algorithm for solving assignment model

Main content

Everyone's talking about OpenAI's Q*. Here's what you need to know about the mysterious project.

A mysterious new OpenAI model known as Q* has got the tech world talking.
The model is said to have sparked concern at the startup that led to the resulting chaos.
AI experts say the model could be a big step forward but is unlikely to end the world anytime soon.

As the dust settles on the chaos at OpenAI, we still don't know why CEO Sam Altman was fired — but reports have suggested it could be linked to a mysterious AI model .

The Information reported that a team led by OpenAI chief scientist Ilya Sutskever had made a breakthrough earlier this year, which allowed them to build a new model known as Q* (pronounced "Q star.") The outlet reported that the model could solve basic math problems.

Sources told Reuters that this model provoked an internal firestorm , with several staff members writing a letter to OpenAI's board warning that the new breakthrough could threaten humanity.

This warning was cited as one of the reasons that the board chose to fire Sam Altman, who returned as CEO on Wednesday after days of turmoil at the company, Reuters reported.

The ability to solve basic math problems may not sound that impressive, but AI experts told Business Insider it would represent a huge leap forward from existing models, which struggle to generalize outside the data they are trained on.

"If it has the ability to logically reason and reason about abstract concepts, which right now is what it really struggles with, that's a pretty tremendous leap," said Charles Higgins, a cofounder of the AI-training startup Tromero who's also a Ph.D. candidate in AI safety.

He added, "Maths is about symbolically reasoning — saying, for example, 'If X is bigger than Y and Y is bigger than Z, then X is bigger than Z.' Language models traditionally really struggle at that because they don't logically reason, they just have what are effectively intuitions."

Sophia Kalanovska, a fellow Tromero cofounder and Ph.D. candidate, told BI that Q*'s name implied it was a combination of two well-known AI techniques, Q-learning and A* search.

She said this suggested the new model could combine the deep-learning techniques that power ChatGPT with rules programmed by humans. It's an approach that could help fix the chatbot's hallucination problem .

"I think it's symbolically very important. On a practical level, I don't think it's going to end the world," Kalanovska said.

"I think the reason why people believe that Q* is going to lead to AGI is because, from what we've heard so far, it seems like it will combine the two sides of the brain and be capable of knowing some things out of experience, while still being able to reason about facts," she added, referring to artificial general intelligence.

"That is definitely a step closer to what we consider intelligence, and it is possible that it leads to the model being able to have new ideas, which is not the case with ChatGPT."

The inability to reason and develop new ideas, rather than just regurgitating information from within their training data, is seen as a huge limitation of existing models, even by the people building them .

Andrew Rogoyski, a director at the Surrey Institute for People-Centered AI, told BI that solving unseen problems was a key step toward creating AGI.

"In the case of math, we know existing AIs have been shown to be capable of undergraduate-level math but to struggle with anything more advanced," he said.

"However, if an AI can solve new, unseen problems, not just regurgitate or reshape existing knowledge, then this would be a big deal, even if the math is relatively simple," he added.

Not everyone was so enthused by the reported breakthrough. Gary Marcus, an AI expert and deep-learning critic , expressed doubts about Q*'s reported capabilities in a post on his Substack .

"If I had a nickel for every extrapolation like that—'today , it works for grade school students! next year, it will take over the world!'—I'd be Musk-level rich," wrote Marcus.

OpenAI did not immediately respond to a request for comment from Business Insider, made outside normal working hours.

Watch: Sam Altman moves to Microsoft after OpenAI fires him as CEO

theintactone

Read MBA, BBA, B.COM Notes

Assignment Model: Hungarian Algorithm and its Applications

Assignment Problem is a special type of linear programming problem which deals with the allocation of the various resources to the various activities on one to one basis. It does it in such a way that the cost or time involved in the process is minimum and profit or sale is maximum. Though there problems can be solved by simplex method or by transportation method but assignment model gives a simpler approach for these problems.

In a factory, a supervisor may have six workers available and six jobs to fire. He will have to take decision regarding which job should be given to which worker. Problem forms one to one basis. This is an assignment problem.

Assignment Model:

Suppose there are n facilitates and n jobs it is clear that in this case, there will be n assignments. Each facility or say worker can perform each job, one at a time. But there should be certain procedure by which assignment should be made so that the profit is maximized or the cost or time is minimized.

In the table, Co ij is defined as the cost when j th job is assigned to i th worker. It maybe noted here that this is a special case of transportation problem when the number of rows is equal to number of columns.

Mathematical Formulation:

Any basic feasible solution of an Assignment problem consists (2n – 1) variables of which the (n – 1) variables are zero, n is number of jobs or number of facilities. Due to this high degeneracy, if we solve the problem by usual transportation method, it will be a complex and time consuming work. Thus a separate technique is derived for it. Before going to the absolute method it is very important to formulate the problem.

Suppose x jj is a variable which is defined as

1 if the i th job is assigned to j th machine or facility

0 if the i th job is not assigned to j th machine or facility.

Now as the problem forms one to one basis or one job is to be assigned to one facility or machine.

The total assignment cost will be given by

The above definition can be developed into mathematical model as follows:

Determine x ij > 0 (i, j = 1,2, 3…n) in order to

Subjected to constraints

and x ij is either zero or one.

Method to solve Problem (Hungarian Technique):

Consider the objective function of minimization type. Following steps are involved in solving this Assignment problem,

Locate the smallest cost element in each row of the given cost table starting with the first row. Now, this smallest element is subtracted form each element of that row. So, we will be getting at least one zero in each row of this new table.
Having constructed the table (as by step-1) take the columns of the table. Starting from first column locate the smallest cost element in each column. Now subtract this smallest element from each element of that column. Having performed the step 1 and step 2, we will be getting at least one zero in each column in the reduced cost table.
Now, the assignments are made for the reduced table in following manner.

