Sparse autoencoders (SAEs) are typically applied at the single layer they were trained on. We ask whether a pretrained SAE’s per-prompt feature activations persist when the same SAE is applied to residuals at deeper layers of the underlying language model, and whether the resulting cross-layer signal is strong enough to drive per-prompt FFN neuron pruning without any training or calibration data. Testing three SAE families on three roughly 8B-scale language models, we find adjacent-layer carry-through is high across families (0.72–0.82 at L_src+1) and its rate of decay differs qualitatively across sparsification mechanisms, with JumpReLU still activating half the features 17 layers downstream while TopK degrades within about five. We propose FARN (Feature and Anchor-based Removal of Neurons), a training-free per-prompt FFN pruner that scores each downstream neuron on the SAE’s decoder columns weighted by the current prompt’s active features, plus a prompt-independent anchor from the decoder bias. On six multiple-choice benchmarks, keeping roughly 17–20% of FFN neurons per layer, FARN closes the gap to an activation oracle (a baseline that peeks at the true downstream activations to pick the top-firing neurons) to within 1.5 percentage points and outperforms random, magnitude, and calibrated static-activation baselines on every model.

In this paper, we propose a novel negotiation agent designed for the online marketplace. Our dialogue agent is integrative in nature i.e, it possesses the capability to negotiate on price as well as other factors, such as the addition or removal of items from a deal bundle, thereby offering a more flexible and comprehensive negotiation experience. To enable this functionality, we create a new dataset called Integrative Negotiation Dataset (IND). For this dataset creation, we introduce a new semi-automated data creation method, which combines defining negotiation intents, actions, and intent-action simulation between users and the agent to generate potential dialogue flows. Finally, the prompting of GPT-J, a state-of-the-art language model, is done to generate dialogues for a given intent, with a human-in-the-loop process for post-editing and refining minor errors to ensure high data quality. We first train a maximum likelihood loss based model on IND, and then employ a set of novel rewards specifically tailored for the negotiation task to train our Integrative Negotiation Agent (INA). These rewards incentivize the agent to learn effective negotiation strategies that can adapt to various contextual requirements and price proposals. We train our model and conduct experiments to evaluate the effectiveness of our reward-based dialogue agent for negotiation. Our results demonstrate that the proposed approach and reward functions significantly enhance the negotiation capabilities of the dialogue agent. The INA successfully engages in integrative negotiations, displaying the ability to dynamically adjust prices and negotiate the inclusion or exclusion of items in a deal bundle.