This post continues from the earlier post on fixing DPO (https://kyunghyuncho.me/a-proper-preference-optimization-loss-and-its-gradient/). by the way, the dinner reservation was at Ramro (https://www.ramronyc.com/, https://maps.app.goo.gl/jwpyPvy2pjNsxS6h9), and i recommend you try it out. a very interesting cuisine! Direct Preference Optimization let’s start by stating the direct preference optimization (DPO) loss for each example $(x,y_+, y_-)$: \[\log \left( 1 + \exp \left(-\left(\beta \log \frac{\pi(y_+)}{\pi(y_-)}-\gamma \log \frac{\pi_0(y_+)}{\pi_0(y_-)}\right) \right) \right).\] this takes a slightly different form from the original DPO loss. in the original DPO loss, $\gamma = \beta$ was forced, which leaves the scale (or entropy) of the reference model $\pi_0$ uncontrollable. this formulation above is

# Category: Research

## Fixing DPO but I have a dinner reservation …

Direct preference optimization (DPO; https://arxiv.org/abs/2305.18290) is all the rage, i heard. i also hear from my students that DPO, which minimizes the following loss, often results in weird behaviours, such as unreasonable preference toward lengthy responses (even when there is no statistical difference in lengths between desirable and undesirable responses.) i won’t go into details of these issues, but i feel like there’s a relatively simple reason behind these pathologies based on basic calculus. \[\mathcal{L}_{\mathrm{dpo}}(\theta) = -\log \left(1 + \exp \left(- \log \frac{p_{\theta}(y|x)}{p_{0}(y|x)}+ \log \frac{p_\theta(y’|x)}{p_{0}(y’|x)}\right)\right),\] where $p_0$ is the so-called reference model from which $y$ and $y’$ were drawn independently

## Gradient-based planning, mapping and execution

this post continues from the previous post <Gradient-based trajecotry planning>, because i became even busier. in fact, i should work on my presentation slide for my talk at the University of Washington tomorrow (sorry, Yejin and Noah!), and probably because of that, i decided to push it a bit further. the main assumption i made in the previous slide was that our bot has access to the entire map. this is a huge assumption that does not often hold in practice. instead, i decided to restrict the visibility of our bot. it will be able to see the obstacles in

## Gradient-based trajectory planning

this semester has been completely crazy for me, and i anticipate that this madness will only worsen over the next couple of months. of course, because of this crazy schedule, my brain started to revolt by growing a doubt inside me on how much i trust gradient descent. crazy, right? yes. i then succumbed to this temptation and looked for some simple example to test my trust in gradient descent. yes, i know that i should never doubt our lord Gradient Descent, but my belief is simply too weak. so, i decided to use gradient descent for simple trajectory planning

## A short thought on watermarking

so, it looks like watermarking is a thing that is coming back to its (controversial) life. the idea of watermarking is to enable content producers to mark their own contents so as to track where those contents are being consumed without introducing too much of disruption. one of the simplest watermarking techniques i run into quite often is on a plan with their entertainment system; when you watch a movie on an airplane, you often notice the airline code (e.g. “DL” in the case of Delta) embroiled on the screen once a while. i presume the heightened interest in watermarking