(i) Rows are examined successively, until the row with exactly single (one) zero is found. Assignment is made to this single zero by putting square □ around it and in the corresponding column, all other zeros are crossed out (x) because these will not be used to make any other assignment in this column. Step is conducted for each row.

(ii) Step 3 (i) in now performed on the columns as follow:- columns are examined successively till a column with exactly one zero is found. Now , assignment is made to this single zero by putting the square around it and at the same time, all other zeros in the corresponding rows are crossed out (x) step is conducted for each column.

(iii) Step 3, (i) and 3 (ii) are repeated till all the zeros are either marked or crossed out. Now, if the number of marked zeros or the assignments made are equal to number of rows or columns, optimum solution has been achieved. There will be exactly single assignment in each or columns without any assignment. In this case, we will go to step 4.

At this stage, draw the minimum number of lines (horizontal and vertical) necessary to cover all zeros in the matrix obtained in step 3, Following procedure is adopted:

(i) Tick mark () all rows that do not have any assignment.

(ii) Now tick mark() all these columns that have zero in the tick marked rows.

(iii) Now tick mark all the rows that are not already marked and that have assignment in the marked columns.

(iv) All the steps i.e. (4(i), 4(ii), 4(iii) are repeated until no more rows or columns can be marked.

(v) Now draw straight lines which pass through all the un marked rows and marked columns. It can also be noticed that in an n x n matrix, always less than ‘n’ lines will cover all the zeros if there is no solution among them.

In step 4, if the number of lines drawn are equal to n or the number of rows, then it is the optimum solution if not, then go to step 6.
Select the smallest element among all the uncovered elements. Now, this element is subtracted from all the uncovered elements and added to the element which lies at the intersection of two lines. This is the matrix for fresh assignments.
Repeat the procedure from step (3) until the number of assignments becomes equal to the number of rows or number of columns.

Hungarian Algorithm for Assignment Problem | Set 1 (Introduction)

For each row of the matrix, find the smallest element and subtract it from every element in its row.
Do the same (as step 1) for all columns.
Cover all zeros in the matrix using minimum number of horizontal and vertical lines.
Test for Optimality: If the minimum number of covering lines is n, an optimal assignment is possible and we are finished. Else if lines are lesser than n, we haven’t found the optimal assignment, and must proceed to step 5.
Determine the smallest entry not covered by any line. Subtract this entry from each uncovered row, and then add it to each covered column. Return to step 3.

Try it before moving to see the solution

Explanation for above simple example:

An example that doesn’t lead to optimal value in first attempt: In the above example, the first check for optimality did give us solution. What if we the number covering lines is less than n.

Time complexity : O(n^3), where n is the number of workers and jobs. This is because the algorithm implements the Hungarian algorithm, which is known to have a time complexity of O(n^3).

Space complexity : O(n^2), where n is the number of workers and jobs. This is because the algorithm uses a 2D cost matrix of size n x n to store the costs of assigning each worker to a job, and additional arrays of size n to store the labels, matches, and auxiliary information needed for the algorithm.

In the next post, we will be discussing implementation of the above algorithm. The implementation requires more steps as we need to find minimum number of lines to cover all 0’s using a program. References: http://www.math.harvard.edu/archive/20_spring_05/handouts/assignment_overheads.pdf https://www.youtube.com/watch?v=dQDZNHwuuOY Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

DSA in Java
DSA in Python
DSA in JavaScript

Please Login to comment...

Rohit_Goyal
devendrasalunke
surinderdawra388
sagartomar9927
spacetechbytes
classroompxico
esrinivasa7kps

Please write us at contrib[email protected] to report any issue with the above content

Improve your Coding Skills with Practice

Google OR-Tools
Español – América Latina
Português – Brasil
Tiếng Việt

Solving an Assignment Problem

This section presents an example that shows how to solve an assignment problem using both the MIP solver and the CP-SAT solver.

In the example there are five workers (numbered 0-4) and four tasks (numbered 0-3). Note that there is one more worker than in the example in the Overview .

The costs of assigning workers to tasks are shown in the following table.

The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost. Since there are more workers than tasks, one worker will not be assigned a task.

MIP solution

The following sections describe how to solve the problem using the MPSolver wrapper .

Import the libraries

The following code imports the required libraries.

Create the data

The following code creates the data for the problem.

The costs array corresponds to the table of costs for assigning workers to tasks, shown above.

Declare the MIP solver

The following code declares the MIP solver.

Create the variables

The following code creates binary integer variables for the problem.

Create the constraints

Create the objective function.

The following code creates the objective function for the problem.

The value of the objective function is the total cost over all variables that are assigned the value 1 by the solver.

Invoke the solver

The following code invokes the solver.

Print the solution

The following code prints the solution to the problem.

Here is the output of the program.

Complete programs

Here are the complete programs for the MIP solution.

CP SAT solution

The following sections describe how to solve the problem using the CP-SAT solver.

Declare the model

The following code declares the CP-SAT model.

The following code sets up the data for the problem.

The following code creates the constraints for the problem.

Here are the complete programs for the CP-SAT solution.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-02 UTC.

Hungarian Method

The Hungarian method is a computational optimization technique that addresses the assignment problem in polynomial time and foreshadows following primal-dual alternatives. In 1955, Harold Kuhn used the term “Hungarian method” to honour two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry. Let’s go through the steps of the Hungarian method with the help of a solved example.

Hungarian Method to Solve Assignment Problems

The Hungarian method is a simple way to solve assignment problems. Let us first discuss the assignment problems before moving on to learning the Hungarian method.

What is an Assignment Problem?

A transportation problem is a type of assignment problem. The goal is to allocate an equal amount of resources to the same number of activities. As a result, the overall cost of allocation is minimised or the total profit is maximised.

