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OpenAI

16 ta’ April 2025

RilaxxProdott

Introducing OpenAI o3 and o4-mini

Ipprova fuq ChatGPT(jinfetaħ f’tieqa ġdida)
Qed jillowdja…

Aġġornament tal-10 ta’ Ġunju 2025: OpenAI o3‑pro issa huwa disponibbli għall-utenti Pro f’ChatGPT, kif ukoll fl-API tagħna. Bħal OpenAI o1‑pro, o3‑pro huwa verżjoni tal-aktar mudell intelliġenti tagħna, OpenAI o3, iddisinjata biex taħseb għal aktar żmien u tipprovdi l-aktar tweġibiet affidabbli. Id-dettalji kollha jinsabu fin-noti tar-rilaxx⁠(jinfetaħ f’tieqa ġdida).

Illum, qed noħorġu OpenAI o3 u o4-mini, l-aktar żidiet reċenti fis-serje o tagħna ta’ mudelli mħarrġa biex jaħsbu għal aktar żmien qabel iwieġbu. Dawn huma l-aktar mudelli intelliġenti li ħriġna sal-lum, u jirrappreżentaw bidla sinifikanti fil-kapaċitajiet ta’ ChatGPT għal kulħadd, minn utenti kurjużi sa riċerkaturi avvanzati. Għall-ewwel darba, il-mudelli tar-raġunament tagħna jistgħu jużaw b’mod aġentiku u jgħaqqdu kull għodda fi ħdan ChatGPT—dan jinkludi t-tfittxija fil-web, l-analiżi ta’ fajls imtellgħin u data oħra b’Python, ir-raġunament profond dwar inputs viżivi, u anke l-ġenerazzjoni tal-immaġnijiet. B’mod kruċjali, dawn il-mudelli huma mħarrġa biex jirraġunaw dwar meta u kif jużaw l-għodod biex jipproduċu tweġibiet dettaljati u maħsuba sew fil-formati t-tajba tal-output, tipikament f’inqas minn minuta, sabiex isolvu problemi aktar kumplessi. Dan jippermettilhom jindirizzaw mistoqsijiet b’ħafna aspetti b’mod aktar effettiv, pass lejn ChatGPT aktar aġentiku li jista’ jwettaq kompiti b’mod indipendenti f’ismek. Il-qawwa magħquda ta’ raġunament state-of-the-art b’aċċess sħiħ għall-għodod tissarraf f’prestazzjoni ferm aktar b’saħħitha fuq benchmarks akkademiċi u kompiti tad-dinja reali, u tistabbilixxi standard ġdid kemm fl-intelliġenza kif ukoll fl-utilità.

X’inbidel

OpenAI o3 huwa l-aktar mudell tar-raġunament b’saħħtu tagħna li jimbotta l-fruntiera fil-kodifikazzjoni, matematika, xjenza, perċezzjoni viżiva, u aktar. Jistabbilixxi SOTA ġdid fuq benchmarks inklużi Codeforces, SWE-bench (mingħajr ma jibni scaffold apposta speċifiku għall-mudell), u MMMU. Huwa ideali għal mistoqsijiet kumplessi li jeħtieġu analiżi minn bosta angoli u li t-tweġibiet tagħhom jistgħu ma jkunux ovvji minnufih. Jagħti prestazzjoni partikolarment qawwija f’kompiti viżivi bħall-analiżi ta’ stampi, charts, u grafika. F’evalwazzjonijiet minn esperti esterni, o3 jagħmel 20 fil-mija inqas żbalji kbar minn OpenAI o1 fuq kompiti diffiċli tad-dinja reali—u jispikka b’mod speċjali f’oqsma bħall-ipprogrammar, in-negozju/konsulenza, u l-ideazzjoni kreattiva. Testers bikrin enfasizzaw ir-rigorożità analitika tiegħu bħala sieħeb tal-ħsieb u saħqu fuq il-kapaċità tiegħu li jiġġenera u jevalwa b’mod kritiku ipoteżijiet ġodda—b’mod partikolari f’kuntesti tal-bijoloġija, matematika, u inġinerija.

OpenAI o4-mini huwa mudell iżgħar ottimizzat għal raġunament veloċi u effiċjenti fl-ispejjeż—jikseb prestazzjoni notevoli għad-daqs u l-ispiża tiegħu, partikolarment fil-matematika, kodifikazzjoni, u kompiti viżivi. Huwa l-aqwa mudell b’benchmark fuq AIME 2024 u 2025. Għalkemm l-aċċess għal kompjuter inaqqas b’mod sinifikanti d-diffikultà tal-eżami AIME, sibna wkoll li hu notevoli li o4-mini jikseb 99.5% pass@1 (100% consensus@8) fuq AIME 2025 meta jingħata aċċess għal interpretu ta’ Python. Filwaqt li dawn ir-riżultati m’għandhomx jitqabblu mal-prestazzjoni ta’ mudelli mingħajr aċċess għall-għodod, huma eżempju ta’ kemm o4-mini juża b’mod effettiv l-għodod disponibbli; o3 juri titjib simili fuq AIME 2025 mill-użu tal-għodod (98.4% pass@1, 100% consensus@8).

