevant parts and agree that it would be advantageous.

Regarding the results, we note that the term "impressive" does not appear in our manuscript. We interpret this quotation as a positive indication of the reviewer’s assessment and sincerely thank their acknowledgment. Nevertheless, we will elaborate on the significance of our results while also addressing Reviewer KR8h's concerns, particularly their issues regarding Claim 2.

The averaged metrics in Table 1 represent rigorous evaluation across 13 distinct benchmark tasks, systematically demonstrating IV's cross-task proficiency. To enhance interpretability, we now focus our presentation on the mean relative performance gains compared to the fundamental ICL baseline, intentionally omitting exhaustive task-specific data to highlight core comparative insights.

1. The improvements in IV are significant, whereas FV and TV lag considerably behind. Our method demonstrates superior performance across all models, achieving an average relative score of 3.21—5.4x higher than FV (0.60) and 80x greater than TV (0.04).
2. The performance of IV scales with increased model capacity. IV consistently outperforms baseline methods in every model configuration, with particularly strong results in larger models (4.69 vs 1.36/0.25 for llama-2-13b). This indicates a promising potential for application to even larger models, as evidenced by our experiments with the Llama-2-70b model, detailed in the supplementary experiment in Table 8.
3. While FV/TV demonstrate limitations in practical applications, IV consistently excels across real-world tasks. IV maintains robust performance gains in all evaluated scenarios, whereas FV/TV exhibit significant performance degradation compared to standard ICL in 37% of the cases (3/8)—a concerning regression that undermines their viability despite their computational overhead. This empirical evidence directly refutes Reviewer KR8h's skepticism by demonstrating that FV/TV's shortcomings extend beyond synthetic environments to critically impact real-world effectiveness.
4. Table 2: IV achieves optimal efficiency without compromising performance. In 2-shot and 3-shot settings, the inference times are 2,434s and 3,426s, respectively. However, IV achieves the same score of 12.90 as the 2-shot setting in 1,452s—41% faster—and exceeds the 3-shot performance (12.64). Crucially, IV reduces feature extraction time by 95% compared to FV (23.75 min vs 438.3 min), while maintaining a 20% performance advantage over TV (12.90 vs 10.30). While TV's naive architecture enables rapid extraction, this approach exhibits catastrophic failure in 50% of the model averages, as previously shown. This positions IV as the most time-effective solution, balancing accuracy with practical computational demands.
5. Table 3: IV boosts high baselines while maintaining ICL compatibility, delivering +3.37% on AG News’ near-peak 5-shot (82.47%→85.84%) and +17.22% on Rotten Tomatoes’ 2-shot (70.28%→87.50%). Consistent gains across all shots (1-5) confirm its compatibility with the ICL framework.
6. Table 4: IVs surpass ICL prompt limitations through scalable example utilization, delivering consistent gains with ≥3 episodes (+0.57–7.6%) even under fixed hyperparameters. While minor fluctuations occur with fewer episodes (≤2), performance robustly scales with example volume, proving IVs extract value beyond conventional ICL ceilings.
7. Figure 3: The hyperparameter interactions enable adaptive optimization. Larger batches enable the utilization of refined vectors through increased inference strength ($\alpha_2$). Incorporating iterative refinements yields significant gains, demonstrating their essential role in our contribution.

In summary, IV demonstrates consistent superiority across three critical dimensions: (1) performance (3.21 average gain vs 0.60/0.04 for FV/TV), (2) efficiency (95% faster extraction than FV, near-ICL inference speeds), and (3) scalability (robust gains from higher-shot settings and more demonstrations). We affirm that IV represents a practical, theoretically grounded advance for activation vectors, with broader implications for resource-efficient NLP.

1. Thank you for your thoughtful review and engagement with our work. We acknowledge that certain technical aspects may require further clarification to ensure our contributions are clearly communicated. We will strive to refine our explanation by addressing the points raised.
2. The term “activation vector” serves as an umbrella concept encompassing lightweight vectors that manipulate language model within their representation space (Lines 91–94). Depending on implementation specifics, these vectors may interact with FFN layers, attention mechanisms, or both, and their positioning can vary. Formulas 12 and 13 are presented to illustrate the general principle of activation vector extraction and application. These formulations are intentionally abstract, as their instantiations necessitate flexibility. For IV, we have provided explicit explanations of all these concepts. IVs are clearly defined in Formulas 21 (preliminary version) and 24 (final version) as a set of vectors. The position is specified in Line 262 for extraction ("each attention layer $l$ of the LM") and Line 306 for application ("the $l$-th attention layer $\text{Attn}_l(\cdot)$"). This is also directly deducible from the theoretical foundations.
3. We clarify that Figure 1 is not intended to demonstrate the proposed methodology. As stated in its caption (“A general illustration of [...] activation vectors”, instead of IV), its purpose is solely to provide conceptual grounding for readers less familiar with activation vectors. We explored incorporating the iterative aspect into Figure 2 during development. However, this introduced significant visual complexity that risked obscuring the core concept, which the reviewer already find challenging to grasp. We reasoned that readers familiar with gradient-based training processes—where iterative steps are inherently extrapolated from single-step mechanics—would find the progression to an iterative framework intuitive. For full transparency, the iterative procedure has been relocated and is rigorously detailed in Algorithm 1. That said, we thank the reviewer for this feedback and acknowledge the value of visual documentation. We will revise the figure to include the iterative process in the final version.
4. This subtraction becomes readily apparent through the theoretical development in Section 3.1. As demonstrated in Formula 9, in-context demonstrations function analogously to meta-gradients, decomposing the activation during inference into two components: a) Zero-shot activation: The baseline behavior inherently generated by the language model for a given query. b) ICL-derived meta-gradients: Task-specific updates learned from in-context demonstrations. By isolating and subtracting the zero-shot component (which is constant across inference passes for the same query), we select and extract the meta-gradients representing the ICL adjustments. This ensures that only the refined updates—not the baseline behavior—are applied to subsequent inferences. Furthermore, consider the activation's magnitude. Our approach involves adjusting it in our desired direction using potentially small amounts of meta-gradients. Without the subtraction, the process reduces to simply adding raw activations from one run to another, which could confuse or potentially overwhelm the model.
5. As defined in Line 259, $\text{Act}(x_i)$ represents the activation for the $i$-th input-output separator. These separators are integral to each $x_i$, specifically as the last token of each, and the subsequent token, denoted as $y_i$, is generated by the language model at the position of the separator token. This generation process causally considers all preceding tokens, including all prior $(x_i, y_i)$ demonstration pairs. Therefore, by definition, each $\text{Act}(x_i)$ has access to the information contained in all preceding pairs $\{(x_j, y_j) \mid j < i\}$ as well as the current $x_i$. Next, regarding "different demonstrations," we assume the reviewer intended to refer to either: a) distinct $(x_i, y_i)$ pairs within a single prompt, as discussed previously, or b) separate prompts with various sets of example prefixes. This is pertinent to the iterative refinement process, where additional demonstrations are integrated.
6. The proposed method is applicable to generative tasks. However, incorporating it would further complicate the evaluation framework and comprehension. Therefore, we have decided to address this in future work.
7. To address this issue, we conducted an additional experiment, testing Llama-3.1-8b on ag_news with a near-upper-bound few-shot selection baseline (200 selections $\times$ 200 validations = 40,000 episodes, twice as many as IV's setup). Its macro-F1 score of +6.87 still underperformed compared to IV’s +7.66 by 10%, demonstrating IV’s superiority even against extensive demonstration tuning.

We value your expertise and look forward to addressing any remaining questions.