Because available resources such as workers, machines, and other resources have varying degrees of efficiency for executing different activities, and hence the cost, profit, or loss of conducting such activities varies.

Assume we have ‘n’ jobs to do on ‘m’ machines (i.e., one job to one machine). Our goal is to assign jobs to machines for the least amount of money possible (or maximum profit). Based on the notion that each machine can accomplish each task, but at variable levels of efficiency.

Hungarian Method Steps

Check to see if the number of rows and columns are equal; if they are, the assignment problem is considered to be balanced. Then go to step 1. If it is not balanced, it should be balanced before the algorithm is applied.

Step 1 – In the given cost matrix, subtract the least cost element of each row from all the entries in that row. Make sure that each row has at least one zero.

Step 2 – In the resultant cost matrix produced in step 1, subtract the least cost element in each column from all the components in that column, ensuring that each column contains at least one zero.

Step 3 – Assign zeros

Analyse the rows one by one until you find a row with precisely one unmarked zero. Encircle this lonely unmarked zero and assign it a task. All other zeros in the column of this circular zero should be crossed out because they will not be used in any future assignments. Continue in this manner until you’ve gone through all of the rows.
Examine the columns one by one until you find one with precisely one unmarked zero. Encircle this single unmarked zero and cross any other zero in its row to make an assignment to it. Continue until you’ve gone through all of the columns.

Step 4 – Perform the Optimal Test

The present assignment is optimal if each row and column has exactly one encircled zero.
The present assignment is not optimal if at least one row or column is missing an assignment (i.e., if at least one row or column is missing one encircled zero). Continue to step 5. Subtract the least cost element from all the entries in each column of the final cost matrix created in step 1 and ensure that each column has at least one zero.

Step 5 – Draw the least number of straight lines to cover all of the zeros as follows:

(a) Highlight the rows that aren’t assigned.

(b) Label the columns with zeros in marked rows (if they haven’t already been marked).

(d) Continue with (b) and (c) until no further marking is needed.

(f) Simply draw the lines through all rows and columns that are not marked. If the number of these lines equals the order of the matrix, then the solution is optimal; otherwise, it is not.

Step 6 – Find the lowest cost factor that is not covered by the straight lines. Subtract this least-cost component from all the uncovered elements and add it to all the elements that are at the intersection of these straight lines, but leave the rest of the elements alone.

Step 7 – Continue with steps 1 – 6 until you’ve found the highest suitable assignment.

Hungarian Method Example

Use the Hungarian method to solve the given assignment problem stated in the table. The entries in the matrix represent each man’s processing time in hours.

$\begin{array}{l}\begin{bmatrix} & I & II & III & IV & V \\1 & 20 & 15 & 18 & 20 & 25 \\2 & 18 & 20 & 12 & 14 & 15 \\3 & 21 & 23 & 25 & 27 & 25 \\4 & 17 & 18 & 21 & 23 & 20 \\5 & 18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} $

With 5 jobs and 5 men, the stated problem is balanced.

$\begin{array}{l}A = \begin{bmatrix}20 & 15 & 18 & 20 & 25 \\18 & 20 & 12 & 14 & 15 \\21 & 23 & 25 & 27 & 25 \\17 & 18 & 21 & 23 & 20 \\18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} $

Subtract the lowest cost element in each row from all of the elements in the given cost matrix’s row. Make sure that each row has at least one zero.

$\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 5 & 10 \\6 & 8 & 0 & 2 & 3 \\0 & 2 & 4 & 6 & 4 \\0 & 1 & 4 & 6 & 3 \\2 & 2 & 0 & 3 & 4 \\\end{bmatrix}\end{array} $

Subtract the least cost element in each Column from all of the components in the given cost matrix’s Column. Check to see if each column has at least one zero.

$\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 3 & 7 \\6 & 8 & 0 & 0 & 0 \\0 & 2 & 4 & 4 & 1 \\0 & 1 & 4 & 4 & 0 \\2 & 2 & 0 & 1 & 1 \\\end{bmatrix}\end{array} $

When the zeros are assigned, we get the following:

The present assignment is optimal because each row and column contain precisely one encircled zero.

Where 1 to II, 2 to IV, 3 to I, 4 to V, and 5 to III are the best assignments.

Hence, z = 15 + 14 + 21 + 20 + 16 = 86 hours is the optimal time.

Practice Question on Hungarian Method

Use the Hungarian method to solve the following assignment problem shown in table. The matrix entries represent the time it takes for each job to be processed by each machine in hours.

$\begin{array}{l}\begin{bmatrix}J/M & I & II & III & IV & V \\1 & 9 & 22 & 58 & 11 & 19 \\2 & 43 & 78 & 72 & 50 & 63 \\3 & 41 & 28 & 91 & 37 & 45 \\4 & 74 & 42 & 27 & 49 & 39 \\5 & 36 & 11 & 57 & 22 & 25 \\\end{bmatrix}\end{array} $

Stay tuned to BYJU’S – The Learning App and download the app to explore all Maths-related topics.

Frequently Asked Questions on Hungarian Method

What is hungarian method.

The Hungarian method is defined as a combinatorial optimization technique that solves the assignment problems in polynomial time and foreshadowed subsequent primal–dual approaches.

What are the steps involved in Hungarian method?

The following is a quick overview of the Hungarian method: Step 1: Subtract the row minima. Step 2: Subtract the column minimums. Step 3: Use a limited number of lines to cover all zeros. Step 4: Add some more zeros to the equation.

What is the purpose of the Hungarian method?

When workers are assigned to certain activities based on cost, the Hungarian method is beneficial for identifying minimum costs.