F’evalwazzjonijiet ta’ esperti, o4-mini jegħleb ukoll lill-predeċessur tiegħu, o3‑mini, fuq kompiti mhux STEM kif ukoll fuq oqsma bħax-xjenza tad-data. Grazzi għall-effiċjenza tiegħu, o4-mini jappoġġa limiti ta’ użu ferm ogħla minn o3, u jagħmluh għażla b’saħħitha għal volum għoli u throughput għoli għal mistoqsijiet li jibbenefikaw mir-raġunament. Evalwaturi esperti esterni kklassifikaw liż-żewġ mudelli bħala li juru segwitu mtejjeb tal-istruzzjonijiet u tweġibiet aktar utli u verifikabbli mill-predeċessuri tagħhom, grazzi għal intelliġenza mtejba u l-inklużjoni ta’ sorsi mill-web. Meta mqabbla ma’ iterazzjonijiet preċedenti tal-mudelli tar-raġunament tagħna, dawn iż-żewġ mudelli għandhom ukoll iħossuhom aktar naturali u konversazzjonali, speċjalment hekk kif jirreferu għall-memorja u konversazzjonijiet tal-passat biex jagħmlu t-tweġibiet aktar personalizzati u rilevanti.

Multimodali

Kodifikazzjoni

Ir-runs kollha tal-evalwazzjoni SWE-bench jużaw subset fiss ta’ n=477 kompiti verifikati li ġew ivvalidati fuq l-infrastruttura interna tagħna.

Segwitu tal-istruzzjonijiet u użu aġentiku tal-għodod

Il-mudelli kollha jiġu evalwati f’settings għoljin ta’ ‘sforz ta’ raġunament’—simili għal varjanti bħal ‘o4-mini-high’ f’ChatGPT.

Inkomplu niskalaw l-apprendiment ta' tisħiħ

Matul l-iżvilupp ta’ OpenAI o3, osservajna li l-apprendiment ta' tisħiħ fuq skala kbira juri l-istess xejra ta’ “aktar compute = prestazzjoni aħjar” osservata fil-pretraining tas-serje GPT. Billi erġajna segwejna t-triq tal-iskalar—din id-darba fir-RL—imbuttajna ordni oħra ta’ kobor kemm fil-compute tat-taħriġ kif ukoll fir-raġunament fil-ħin tal-inferenza, u xorta qed naraw qligħ ċar fil-prestazzjoni, li jivvalida li l-prestazzjoni tal-mudelli tkompli titjieb aktar ma jitħallew jaħsbu. Bl-istess latency u spiża bħal OpenAI o1, o3 jagħti prestazzjoni ogħla f’ChatGPT—u vvalidajna li jekk inħalluh jaħseb għal aktar żmien, il-prestazzjoni tiegħu tkompli titla’.

Ħarriġna wkoll liż-żewġ mudelli biex jużaw l-għodod permezz tal-apprendiment ta' tisħiħ—ngħallmuhom mhux biss kif jużaw l-għodod, iżda wkoll jirraġunaw dwar meta jużawhom. Il-kapaċità tagħhom li jimpjegaw l-għodod skont ir-riżultati mixtieqa tagħmilhom aktar kapaċi f’sitwazzjonijiet miftuħa—partikolarment dawk li jinvolvu raġunament viżiv u flussi ta’ xogħol b’ħafna passi. Dan it-titjib huwa rifless kemm fil-benchmarks akkademiċi kif ukoll fil-kompiti tad-dinja reali, kif irrappurtaw it-testers bikrin.

Naħsbu bl-immaġnijiet

ChatGPT thinking with images

Għall-ewwel darba, dawn il-mudelli jistgħu jintegraw immaġnijiet direttament fil-katina tal-ħsieb tagħhom. Ma jarawx biss immaġni—jaħsbu biha. Dan jiftaħ klassi ġdida ta’ soluzzjoni ta’ problemi li tgħaqqad ir-raġunament viżiv u testwali, riflessa fil-prestazzjoni state-of-the-art tagħhom fuq benchmarks multimodali.

In-nies jistgħu jtellgħu ritratt ta’ whiteboard, dijagramma minn ktieb tat-test, jew skeċċ magħmul bl-idejn, u l-mudell jista’ jinterpretah—anke jekk l-immaġni tkun imċajpra, maqluba, jew ta’ kwalità baxxa. Bl-użu tal-għodod, il-mudelli jistgħu jimmanipulaw l-immaġnijiet fuq il-post—idawruhom, jagħmlu zoom, jew jittrasformawhom bħala parti mill-proċess tar-raġunament tagħhom.

Dawn il-mudelli jagħtu l-aħjar preċiżjoni fil-klassi fuq kompiti ta’ perċezzjoni viżiva, u b’hekk jippermettulhom isolvu mistoqsijiet li qabel kienu barra mil-limiti. Agħti ħarsa lejn il-blog tar-riċerka dwar ir-raġunament viżiv⁠ biex titgħallem aktar.

Lejn użu aġentiku tal-għodod

OpenAI o3 u o4-mini għandhom aċċess sħiħ għall-għodod fi ħdan ChatGPT, kif ukoll għall-għodod personalizzati tiegħek stess permezz tas-sejħa għall-funzjoni fl-API. Dawn il-mudelli huma mħarrġa biex jirraġunaw dwar kif isolvu l-problemi, billi jagħżlu meta u kif jużaw l-għodod biex jipproduċu tweġibiet dettaljati u maħsuba sew fil-formati t-tajba tal-output malajr—tipikament f’inqas minn minuta.

