Multimodal Large Language Models (MLLMs) frequently suffer from hallucination issues, generating information about objects that are not present in input images during vision-language tasks. These hallucinations particularly undermine model reliability in practical applications requiring accurate object identification. To address this challenge, we propose TL-DPO, a preference learning approach that mitigates hallucinations by focusing on targeted areas where they occur. To implement this, we build a dataset containing hallucinated responses, correct responses, and target information (i.e., objects present in the images and the corresponding chunk positions in responses affected by hallucinations). By applying a preference learning method restricted to these specific targets, the model can filter out irrelevant signals and focus on correcting hallucinations. This allows the model to produce more factual responses by concentrating solely on relevant information. Experimental results demonstrate that TL-DPO effectively reduces hallucinations across multiple vision hallucination tasks, improving the reliability and performance of MLLMs without diminishing overall performance.

We design polar codes for q-ary input, q = 2r, that polarize to an arbitrary given subset of extremal configurations out of the original triangular array of r +1 such configurations. We also obtain a new proof of the known result about 2-level polarization of q-ary codes.

We study polarization for nonbinary channels with input alphabet of sizeq=2r,r=2,3,.... Using Arıkan's polarizing kernelH2, we prove that the virtual channels that arise in the process of channel evolution converge toq-ary channels with capacity 0,1,2,...,rbits. As a result of this analysis, we show that polar codes support reliable transmission over discrete memoryless channels withq-ary input for all rates below the symmetric capacity of the channel. This leads to an explicit transmission scheme forq-ary channels. The block error probability of decoding using successive cancellation behaves as exp(-Nα), whereNis the code length and α is any constant less than 0.5.

We study polarization for nonbinary channels with input alphabet of size q = 2r, r = 2,3,.... Using Arikan's polarizing kernel H2, we prove that virtual channels that arise in the process of polarization converge to q-ary channels with capacity 1,2,..., r bits, and that the total transmission rate approaches the symmetric capacity of the channel. This leads to an explicit transmission scheme for q-ary channels. The error probability of decoding using successive cancellation behaves as exp(-Nα), where N is the code length and α is any constant less than 0.5.

The ordered Hamming metric is a generalization of the usual Hamming distance derived from a partial order on the set of coordinates. So far, coding theory in ordered spaces has primarily focused on combinatorial aspects. The main object of this paper is to develop the relation of the ordered Hamming space to the context of information transmission. Using the models in previous works of Rosenbloom and Tsfasman (1997) and Tavildar and Viswanath (2006) as a starting point, we define the ordered symmetric channel and the ordered erasure channel which are counterparts of the q-ary symmetric channel and the q-ary erasure channel, respectively. We establish a set of basic results for these channels as well as their relation to linear ordered codes.