Register with BYJU'S & Download Free PDFs

November 21, 2023

When It Comes to AI Models, Bigger Isn’t Always Better

Artificial intelligence models are getting bigger, along with the data sets used to train them. But scaling down could solve some big AI problems

By Lauren Leffer

Brain image on laptop screen downloading images from the cloud

Malte Mueller/Getty Images

Artificial intelligence has been growing in size. The large language models (LLMs) that power prominent chatbots, such as OpenAI’s ChatGPT and Google’s Bard, are composed of well more than 100 billion parameters—the weights and variables that determine how an AI responds to an input. That’s orders of magnitude more information and code than was common among the most advanced AI models just a few years ago.

In broad strokes, bigger AI tends to be more capable AI. Ever larger LLMs and increasingly massive training datasets have resulted in chatbots that can pass university exams and even entrance tests for medical schools. Yet there are drawbacks to all this growth: As models have gotten bigger, they’ve also become more unwieldy, energy-hungry and difficult to run and build. Smaller models and datasets could help solve this issue. That’s why AI developers, even at some of the largest tech companies, have begun to revisit and reassess miniaturized AI models.

In September, for instance, a team of Microsoft researchers released a technical report on a new language model named phi-1.5. Phi-1.5 is made up of 1.3 billion parameters, which is about one one-hundredth the size of GPT-3.5, the model that underlies the free version of ChatGPT. GPT-3.5 and phi-1.5 also share the same general architecture: they are both transformer-based neural networks, meaning they work by mapping the context and relationships of language.

But despite its relatively diminutive size, phi-1.5 “exhibits many of the traits of much larger LLMs,” the authors wrote in their report, which was released as a preprint paper that has not yet been peer-reviewed. In benchmarking tests, the model performed better than many similarly sized models. It also demonstrated abilities that were comparable to those of other AIs that are five to 10 times larger. And recent updates made in October even allow phi-1.5 to display multimodality —an ability to interpret images as well as text. Last week Microsoft announced the release of phi-2, a 2.7-billion-parameter follow-up to phi-1.5, which demonstrates even more ability in a still relatively compact package, the company claims.

Make no mistake, massive LLMs such as Bard, GPT-3.5 and GPT-4 are still more capable than the phi models. “I would say that comparing phi-1.5 to GPT-4 is like comparing a middle school student and an undergraduate student,” says Ronen Eldan, a principal AI researcher at Microsoft Research and one of the authors of the September report. But phi-1.5 and phi-2 are just the latest evidence that small AI models can still be mighty—which means they could solve some of the problems posed by monster AI models such as GPT-4.

For one, training and running an AI model with more than 100 billion parameters takes a lot of energy. A standard day of global ChatGPT usage can consume as much electricity as about 33,000 U.S. households do in the same time period, according to one estimate from University of Washington computer engineer Sajjad Moazeni. If Google were to replace all of its users’ search engine interactions with queries to Bard, running that search engine would use as much power as Ireland does , according to an analysis published last month in Joule . That electricity consumption comes, in large part, from all the computing power required to send a query through such a dense network of parameters, as well as from the masses of data used to train mega models. Smaller AI needs far less computing power and energy to run, says Matthew Stewart, a computer engineer at Harvard University. This energy payoff is a sustainability boost.

Plus, less resource-intensive AI is more accessible AI. As it stands now, just a handful of private companies have the funds and server space to build, store, train and modify the biggest LLMs. Smaller models can be developed and studied by more people. Thinking small “can in some sense democratize AI,” says Eva Portelance, a computational and cognitive linguistics researcher at the Mila-Quebec Artificial Intelligence Institute. “In not requiring as much data and not requiring the models to be as big..., you’re making it possible for people outside of these large institutions” to innovate. This is one of multiple ways that scaled-down AI enables new possibilities.

For one thing, smaller AI can fit into smaller devices. Currently, the size of most LLMs means they have to run on the cloud—they’re too big to store locally on an unconnected smartphone or laptop. Smaller models could run on personal devices alone, however. For example, Stewart researches so-called edge computing, in which the goal is to stuff computation and data storage into local machines such as “ Internet of Things ” gadgets. He has worked on machine-learning-powered sensor systems compact enough to run on individual drones—he calls this “tiny machine learning.” Such devices, Stewart explains, can enable things like much more advanced environmental sensing in remote areas. If competent language models were to become similarly small, they would have myriad applications. In modern appliances such as smart fridges or wearables such as Apple Watches, a smaller language model could enable a chatbotesque interface without the need to transmit raw data across a cloud connection. That would be a massive boon for data security. “Privacy is one of the major benefits,” Stewart says.

And although the general rule is that larger AI models are more capable, not every AI has to be able to do everything. A chatbot inside a smart fridge might need to understand common food terms and compose lists but not need to write code or perform complex calculations. Past analyses have shown that massive language models can be pared down , even by as much as 60 percent , without sacrificing performance in all areas. In Stewart’s view, smaller and more specialized AI models could be the next big wave for companies looking to cash in on the AI boom.

Then there’s the more fundamental issue of interpretability: the extent to which a machine-learning model can be understood by its developers. For larger AI models, it is essentially impossible to parse the role of each parameter, explains Brenden Lake, a computational cognitive scientist researching artificial intelligence at New York University. This is the “black box” of AI: developers build and run models without any true knowledge of what each weight within an algorithm accomplishes. In smaller models, it is easier, though often still difficult, to determine cause and effect and adjust accordingly. “I’d rather try to understand a million parameters than a billion parameters,” Lake says.

For both Lake and Portelance, artificial intelligence isn’t just about building the most capable language model possible but also about gaining insight into how humans learn and how we can better mimic that through machines. Size and interpretability are key factors in creating models that help illuminate things about our own mind. With mega AI models—generally trained on much bigger datasets—the breadth of that training information can conceal limitations and make it seem like an algorithm understands something it doesn’t. Conversely, with smaller, more interpretable AI, it is far easier to parse why an algorithm is producing an output. In turn, scientists can use that understanding to create “more cognitively plausible” and possibly better overall AI models, Portelance says. Humans, they point out, are the gold standard for cognition and learning: we can absorb so much and infer patterns from very small amounts of information. There are good reasons to try to study that phenomenon and replicate it through AI.