Pereżempju, utent jista’ jistaqsi: “Kif se jitqabbel l-użu tal-enerġija fis-sajf f’California mas-sena l-oħra?” Il-mudell jista’ jfittex fil-web għal data ta’ utilitajiet pubbliċi, jikteb kodiċi Python biex jibni tbassir, jiġġenera graff jew immaġni, u jispjega l-fatturi ewlenin wara t-tbassir, billi jgħaqqad flimkien bosta sejħiet ta’ għodod. Ir-raġunament jippermetti lill-mudelli jirreaġixxu u jibdlu d-direzzjoni kif meħtieġ skont l-informazzjoni li jiltaqgħu magħha. Pereżempju, jistgħu jfittxu fil-web bosta drabi bl-għajnuna ta’ fornituri tat-tiftix, iħarsu lejn ir-riżultati, u jippruvaw tfittxijiet ġodda jekk ikollhom bżonn aktar informazzjoni.

Dan l-approċċ flessibbli u strateġiku jippermetti lill-mudelli jindirizzaw kompiti li jeħtieġu aċċess għal informazzjoni aġġornata lil hinn mill-għarfien integrat tal-mudell, raġunament estiż, sintesi, u ġenerazzjoni ta’ output fuq modalitajiet differenti.

L-eżempji kollha tlestew b’OpenAI o3.

OpenAI o3

Solve the following very hard math problem using your in-built knowledge of the literature:

Construct a degree 19 polynomial \ (p(x)) \ in \ mathbb{C}[x] such that \ (X := \ {\, p(x) = p(y) \, \} \ subset \ mathbb{P}^{1} \ times \ mathbb{P}^{1}\ ) has at least 3 (but not all linear) irreducible components over \ mathbb{C}. Choose \ (p(x)\ ) to be odd, monic, have real coefficients and linear coefficient \ (-19\ ) and calculate \ (p(19)\ ).

Ikkalkula dwar il-kostruzzjoni tal-polinomju għal 55 sekonda
  • The curve defined by p(x) = p(y) factors if p(x) is decomposable or has repeated factors. Actually, p(x)-p(y) always factors, and it’s divisible by (x-y). This gives one factor, and the rest is a degree d-1 polynomial in x and y. For the curve to have at least three irreducible components, p(x)-p(y) must factor into at least three nontrivial factors. Each factor corresponds to a component in projective space, and at least one must be nonlinear.
  • I’m checking the Dickson polynomials D_n(x,a) and focusing on their coefficients. With a=1, it seems the leading coefficient is always 1, confirming that Dickson polynomials are monic. The linear coefficient for odd n is following a predictable sign pattern: for n=19, it gives a coefficient of -19, which is exactly what I need. So the Dickson polynomial D_n(x,1) with odd n fits nicely with the linear coefficient I was looking for.
  • I've confirmed that the linear coefficient for p(x)=D19(x)p(x) = D_{19}(x)p(x)=D19​(x) is correct, with the necessary scaling factor to match. Now for the next step, I need to compute D19(19)D_{19}(19)D19​(19). Since Tn(z)T_n(z)Tn​(z) grows quickly for real z>1z > 1z>1, I plan to compute this value using Python, leveraging the recurrence to avoid mistakes—it's going to be a big number. I'll make sure to present the numeric result neatly so it's understandable since the coefficients are integers.
  • The Dickson polynomial D_{19}(x,1) is confirmed to have the required properties: monic, odd, real coefficients, and a linear coefficient of -19. The factorization of D_{19}(x) into irreducible components is also verified and satisfies the condition of having at least 10 components (1 linear + 9 quadratics). To compute p(19), we'll use the recurrence relation for Dickson polynomials, but there's also a closed-form expression involving cosine that could be handy here. I'll proceed accordingly!
  • I confirmed the linear coefficient is working correctly, which means now I need to calculate p(19)=D19(19)p(19) = D_{19}(19)p(19)=D19​(19). This involves evaluating T19(9.5)T_{19}(9.5)T19​(9.5), which grows rapidly. To ensure I get an accurate result, I'll compute this using recurrence in Python. The result is a large number: 1,876,572,071,974,094,803,391,179. I'll use the commas to make it easier to read: p(19)=1,876,572,071,974,094,803,391,179p(19) = 1,876,572,071,974,094,803,391,179p(19)=1,876,572,071,974,094,803,391,179.
  • For a = 1, there’s a relationship between Dickson polynomials and Chebyshev polynomials: D_n(x, 1) = 2^(n-1) T_n(x/2). Checking this, we see that the definition of D_n(u + 1/u) aligns well with Chebyshev’s formula. By setting x = 2 cos(θ), we find that D_n(x) equals 2 T_n(x/2). Importantly, the leading coefficient works out to 1, confirming the identity holds. This is nice!
  • Now, I need to verify that p(x)−p(y)p(x) - p(y)p(x)−p(y) factors as desired, relying on the known Dickson polynomial factorization. According to the literature (like Fried and Jarden), the difference Dn(x)−Dn(y)D_n(x) - D_n(y)Dn​(x)−Dn​(y) factors into a product involving (x−y)(x - y)(x−y) and other expressions. I'll provide the explicit polynomial D19(x,1)D_{19}(x, 1)D19​(x,1), list the coefficients, and explain how it satisfies the desired properties: monic, odd, etc. Lastly, I'll compute p(19)p(19)p(19).

