One of the key technologies for the success of Large Language Models (LLMs) is preference alignment. However, a notable side effect of preference alignment is poor calibration: while the pre-trained models are typically well-calibrated, LLMs tend to become poorly calibrated after alignment with human preferences. In this paper, we investigate why preference alignment affects calibration and how to address this issue. For the first question, we observe that the preference collapse issue in alignment undesirably generalizes to the calibration scenario, causing LLMs to exhibit overconfidence and poor calibration. To address this, we demonstrate the importance of fine-tuning with domain-specific knowledge to alleviate the overconfidence issue. To further analyze whether this affects the model’s performance, we categorize models into two regimes: calibratable and non-calibratable, defined by bounds of Expected Calibration Error (ECE). In the calibratable regime, we propose a calibration-aware fine-tuning approach to achieve proper calibration without compromising LLMs’ performance. However, as models are further fine-tuned for better performance, they enter the non-calibratable regime. For this case, we develop an EM-algorithm-based ECE regularization for the fine-tuning loss to maintain low calibration error. Extensive experiments validate the effectiveness of the proposed methods.

Our previous research introduced a novel Flat-ted Grating Folded Waveguide (FGFW) slow wave structure (SWS) for G-band traveling wave tubes (TWT). Compared to conventional folded waveguide (FW), FGFW demonstrates better EM characteristics. To further enhance performance, this paper proposes the ridge-enhanced flat-ted grating folded waveguide (RE-FGFW), which significantly increases interaction impedance and saturated output power. The RE-FGFW demonstrates superior interaction impedance and amplification performance in TWT applications compared to both the FGFW and FW.

This paper focuses on the problem of low-rank tensor completion, the goal of which is to recover an underlying low-rank tensor from incomplete observations. Our method is motivated by the recently proposed t-product [8] based on any invertible linear transforms. First, we define the new tensor average rank under the invertible real linear trans-forms. We then propose a tensor completion model using a nonconvex surrogate to approximate the tensor average rank. This surrogate overcomes the discontinuity of the tensor average rank and alleviates the bias problem caused by the convex relaxation. Further, we develop an efficient algorithm to solve the proposed model and establish its convergence. Finally, experimental results on both synthetic and real data demonstrate the superiority of our method.