At the same time, “there are diminishing returns for training large models on big datasets,” Lake says. Eventually, it becomes a challenge to find high-quality data, the energy costs rack up and model performance improves less quickly. Instead, as his own past research has demonstrated, big strides in machine learning can come from focusing on slimmer neural networks and testing out alternate training strategies .

Sébastien Bubeck, a senior principal AI researcher at Microsoft Research, agrees. Bubeck was one of the developers behind phi-1.5. For him, the purpose of studying scaled-down AI is “about finding the minimal ingredients for the sparks of intelligence to emerge” from an algorithm. Once you understand those minimal components, you can build on them. By approaching these big questions with smaller models, Bubeck hopes to improve AI in as economical a way as possible.

“With this strategy, we’re being much more careful with how we build models,” he says. “We’re taking a slower and more deliberate approach.” Sometimes slow and steady wins the race—and sometimes smaller can be smarter.

What is Q*? And when we will hear more?

The cats out of the bag. Reuters published. Any interpretations? Any knowledge files out there on the subject?

Definitely makes me question Sam’s motives and puts the recent drama in a different light.

This is moving towards more existential questions, faster than anyone imagined, and I’d rather not have Microsoft, Larry Summers or the ex-CEO of fricking Salesforce making the calls whether or not something is AGI.

It’s shades of ‘repealing Glass-Steagall’ to leave it up to those w/ a literal vested interest in keeping AI commercially-viable to make the call whether AGI has been achieved.

One does not mistakenly keep board members ‘out of the loop’ re: discovering AGI and possibly the biggest breakthrough in human civilization

Can of worms for sure… Real time! I wonder what I will wake up to tomorrow. But the currant chatter feels like ripple echos to me. Probably an announcement on Q* before Christmas.

Exclusive: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster -sources | Reuters .

The maker of ChatGPT had made progress on Q* (pronounced Q-Star), which some internally believe could be a breakthrough in the startup’s search for superintelligence, also known as artificial general intelligence (AGI), one of the people told Reuters. OpenAI defines AGI as AI systems that are smarter than humans.

As someone who’s done a fair amount of ML/AI research, I can tell you that it is very very easy to think you’ve discovered a breakthrough.

There is a great deal of cognitive bias in AI, and you have to falsify very aggressively.

I am deeply skeptical.

It’s also worth noting that in the news today we found out that the 86B share-sale is back on. I’m sure this ‘breakthrough’ will get investors quite interested.

Separately, a person familiar with the matter told The Verge that the board never received a letter about such a breakthrough and that the company’s research progress didn’t play a role in Altman’s sudden firing.

It wouldn’t be a bad time to start thinking about community AI boards to start the alignment aspects of the transition we face. The last week gives us clues to what we could expect in the future. Uncharted territory.

Q-learning is an algorithm that helps an agent learn the best actions to take in a given state to maximize a reward.

That’s it pretty much

I believe the ongoing discussions are less about AGI itself and more about concerns regarding leadership decisions and safety protocols. AGI has the potential to revolutionize every aspect of society, and it’s crucial that we prepare for its impact across all spheres of humanity. It represents a pivotal key—with one turn, it could unlock tremendous benefits or pose significant risks. Ensuring that robust safety measures are in place is essential.

The leaders in the field, including Sam and other directors, are tasked with navigating this complex landscape. I trust they are doing their utmost to secure a safe transition into this new era. We will reach our goals with AGI, but let’s proceed with the necessary precautions—better safe than sorry in the realm of transformative technologies.

I did an eval on q-learning “way back” when gpt-4 was released!

I never had the time to fully finish it and I might’ve got some stuff wrong.

Was it a basic algo of high school mathematics and better rewards ?

https://chat.openai.com/share/a47f380f-b6d1-4885-9287-05d9c8dae114

Some interesting ideas on how to use q-learning to train LLMs.

The first idea matches a bit with the synthetic data comments we are hearing.

Interactive Learning Environment: Q-learning requires an environment where it can interact and receive feedback. For LLMs, this could be a simulated or real-world interface where the model can perform tasks, ask questions, or engage in dialogues and receive rewards based on the quality and relevance of its responses or actions.

I would argue that intelligence is smart enough to not fall for the wiles of short-term goals. With the firm grasp the ChatGPTs had of ethics, I would argue we are in good hands.

AGI will be achieved in the next 6 - 24 months. It is inevitable and it would be better to prepare for it now than trying to stop it (which is a futile effort) and may mean other less well meaning actors will be in charge of humanities most powerful invention ever to exist, and perhaps something that turns out to be the most most advanced evolutionary species since human beings

I don’t think that’s true. NLP is widely considered to be the main barrier to achieving AGI. OpenAI’s success in the area caused me and many others to think we could see AGI within a couple of years. I’ve been telling people for months that they should shorten their mental time frames from years to months. I don’t mean that I think AGI will happen that quickly; I just mean that advancements we thought were years away are now happening on an almost weekly basis.

So, if the Reuters article is true, it’s not surprising. If we haven’t had a breakthrough with AGI already, then we almost certainly will soon.

From deepmind, some cute bot animations and a good visual explanation

It’s robotics, but transformers are the basis of LLMs.

My goal is to get a q* post ‘community flagged’. That will be a sign!

Heh. Must be tough working at such a core company that could potentially have a very broad impact on humanity. All that kibitizing…

Don’t worry folks, the 86B+ share sale should help a bit.

The acronym RACE - Real-time Antiquation of Current Ecosystem , meaning everything you make, AI will break is about right here.

