Weighted Stochastic Differential Equation to Implement Wasserstein-Fisher-Rao Gradient Flow
Herlock Rahimi
https://arxiv.org/abs/2512.17878 https://arxiv.org/pdf/2512.17878 https://arxiv.org/html/2512.17878
arXiv:2512.17878v1 Announce Type: new
Abstract: Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in which sampling is driven by a combination of deterministic drift and Brownian diffusion, resulting in continuous particle trajectories in the ambient space. While such dynamics enjoy exponential convergence guarantees for strongly log-concave target distributions, it is well known that their mixing rates deteriorate exponentially in the presence of nonconvex or multimodal landscapes, such as double-well potentials. Since many practical generative modeling tasks involve highly non-log-concave target distributions, considerable recent effort has been devoted to developing sampling schemes that improve exploration beyond classical diffusion dynamics.
A promising line of work leverages tools from information geometry to augment diffusion-based samplers with controlled mass reweighting mechanisms. This perspective leads naturally to Wasserstein--Fisher--Rao (WFR) geometries, which couple transport in the sample space with vertical (reaction) dynamics on the space of probability measures. In this work, we formulate such reweighting mechanisms through the introduction of explicit correction terms and show how they can be implemented via weighted stochastic differential equations using the Feynman--Kac representation. Our study provides a preliminary but rigorous investigation of WFR-based sampling dynamics, and aims to clarify their geometric and operator-theoretic structure as a foundation for future theoretical and algorithmic developments.
toXiv_bot_toot
I did a lot of stretching and used the massage gun this morning to deal with the sciatica and felt pretty much fine when it was time to leave for work, so I biked in.
A bit cold, but no wind, so that's good. I keep a log of temperature and wind and what I wore for my rides to work so I can check back if I was too cold/too warm, etc.
I'll see my PT tomorrow for the sciatica so no biking into work.
PCIe any% speedrun, day 6: Almost at minimum-viable-baseline-happy-path status!
It's still 2.5 GT/s only, I haven't implemented up-negotiation to 5 GT/s speed yet (or tested that on the SoC side for that matter).
Configuration reads and writes work; they're translated to APB bus transactions and bridged to an APB register block that reports a bunch of hard coded default values and lets you change a few things like BARs.
Added a zoom level to the Category page on the Exocortex-Log app. Can make the graphs look a lot cleaner now.
Looking back over the last 100 months here, we can see in general my social life is quite seasonal -- Festivals are a lot of social all weekend long and a couple of them in a month really bumps up the hours from my usual habit of sitting alone in a dark room pressing buttons.
The peak in 2019 is a summer filled with Glasto and Noisily and another festival or camping trip I don’t seem to have recorded the name of.
Then clearly visible is the drop-off in social activity as the COVID pandemic hit. Virtual-Social (IE zoom meetings and the like) picked up quite a bit around there but had died back to almost nothing way before the hours spent with actual people started to tick up.
Annoyingly, I have my biggest gap in data right on top of the pandemic there, where I failed to back up for months and then data became corrupted.
When the data-hole is over we see social life still not really returning until the middle of 2021 and not really getting back into stride until summer 2022.
It remains much lower now on average with lower peaks than before the pandemic too. Multiple reasons.
Work is pretty constant all the way though other than the data-hole. Dipping when I take time off for social mostly.
That data-hole is annoying. Back up your data kids.
#lifeLog #app #exocortexLog
Long winter nights, red light on, UV burner on... So have missed making my own prints, and so glad to be able to pick this up again (and also working with older techniques, which are new to me), all after more than three decades... Still some more kinks to work out before I can share some proper prints, e.g. experimenting with different exposure times, toners (gold/selenium), fixers, concentrations... All very much like a science experiment and meticulous log keeping has been key (as have be…
STM32MP2 update: I have logging on the A35 cores via the UART on the M33!
It took a bit of work to get the IPC channels up and running (using the IPCC to handshake a buffer in SRAM2) but now you can just log by invoking g_log("foo") like you could anywhere else in my platform and it a) goes to the right place and b) is tagged with the core ID.
The thing about a life-logger, is you input sensitive data about your life, lifestyle and activities, so privacy and data-integrity are some of the most important issues.
There can be no server, the data has to be yours and yours alone. Because you can’t tell what is happening to the data in a closed-source app, it must be completely free and open source.
You can’t trust a corporate diary, they must sell to anyone offering enough money.
So it is with my life log app, all data completely in your own device. No home server ever sees anything.
There is no home server. Just the code.
To achieve this Exocortex Log is a Progressive Web App. It downloads when you are online at the website and can be installed onto the homepage of your phone.
It keeps all data on the local device using indexdb.
This means you must be responsible for your own backups. Be sure to export and back up your data regularly. I have gaps in my ten year record where my phone was stolen and most recent backup was months prior.
Once installed it will work offline, airplane mode, no internet, down in the tube station at midnight, anywhere.
There's a blog on the website saying this and more: https://exocortexlog.com/news/articles/2025-12-06-release/
Occasionally, I log into LinkedIn purely to check messages. Sometimes, I find a promoted message or an ad, maybe a connection request. Usually, nothing. Content often feel fake, and it's often difficult to find content that I'm interested in there. Is it even a site for businesses to connect, and people find work any more?
Back when it wasn't owned by Meta, I used to enjoy Instagram. Now it feels like a shop. I still miss scrolling through the feed, discovering content from the people that I followed. Sadly, a lot of creators that I liked are still on there, and nowhere else.
Mastodon is pretty much my only online home now, and I'm very thankful for it!
#linux #openwrt
Q: I am starting with open wrt. My problem is that I want to reach it over my LAN. The default ip is 192.168.1 but I have 192.168.0 as a default and I can not change it (ISP restriction). I have googled and youtubed it but I still can't get it to work. I can log in to t…
Added a category manager and category state section to the Exocortex Log app.
Have now organized and cleaned up the categories in my ten year database and so we can get some views of the time spent in each category.
We see that through September and October I was in a routine of work and slack with a bit of social a couple of times a week, until the end of November when I went away for social at a conference all weekend. I saw a demo there of a person using Shakespeare, and then when I got back started doing some vibe-coding, shown in in Red.
A break from that to go away at the weekend to a long social party then finish it off and publish a few days ago, since when Vibe Coding has dropped off a little.
#lifeLog #app #exocortexLog
from my link log —
Experience report: it will never work in theory.
https://www.computer.org/csdl/magazine/so/2024/03/10424425/1Ulj1Qa8tJ6
saved 2025-11-09
@fanf@mendeddrum.org
![Serial console log showing a bunch of log messages tagged [m33] then hello world messages from [a35-0] and [a35-1]](https://files.ioc.exchange/media_attachments/files/115/625/422/529/668/167/original/7306df4e36d6e3ca.png)