Analyzed

Unknown component type: componentCodeExample

Analyzed

Unknown component type: componentCodeExample

Analyzed

Unknown component type: componentCodeExample

Analyzed

Unknown component type: componentCodeExample

Analyzed

Unknown component type: componentCodeExample

Analyzed

Unknown component type: componentCodeExample

Done

A convenient way to force many factors in
p(x)  −  p(y)p(x) \;-\; p(y) is to use a Dickson polynomial of the first kind.
For a parameter a∈Ca \in \mathbb{C} in math these are defined by

D0 ⁣(x, a)=2,  D1 ⁣(x, a)=x,  Dn ⁣(x, a)=x Dn−1 ⁣(x, a)−a Dn−2 ⁣(x, a)(n≥2),D_0\!\left(x,\, a\right) = 2,\; D_1\!\left(x,\, a\right) = x,\; D_n\!\left(x,\, a\right) = x\,D_{n-1}\!\left(x,\, a\right) - a\,D_{n-2}\!\left(x,\, a\right)\quad (n \ge 2),

and satisfy the functional identity

Dn ⁣(u+au, a)=un+anun.D_n\!\left(u + \frac{a}{u},\, a\right) = u^{n} + \frac{a^{n}}{u^{n}}.

1. Choosing the polynomial

Take a=1a = 1 and n=19n=19.
Because nn is odd, D19 ⁣(x, 1)D_{19}\!\left(x,\, 1\right) is an odd polynomial; the recurrence immediately shows it is monic and has integer (hence real) coefficients.
The coefficient of xx is x=(−1)n−12 n=−19,x = (-1)^{\frac{n-1}{2}}\,n = -19, so all requested normalisations are satisfied.

Writing it out gives

p(x)=D19 ⁣(x,1)=x19−19x17+152x15−665x13+1729x11−2717x9+2508x7−1254x5+285x3−19x . \boxed{% p(x) = D_{19}\!\left(x,1\right) = x^{19} - 19x^{17} + 152x^{15} - 665x^{13} + 1729x^{11} - 2717x^{9} + 2508x^{7} - 1254x^{5} + 285x^{3} - 19x% }\,.

2. Irreducible components of fX  =  { p(x)=p(y) }fX \;=\; \bigl\{\, p(x) = p(y) \,\bigr\}

For Dickson polynomials one has the classical factorisation

Dn ⁣(x,1)  −  Dn ⁣(y,1)  =  (x−y) ∏j=1n−12(x2+y2−2cos⁡ ⁣(2πjn) xy−4sin⁡2 ⁣(πjn)),D_n\!\left(x,1\right) \;-\; D_n\!\left(y,1\right) \;=\; (x - y)\, \prod_{j=1}^{\frac{n-1}{2}} \Bigl( x^{2} + y^{2} - 2\cos\!\bigl(\tfrac{2\pi j}{n}\bigr)\,xy - 4\sin^{2}\!\bigl(\tfrac{\pi j}{n}\bigr) \Bigr),

where each quadratic factor is irreducible over C\mathbb{C} (see, e.g., Lidl–Niederreiter, Finite Fields, §3.6).
For n=19n=19 this gives

  • one linear component x=y;x=y;
  • nine quadratic components (corresponding to (j=1, …, 9).\bigl(j = 1,\,\ldots,\,9\bigr).

Hence X⊂P1×P1X \subset \mathbb{P}^{1} \times \mathbb{P}^{1} has 1010 irreducible components, at least three of them and not all linear, as required.

3. Evaluating p(19)p(19)

Using the recurrence (or the identity Dn ⁣(x, 1)  =  2 Tn ⁣(x2)D_n\!\left(x,\,1\right) \;=\; 2\,T_n\!\bigl(\tfrac{x}{2}\bigr) with Chebyshev TnT_n one obtains

p(19)  =  D19 ⁣(19, 1)  =  1 876 572 071 974 094 803 391 179.p(19) \;=\; D_{19}\!\left(19,\,1\right) \;=\; 1\,876\,572\,071\,974\,094\,803\,391\,179.

Thus the polynomial above fulfils every condition, and

p(19)  =  1,876,572,071,974,094,803,391,179.\boxed{% p(19) \;=\; 1{,}876{,}572{,}071{,}974{,}094{,}803{,}391{,}179 }.

OpenAI o1

Solve the following very hard math problem using your in-built knowledge of the literature:

Construct a degree 19 polynomial \ (p(x)) \ in \ mathbb{C}[x] such that \ (X := \ {\, p(x) = p(y) \, \} \ subset \ mathbb{P}^{1} \ times \ mathbb{P}^{1}\ ) has at least 3 (but not all linear) irreducible components over \ mathbb{C}. Choose \ (p(x)\ ) to be odd, monic, have real coefficients and linear coefficient \ (-19\ ) and calculate \ (p(19)\ ).

Ħaseb għal 1m 19s

I’m piecing together a degree 19 polynomial with only odd powers and a linear coefficient of -19, like: p(x)=x19+a17x17+…+a1xp(x) = x^{19} + a_{17}x^{17} + \ldots + a_1xp(x)=x19+a17​x17+…+a1​x.