Every advancement that OpenAI makes implementation of the current AI out of date. I remember watching Khan Academy describe their education platform saying ‘This AI will watch this AI’ - that’s basically agents, but the way they probably implemented it was probably much different and very expensive to build. Autogen / Assistants made that simple.

The paradigm of building AI applications is different than other tech. Every time you finish building a lunar rocket for $10bn just as you apply the paintwork, there are rockets available in Walmart for $9.99m - but can get to Mars, ( deployable living pods, Sirius XM, leatherette seats and aircon extra.)

Given this reality of building. What is your thoughts on a) Technical implementation b) Business strategy

The name “Q*” sounds like it could be a reference to quantum computing, which is a field of research that has the potential to revolutionize many different industries, including artificial intelligence.

Assignment Model | Linear Programming Problem (LPP) | Introduction

What is assignment model.

→ Assignment model is a special application of Linear Programming Problem (LPP) , in which the main objective is to assign the work or task to a group of individuals such that;

i) There is only one assignment.

ii) All the assignments should be done in such a way that the overall cost is minimized (or profit is maximized, incase of maximization).

→ In assignment problem, the cost of performing each task by each individual is known. → It is desired to find out the best assignments, such that overall cost of assigning the work is minimized.

For example:

Suppose there are 'n' tasks, which are required to be performed using 'n' resources.

The cost of performing each task by each resource is also known (shown in cells of matrix)

In the above asignment problem, we have to provide assignments such that there is one to one assignments and the overall cost is minimized.

How Assignment Problem is related to LPP? OR Write mathematical formulation of Assignment Model.

→ Assignment Model is a special application of Linear Programming (LP).

→ The mathematical formulation for Assignment Model is given below:

→ Let, C i j \text {C}_{ij} C ij denotes the cost of resources 'i' to the task 'j' ; such that

→ Now assignment problems are of the Minimization type. So, our objective function is to minimize the overall cost.

→ Subjected to constraint;

(i) For all j t h j^{th} j t h task, only one i t h i^{th} i t h resource is possible:

(ii) For all i t h i^{th} i t h resource, there is only one j t h j^{th} j t h task possible;

(iii) x i j x_{ij} x ij is '0' or '1'.

Types of Assignment Problem:

(i) balanced assignment problem.

It consist of a suqare matrix (n x n).
Number of rows = Number of columns

(ii) Unbalanced Assignment Problem

It consist of a Non-square matrix.
Number of rows ≠ \not=  = Number of columns

Methods to solve Assignment Model:

(i) integer programming method:.

In assignment problem, either allocation is done to the cell or not.

So this can be formulated using 0 or 1 integer.

While using this method, we will have n x n decision varables, and n+n equalities.

So even for 4 x 4 matrix problem, it will have 16 decision variables and 8 equalities.

So this method becomes very lengthy and difficult to solve.

(ii) Transportation Methods:

As assignment problem is a special case of transportation problem, it can also be solved using transportation methods.

In transportation methods ( NWCM , LCM & VAM), the total number of allocations will be (m+n-1) and the solution is known as non-degenerated. (For eg: for 3 x 3 matrix, there will be 3+3-1 = 5 allocations)

But, here in assignment problems, the matrix is a square matrix (m=n).

So total allocations should be (n+n-1), i.e. for 3 x 3 matrix, it should be (3+3-1) = 5

But, we know that in 3 x 3 assignment problem, maximum possible possible assignments are 3 only.

So, if are we will use transportation methods, then the solution will be degenerated as it does not satisfy the condition of (m+n-1) allocations.

So, the method becomes lengthy and time consuming.

(iii) Enumeration Method:

It is a simple trail and error type method.

Consider a 3 x 3 assignment problem. Here the assignments are done randomly and the total cost is found out.

For 3 x 3 matrix, the total possible trails are 3! So total 3! = 3 x 2 x 1 = 6 trails are possible.

The assignments which gives minimum cost is selected as optimal solution.

But, such trail and error becomes very difficult and lengthy.

If there are more number of rows and columns, ( For eg: For 6 x 6 matrix, there will be 6! trails. So 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 trails possible) then such methods can't be applied for solving assignments problems.

(iv) Hungarian Method:

It was developed by two mathematicians of Hungary. So, it is known as Hungarian Method.

It is also know as Reduced matrix method or Flood's technique.

There are two main conditions for applying Hungarian Method:

(1) Square Matrix (n x n). (2) Problem should be of minimization type.

Suggested Notes:

Unbalanced Transportation Problem Numerical

Modified Distribution Method (MODI) | Transportation Problem | Transportation Model

Stepping Stone | Transportation Problem | Transportation Model

Vogel’s Approximation Method (VAM) | Method to Solve Transportation Problem | Transportation Model

Transportation Model - Introduction

North West Corner Method | Method to Solve Transportation Problem | Transportation Model

Least Cost Method | Method to Solve Transportation Problem | Transportation Model

Tie in selecting row and column (Vogel's Approximation Method - VAM) | Numerical | Solving Transportation Problem | Transportation Model

Critical Path Method [CPM] - Steps and Introduction | Network Analysis | Operation Research

Crashing Special Case - Multiple (Parallel) Critical Paths

Crashing Special Case - Indirect cost less than Crash Cost

Basics of Program Evaluation and Review Technique (PERT)

Numerical on PERT (Program Evaluation and Review Technique)

Network Analysis - Dealing with Network Construction Basics

Construct a project network with predecessor relationship | Operation Research | Numerical

Graphical Method | Methods to solve LPP | Linear Programming

Basics of Linear Programming

Linear Programming Problem (LPP) Formulation with Numericals

All comments that you add will await moderation. We'll publish all comments that are topic related, and adhere to our Code of Conduct .

Want to tell us something privately? Contact Us

Post comment

Education Lessons

Stay in touch, [notes] operation research, [notes] dynamics of machinery, [notes] maths, [notes] science, [notes] computer aided design.