I'm examining if the polynomial p(x)=x19+a17x17+…+a3x3−19xp(x) = x^{19} + a_{17}x^{17} + \ldots + a_3x^3 - 19xp(x)=x19+a17​x17+…+a3​x3−19x has a notable classical form, considering symmetry or factorization for multiple irreducible components.

To ensure p(x)p(x)p(x) has three or more irreducible components, I’m considering the factorization of p(x)−p(y)p(x) - p(y)p(x)−p(y) into at least three irreducible factors in C[x,y]\mathbb{C}[x,y]C[x,y].

I'm working through x19−y19x^{19} - y^{19}x19−y19 to ensure it balances linear and nonlinear factors, aiming for a polynomial with at least three irreducible components that aren't all linear.

Taking a closer look at how p(x)−p(y)p(x) - p(y)p(x)−p(y) can be factored into three distinct polynomials in xxx, aiming to achieve the desired irreducible components.

I'm thinking about how composing ppp with simpler polynomials, like xm−cx^m - cxm−c, could result in multiple irreducible components, achieving at least three distinct factors.

I’m exploring the factorization of p(x)−p(y)p(x) - p(y)p(x)−p(y) with cyclotomic polynomials. This method generates nnn linear irreducible factors, which might not achieve the required three distinct components.

I'm focusing on constructing an "odd" and monic polynomial, ensuring all exponents are odd and the leading term is x19x^{19}x19. This approach aims to achieve the desired factorization.

I'm working with the Chebyshev polynomials to ensure p(x)−p(y)p(x) - p(y)p(x)−p(y) has at least three irreducible components, leveraging their even or odd properties to manage coefficients.

Considering the odd Chebyshev polynomial T19(x)T_{19}(x)T19​(x) for potential factorization, while also examining composite polynomials of lower degrees to enhance factorization properties.

I'm analyzing how a polynomial composed of lower-degree polynomials, like (x3−3x)k(x^3 - 3x)^k(x3−3x)k, could yield p(x)−p(y)p(x) - p(y)p(x)−p(y) with at least three irreducible components.

Piecing together polynomials with integer coefficients, like (x3−3x)k(x^3 - 3x)^k(x3−3x)k, to achieve factorization in p(x)−p(y)p(x) - p(y)p(x)−p(y) with at least three irreducible components, aiming for degree 19.

I’m examining how p(x)=(x3−3x)kp(x) = (x^3 - 3x)^kp(x)=(x3−3x)k or p(x)=x19−19xp(x) = x^19 - 19xp(x)=x19−19x might yield p(x)−p(y)p(x) - p(y)p(x)−p(y) with three irreducible components, focusing on ensuring the polynomial is of degree 19.

I’m analyzing p(x)−p(y)p(x) - p(y)p(x)−p(y) into (x−y)(x18+x17y+…+y18−19)(x-y)(x^{18} + x^{17}y + \ldots + y^{18} - 19)(x−y)(x18+x17y+…+y18−19) to identify irreducible components. The polynomial factor x18+x17y+…+y18−19x^{18} + x^{17}y + \ldots + y^{18} - 19x18+x17y+…+y18−19 remains challenging to factor further.

I’m thinking through a new approach: adjusting the Chebyshev polynomial T19(x)T_{19}(x)T19​(x) to make it monic, aiming to achieve at least three irreducible components in p(x)−p(y)p(x) - p(y)p(x)−p(y).

OK, let's think through. I’m tweaking T19(x)T_{19}(x)T19​(x)'s coefficients to keep the polynomial monic and check if it simplifies into multiple irreducible components.

I'm thinking over various factorization strategies for a monic polynomial of degree 19. The goal is to ensure at least one non-linear factor and achieve at least three irreducible components in p(x)−p(y)p(x) - p(y)p(x)−p(y).

I’m updating my approach to factor x2+xy+y2−1x^2 + xy + y^2 - 1x2+xy+y2−1 over complex numbers by exploring change of variables and third roots of unity. This helps in achieving the desired polynomial structure.

I'm combining x3−xx^3 - xx3−x with x19−19xx^{19} - 19xx19−19x to tweak the polynomial's coefficients and complexity, aiming to include more non-linear factors for the desired irreducibility.

Piecing together p(x)=x19−x3−19xp(x) = x^{19} - x^3 - 19xp(x)=x19−x3−19x to ensure it’s odd, monic, and has the required linear coefficient. This targets the desired irreducible factorizations.

I’m mapping out the second factor x18+…+y18−x2−xy−y2−19x^{18} + \ldots + y^{18} - x^2 - xy - y^2 - 19x18+…+y18−x2−xy−y2−19 to see if it can split into three irreducible components.

I’m considering methods to factorize the polynomial by making it divisible by x−yx - yx−y and ensuring the remaining factor splits into exactly two irreducible components, aiming for a less complex factorization.

I’m examining the polynomial x18+x17y+…+y18x^{18} + x^{17}y + \ldots + y^{18}x18+x17y+…+y18 and noting it simplifies to x19−y19x−y\frac{x^{19} - y^{19}}{x - y}x−yx19−y19​, which might reveal further irreducible factors.