International edition
Australia edition
Europe edition

OpenAI CEO and founder Sam Altman has been reinstated as boss.

OpenAI ‘was working on advanced model so powerful it alarmed staff’

Reports say new model Q* fuelled safety fears, with workers airing their concerns to the board before CEO Sam Altman’s sacking

OpenAI was reportedly working on an advanced system before Sam Altman’s sacking that was so powerful it caused safety concerns among staff at the company.

The artificial intelligence model triggered such alarm with some OpenAI researchers that they wrote to the board of directors before Altman’s dismissal warning it could threaten humanity, Reuters reported.

The model, called Q* – and pronounced as “Q-Star” – was able to solve basic maths problems it had not seen before, according to the tech news site the Information, which added that the pace of development behind the system had alarmed some safety researchers. The ability to solve maths problems would be viewed as a significant development in AI.

The reports followed days of turmoil at San Francisco-based OpenAI, whose board sacked Altman last Friday but then reinstated him on Tuesday night after nearly all the company’s 750 staff threatened to resign if he was not brought back. Altman also had the support of OpenAI’s biggest investor, Microsoft.

Many experts are concerned that companies such as OpenAI are moving too fast towards developing artificial general intelligence (AGI), the term for a system that can perform a wide variety of tasks at human or above human levels of intelligence – and which could, in theory, evade human control.

Andrew Rogoyski, of the Institute for People-Centred AI at the University of Surrey, said the ability to solve maths problems not included in a model’s training set would be a significant development.

“A lot of generative AI regurgitates or reshapes existing knowledge, whether text, images or maths, including libraries of known maths solutions. If you can create an AI that can solve a problem where you know it hasn’t already seen the solution somewhere in its vast training sets, then that’s a big deal, even if the maths is relatively simple. Solving complex maths, unseen, would be even more exciting.”

Speaking on Thursday last week, the day before his surprise sacking, Altman indicated that the company behind ChatGPT had made another breakthrough.

In an appearance at the Asia-Pacific Economic Cooperation (Apec) summit, he said: “Four times now in the history of OpenAI, the most recent time was just in the last couple weeks, I’ve gotten to be in the room, when we sort of push the veil of ignorance back and the frontier of discovery forward, and getting to do that is the professional honour of a lifetime.”

OpenAI was founded as a nonprofit venture with a board that governs a commercial subsidiary, run by Altman. Microsoft is the biggest investor in the for-profit business. As part of the agreement in principle for Altman’s return, OpenAI will have a new board chaired by Bret Taylor, a former co-chief executive of software company Salesforce.

after newsletter promotion

The ChatGPT developer states that it was established with the goal of developing “safe and beneficial artificial general intelligence for the benefit of humanity” and that the for-profit company would be “legally bound to pursue the nonprofit’s mission”.

The emphasis on safety at the nonprofit led to speculation that Altman had been sacked for endangering the company’s core mission. However, his brief successor as interim chief executive, Emmett Shear, wrote this week that the board “did *not* remove Sam over any specific disagreement on safety”.

OpenAI has been approached for comment.

Technology sector
Artificial intelligence (AI)
Consciousness
Corporate governance

More on this story

OpenAI’s directors have been anything but open. What the hell happened?

OpenAI staff threaten to quit en masse unless Sam Altman is reinstated

Sam Altman to return as CEO of OpenAI

Sam Altman’s OpenAI exit leads to rollercoaster for sector

Microsoft hires former OpenAI CEO Sam Altman

The OpenAI meltdown will only accelerate the artificial intelligence race

Sam Altman ‘was working on new venture’ before sacking from OpenAI

Microsoft chief says ‘no OpenAI’ without tech giant’s involvement

OpenAI fires co-founder and CEO Sam Altman for allegedly lying to company board

John Legend and Sia among singers to trial AI versions of voices with YouTube

Unpacking the hype around OpenAI’s rumored new Q* model

If OpenAI's new model can solve grade-school math, it could pave the way for more powerful systems.

Melissa Heikkilä archive page

This story is from The Algorithm, our weekly newsletter on AI. To get stories like this in your inbox first, sign up here .

Ever since last week’s dramatic events at OpenAI, the rumor mill has been in overdrive about why the company’s chief scientific officer, Ilya Sutskever, and its board decided to oust CEO Sam Altman.

While we still don’t know all the details, there have been reports that researchers at OpenAI had made a “breakthrough” in AI that had alarmed staff members. Reuters and The Information both report that researchers had come up with a new way to make powerful AI systems and had created a new model, called Q* (pronounced Q star), that was able to perform grade-school-level math. According to the people who spoke to Reuters, some at OpenAI believe this could be a milestone in the company’s quest to build artificial general intelligence, a much-hyped concept referring to an AI system that is smarter than humans. The company declined to comment on Q*.

Social media is full of speculation and excessive hype, so I called some experts to find out how big a deal any breakthrough in math and AI would really be.

Researchers have for years tried to get AI models to solve math problems. Language models like ChatGPT and GPT-4 can do some math, but not very well or reliably. We currently don’t have the algorithms or even the right architectures to be able to solve math problems reliably using AI, says Wenda Li, an AI lecturer at the University of Edinburgh. Deep learning and transformers (a kind of neural network), which is what language models use, are excellent at recognizing patterns, but that alone is likely not enough, Li adds.

Math is a benchmark for reasoning, Li says. A machine that is able to reason about mathematics, could, in theory, be able to learn to do other tasks that build on existing information, such as writing computer code or drawing conclusions from a news article. Math is a particularly hard challenge because it requires AI models to have the capacity to reason and to really understand what they are dealing with.

A generative AI system that could reliably do math would need to have a really firm grasp on concrete definitions of particular concepts that can get very abstract. A lot of math problems also require some level of planning over multiple steps, says Katie Collins, a PhD researcher at the University of Cambridge, who specializes in math and AI. Indeed, Yann LeCun, chief AI scientist at Meta, posted on X and LinkedIn over the weekend that he thinks Q* is likely to be “OpenAI attempts at planning.”

People who worry about whether AI poses an existential risk to humans , one of OpenAI's founding concerns, fear that such capabilities might lead to rogue AI. Safety concerns might arise if such AI systems are allowed to set their own goals and start to interface with a real physical or digital world in some ways, says Collins.

But while math capability might take us a step closer to more powerful AI systems, solving these sorts of math problems doesn’t signal the birth of a superintelligence.

“I don’t think it immediately gets us to AGI or scary situations,” says Collins. It’s also very important to underline what kind of math problems AI is solving, she adds.

“Solving elementary-school math problems is very, very different from pushing the boundaries of mathematics at the level of something a Fields medalist can do,” says Collins, referring to a top prize in mathematics.

Machine-learning research has focused on solving elementary-school problems, but state-of-the-art AI systems haven’t fully cracked this challenge yet. Some AI models fail on really simple math problems, but then they can excel at really hard problems, Collins says. OpenAI has, for example, developed dedicated tools that can solve challenging problems posed in competitions for top math students in high school, but these systems outperform humans only occasionally.

Nevertheless, building an AI system that can solve math equations is a cool development, if that is indeed what Q* can do. A deeper understanding of mathematics could open up applications to help scientific research and engineering, for example. The ability to generate mathematical responses could help us develop better personalized tutoring, or help mathematicians do algebra faster or solve more complicated problems.

This is also not the first time a new model has sparked AGI hype. Just last year, tech folks were saying the same things about Google DeepMind’s Gato , a “generalist” AI model that can play Atari video games, caption images, chat, and stack blocks with a real robot arm. Back then, some AI researchers claimed that DeepMind was “on the verge” of AGI because of Gato’s ability to do so many different things pretty well. Same hype machine, different AI lab.

And while it might be great PR, these hype cycles do more harm than good for the entire field by distracting people from the real, tangible problems around AI. Rumors about a powerful new AI model might also be a massive own goal for the regulation-averse tech sector. The EU, for example, is very close to finalizing its sweeping AI Act. One of the biggest fights right now among lawmakers is whether to give tech companies more power to regulate cutting-edge AI models on their own.

Artificial intelligence

This new data poisoning tool lets artists fight back against generative ai.

The tool, called Nightshade, messes up training data in ways that could cause serious damage to image-generating AI models.

Rogue superintelligence and merging with machines: Inside the mind of OpenAI’s chief scientist

An exclusive conversation with Ilya Sutskever on his fears for the future of AI and why they’ve made him change the focus of his life’s work.

Will Douglas Heaven archive page

Driving companywide efficiencies with AI

Advanced AI and ML capabilities revolutionize how administrative and operations tasks are done.

MIT Technology Review Insights archive page

Generative AI deployment: Strategies for smooth scaling

Our global poll examines key decision points for putting AI to use in the enterprise.

Stay connected

Get the latest updates from mit technology review.

Discover special offers, top stories, upcoming events, and more.

Thank you for submitting your email!

It looks like something went wrong.

We’re having trouble saving your preferences. Try refreshing this page and updating them one more time. If you continue to get this message, reach out to us at [email protected] with a list of newsletters you’d like to receive.

Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

ADVERTISEMENTS:

Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

Hungarian Method to solve Assignment Problem

Hungarian algorithm to solve assignment problem.

The Hungarian algorithm of assignment is an efficient algorithm of finding an optimal solution to the assignment problem. Hungarian method is applicable to a Balanced Assignment problem, i.e., number of rows equals to the number of columns of an assignment problem.

Step by Step procedure

Hungarian algorithm of assignment involves following steps :

Subtract the minimum of each row of the cost matrix,from all the elements of respective rows.

Subtract the minimum of each column of the modified cost matrix, from all the elements of respective columns.

Then draw the minimum number of horizontal and vertical line to cover all the zeros in the modified cost matrix.

Let the number of lines be $N$.

If $N = n$, the number of rows (columns) of given cost matrix, then an optimal assignment can be made. Go to Step 6.
If $N < n$, then go to next step.

Determine the smallest element in the matrix, not covered by the $N$ lines. Subtract this smallest element from all the uncovered elements and add the same element at the intersection of horizontal and vertical lines. And obtain the second modified matrix.

Repeat Steps 3 and 4 until minimum number of lines become equal to the number of rows (columns) of the given matrix i.e. $N =n$.

Examine the row successively until a row-wise exactly single zero is found, mark this zero by $\square$ to make the assignment and mark cross $(\times)$ over all zeros in that column. Continue in this manner until all the rows have been examined. Repeat the same procedure for columns also.

Repeat the Step 6 successively until one of the following situations arise :

if no unmarked zero is left, the process ends; or
if there lie more than one of the unmarked zeros in any column or row, then mark $\square$ one of the unmarked zeros arbitrarily and cross over all zeros lying in that row or column. Repeat the process until no unmarked zero is left in the matrix.

Thus, in each row and in each column exactly one marked $\square$ zero is obtained. The assignment corresponding to these marked zeros will give an optimal assignment.

In this tutorial, you learned about step by step procedure of Hungarian Algorithm to solve assignment problem.

To learn more about Assignment problems please refer to the following tutorials:

Assignment Problems

Read step by step solution

Balanced assignment problem using Hungarian method .

Unbalanced assignment problem using Hungarian method .

Assignment problem of maximization type using Hungarian method .

Assignment problem with restrictions using Hungarian method

Let me know in the comments if you have any questions on Hungarian Algorithm to solve Assignment problems and your thought on this article.