I’m mapping out the polynomial x(x18−1)−y(y18−1)x−y\frac{x(x^{18}-1) - y(y^{18}-1)}{x-y}x−yx(x18−1)−y(y18−1)​ for further factorization. This might yield just two irreducible components, which falls short of three.

I’m exploring whether the polynomial p(x)=x19−(x3)p(x) = x^19 - (x^3)p(x)=x19−(x3) can be expressed as the composition of a smaller polynomial with xkx^kxk, potentially revealing multiple irreducible components.

I'm examining if the polynomial T19(x)T_{19}(x)T19​(x) can be factored using trigonometric identities, seeking partial factorization without fully linearizing, to gain multiple irreducible components.

OK, let me see. Trigonometric identities show multiple solutions for θ\thetaθ and ϕ\phiϕ, likely leading to 19 or 38 linear factors for T19(x)T_{19}(x)T19​(x).

I’m examining how the equation arccos⁡x=±arccos⁡y+2kπ19\arccos x = \pm \arccos y + \frac{2k\pi}{19}arccosx=±arccosy+192kπ​ leads to possible multiple branches, potentially irreducible in the algebraic sense, and needing an example with at least three non-linear irreducible components.

OK, let me see. I’m pulling together details on the polynomial x3(x2−1)8+xx^3 (x^2 - 1)^8 + xx3(x2−1)8+x. It’s monic, with x19x^{19}x19 as the leading term, ensuring it meets key criteria.

I’m noting that the polynomial p(x)=x3(x2−1)8+xp(x) = x^3 (x^2 - 1)^8 + xp(x)=x3(x2−1)8+x is odd, with its linear coefficient patterning to -19.

I’m figuring out how to adjust the linear coefficient of polynomial p(x)p(x)p(x) to -19 by adding a constant factor ccc in front of xxx to ensure it’s adequately modified.

By tweaking the linear coefficient of p(x)=x3(x2−1)8+cxp(x) = x^3 (x^2 - 1)^8 + c xp(x)=x3(x2−1)8+cx to -19, it ensures the polynomial remains monic, odd, and real.

I’m working on adding a constant factor ccc to xxx in p(x)=x3(x2−1)8+cxp(x) = x^3 (x^2 - 1)^8 + c xp(x)=x3(x2−1)8+cx to ensure the linear coefficient is -19, making the polynomial monic, odd, and real.

I'm piecing together the polynomial p(x)=x3(x−1)8(x+1)8p(x) = x^3 (x-1)^8 (x+1)^8p(x)=x3(x−1)8(x+1)8 and considering how p(x)−p(y)p(x) - p(y)p(x)−p(y) might factor with factors like x−yx-yx−y.

I’m confirming p(x)p(x)p(x) is monic, odd, and real, with a linear coefficient of -19, by expanding x3(x2−1)8x^3 (x^2 -1)^8x3(x2−1)8 to set the constant ccc.

I found that for p(x) to have a coefficient of -19 for the x term, c must be -19. The polynomial, p(x), incorporates this constant and preserves the original polynomial's structure.

Below is one concrete example (over the reals) of an odd, monic, degree 19 polynomial with linear coefficient −19-19 whose zero-locus relation { p(x)=p(y) } in P1×P1\{\,p(x)=p(y)\,\}\ \text{in }\mathbb{P}^{1}\times\mathbb{P}^{1} splits into at least three irreducible components (and not all components are linear). We then compute p(19)p(19).

1. The polynomial

Consider

p(x)  =  x3 (x2−1)8  −  19x.p(x) \;=\; x^{3}\,\bigl(x^{2}-1\bigr)^{8} \;-\; 19x.

We can expand

x3 (x2−1)8  =  x19  −  8x17  +  28x15  −  56x13  +  70x11  −  56x9  +  28x7  −  8x5  +  x3.x^{3}\,\bigl(x^{2}-1\bigr)^{8} \;=\; x^{19}\;-\;8x^{17}\;+\;28x^{15}\;-\;56x^{13}\;+\;70x^{11} \;-\;56x^{9}\;+\;28x^{7}\;-\;8x^{5}\;+\;x^{3}.

Hence

p(x)  =  x19  −  8x17  +  28x15  −  56x13  +  70x11  −  56x9  +  28x7  −  8x5  +  x3  −  19x.p(x) \;=\; x^{19} \;-\; 8x^{17} \;+\; 28x^{15} \;-\; 56x^{13} \;+\; 70x^{11} \;-\; 56x^{9} \;+\; 28x^{7} \;-\; 8x^{5} \;+\; x^{3} \;-\; 19x.

Checking the required properties

Degree 19, monic:
The leading term is x19x^{19}with coefficient 11.

Odd polynomial:
All exponents are odd (19, 17, …, 3, 1),\bigl(19,\,17,\,\ldots,\,3,\,1\bigr), and the constant term is 00. Indeed,

p(−x)  =  − p(x),p(-x) \;=\; -\,p(x),

which makes pp an odd polynomial.

Real coefficients:
All coefficients are real integers.

Linear coefficient −19-19:
The coefficient of xx is clearly −19-19.

At least three irreducible components, not all linear:
Over C\mathbb{C}, the locus

X  =  { (x,y):p(x)=p(y) }  ⊂  P1×P1X \;=\; \bigl\{\, (x,y) : p(x)=p(y) \,\bigr\} \;\subset\; \mathbb{P}^{1}\times\mathbb{P}^{1}

factors in part because p(x)p(x) has (for instance) the repeated factors (x2−1)8\bigl(x^{2}-1\bigr)^{8} in the big piece x3 (x2−1)8x^{3}\,\bigl(x^{2}-1\bigr)^{8}. One sees that { p(x)=p(y) }\{\,p(x)=p(y)\,\} contains (at least) the divisor $${x=y\}$$ plus further factors coming from the roots x=0  or  x=±1,x = 0 \;\text{or}\; x = \pm 1, ensuring multiple irreducible components (and not all of them are hyperplanes).

2. Computing p(19)p(19)

A direct substitution x=19x=19 gives a large integer. Symbolic expansion or a computer algebra system yields

p(19)  =  1934999285524070399999639.p(19) \;=\; 1934999285524070399999639.

Hence the required value is

\boxed{\,p(19) \;=\; 1934999285524070399999639\,}. \] ​:contentReference[oaicite:0]{index=0}​

OpenAI o3 jagħti t-tweġiba korretta mingħajr ma juża t-tiftix, filwaqt li o1 jonqos milli jagħti tweġiba korretta.

Inwasslu ’l quddiem ir-raġunament effiċjenti fl-ispejjeż

Spiża vs prestazzjoni: o3‑mini u o4-mini
Evalwazzjonijiet AIME ta’ OpenAI o3-mini u o4-mini
Evalwazzjonijiet GPQA ta’ OpenAI o3-mini u o4-mini
Spiża vs prestazzjoni: o1 u o3
Evalwazzjonijiet AIME ta’ OpenAI o3 u o4
Evalwazzjonijiet GPQA ta’ OpenAI o3 u o4

OpenAI o3 u o4-mini huma l-aktar mudelli intelliġenti li qatt ħriġna, u ħafna drabi huma wkoll aktar effiċjenti mill-predeċessuri tagħhom, OpenAI o1 u o3‑mini. Pereżempju, fil-kompetizzjoni tal-matematika AIME 2025, il-fruntiera spiża-prestazzjoni għal o3 ittejjeb b’mod strett fuq o1, u bl-istess mod, il-fruntiera ta’ o4-mini ttejjeb b’mod strett fuq o3‑mini. B’mod aktar ġenerali, nistennew li għall-biċċa l-kbira tal-użu fid-dinja reali, o3 u o4-mini jkunu wkoll kemm aktar intelliġenti kif ukoll orħos minn o1 u o3‑mini, rispettivament.

Sigurtà

Kull titjib fil-kapaċitajiet tal-mudell jiġġustifika titjib proporzjonat fis-sigurtà. Għal OpenAI o3 u o4-mini, bnejna mill-ġdid kompletament id-data tat-taħriġ tas-sigurtà tagħna, billi żidna prompts ġodda ta’ rifjut f’oqsma bħal theddid bijoloġiku (biorisk), ġenerazzjoni ta’ malware, u jailbreaks. Din id-data mġedda wasslet biex o3 u o4-mini jiksbu prestazzjoni qawwija fuq il-benchmarks interni tagħna ta’ rifjut (eż., ġerarkija tal-istruzzjonijiet⁠, jailbreaks). Minbarra prestazzjoni qawwija għar-rifjuti tal-mudell, żviluppajna wkoll mitigazzjonijiet fil-livell tas-sistema biex jimmarkaw prompts perikolużi f’oqsma ta’ riskju tal-fruntiera. Simili għax-xogħol preċedenti tagħna fil-ġenerazzjoni tal-immaġnijiet⁠, ħarriġna monitor LLM tar-raġunament li jaħdem minn speċifikazzjonijiet tas-sigurtà miktuba mill-bniedem u interpretabbli. Meta applikat għall-biorisk, dan il-monitor irnexxielu jimmarka ~99% tal-konversazzjonijiet fil-kampanja tagħna ta’ red‑teaming uman.

Għamilna stress tests fuq iż-żewġ mudelli bl-aktar programm rigoruż tas-sigurtà tagħna sal-lum. Skont il-Qafas tat-Tħejjija⁠ aġġornat tagħna, evalwajna o3 u o4-mini fit-tliet oqsma ta’ kapaċità segwiti koperti mill-Qafas: bijoloġiku u kimiku, ċibersigurtà, u titjib awtonomu tal-AI. Fuq il-bażi tar-riżultati ta’ dawn l-evalwazzjonijiet, iddeterminajna li kemm o3 kif ukoll o4‑mini jibqgħu taħt il-livell “High” tal-Qafas fit-tliet kategoriji kollha. Ippubblikajna r-riżultati dettaljati ta’ dawn l-evalwazzjonijiet fil-kard tas-sistema⁠.⁠

Codex CLI: raġunament tal-fruntiera fit-terminal

Qed naqsmu wkoll esperiment ġdid: Codex CLI, aġent tal-kodifikazzjoni ħafif li tista’ tħaddem mit-terminal tiegħek. Jaħdem direttament fuq il-kompjuter tiegħek u huwa ddisinjat biex jimmassimizza l-kapaċitajiet tar-raġunament ta’ mudelli bħal o3 u o4-mini, b’appoġġ li ġej għal mudelli API addizzjonali bħal GPT‑4.1⁠.

Tista’ tikseb il-benefiċċji tar-raġunament multimodali mil-linja tal-kmand billi tgħaddi screenshots jew skeċċijiet b’fedeltà baxxa lill-mudell, flimkien ma’ aċċess għall-kodiċi tiegħek lokalment. Aħna nqisuh bħala interfaċċa minima biex tgħaqqad il-mudelli tagħna mal-utenti u l-kompjuters tagħhom. Codex CLI huwa kompletament open-source fuq github.com/openai/codex⁠(jinfetaħ f’tieqa ġdida) mil-lum.

Flimkien ma’ dan, qed invaraw inizjattiva ta’ $1 miljun biex nappoġġaw proġetti li jużaw Codex CLI u mudelli ta’ OpenAI. Se nevalwaw u naċċettaw applikazzjonijiet għal għotjiet f’inkrementi ta’ $25,000 USD fil-forma ta’ krediti tal-API. Il-proposti jistgħu jintbagħtu hawn.

Aċċess

L-utenti ta’ ChatGPT Plus, Pro, u Team se jaraw o3, o4-mini, u o4-mini-high fis-selettur tal-mudell minn illum, minflok o1, o3‑mini, u o3‑mini‑high. L-utenti ta’ ChatGPT Enterprise u Edu se jiksbu aċċess fi żmien ġimgħa. L-utenti b’xejn jistgħu jippruvaw o4-mini billi jagħżlu 'Think' fil-composer qabel jibagħtu l-mistoqsija tagħhom. Il-limiti tar-rata fil-pjanijiet kollha jibqgħu l-istess bħas-sett preċedenti ta’ mudelli.

Nistennew li noħorġu OpenAI o3‑pro fi ftit ġimgħat b’appoġġ sħiħ għall-għodod. Għalissa, l-utenti Pro xorta jistgħu jaċċessaw o1‑pro.

Kemm o3 kif ukoll o4-mini huma disponibbli wkoll għall-iżviluppaturi llum permezz tal-API tat-tlestija taċ-chats u r-Responses API (xi żviluppaturi se jkollhom bżonn jivverifikaw l-organizzazzjonijiet tagħhom⁠(jinfetaħ f’tieqa ġdida) biex jaċċessaw dawn il-mudelli). Ir-Responses API tappoġġa sommarji tar-raġunament, il-kapaċità li żżomm tokens tar-raġunament madwar is-sejħiet tal-funzjoni għal prestazzjoni aħjar, u dalwaqt se tappoġġa għodod integrati bħat-tfittxija fil-web, it-tfittxija fil-fajls, u interpretu tal-kodiċi fi ħdan ir-raġunament tal-mudell. Biex tibda, esplora d-dokumentazzjoni tagħna⁠⁠(jinfetaħ f’tieqa ġdida) u ibqa’ stenna għal aktar aġġornamenti.

X’hemm imiss

L-aġġornamenti tal-lum jirriflettu d-direzzjoni li fiha sejrin il-mudelli tagħna: qed nikkonverġu l-kapaċitajiet speċjalizzati tar-raġunament tas-serje o ma’ aktar mill-abbiltajiet naturali ta’ konversazzjoni u l-użu tal-għodod tas-serje GPT. Billi ngħaqqdu dawn is-saħħiet, il-mudelli futuri tagħna se jappoġġaw konversazzjonijiet bla xkiel u naturali flimkien ma’ użu proattiv tal-għodod u soluzzjoni avvanzata tal-problemi.

Aġġornament tat-28 ta’ Lulju 2025: Id-dataset u r-riżultati ta’ SWE-Lancer ġew aġġornati mis-17 ta’ Lulju 2025, disponibbli fuq: https://github.com/openai/preparedness⁠(jinfetaħ f’tieqa ġdida) u fil-kards tas-sistema tagħna. Dan l-aġġornament isolvi diversi problemi li kienu qed jaffettwaw ir-riżultati tad-dollari miksuba u jneħħi r-rekwiżit tal-konnettività tal-internet waqt l-eżekuzzjoni, u b’hekk jelimina sors prinċipali ta’ varjabbiltà fil-prestazzjoni tal-mudell.

Aġġornament tas-16 ta’ April 2025: ir-riżultati għal o3 fuq Charxiv-r u Mathvista ġew aġġornati biex jirriflettu bidla fis-system prompt li ma kinitx preżenti fl-evalwazzjoni oriġinali.

Replay tal-livestream

Awtur

OpenAI

Noti f’qiegħ il-paġna

* In-numri tal-evalwazzjoni tau-bench huma medji fuq 5 runs biex titnaqqas il-varjanza, u jsiru mingħajr ebda għodda personalizzata jew prompting. Sibna li r-rollouts ta’ tau-bench retail huma aktar suxxettibbli għal żbalji fil-mudell tal-utent. In-numri għall-bar imdella jitħaddmu b’ GPT-4.1 bħala mudell tal-utent għaliex huwa ferm aħjar minn GPT-4o biex isegwi l-istruzzjonijiet.

* SWE-bench juża tul massimu ta’ kuntest ta’ 256k, li jtejjeb ir-rata ta’ soluzzjoni għal o4-mini b’madwar 3% u jaffettwa r-rata ta’ soluzzjoni ta’ o3 b’<1%. Neskludu wkoll 23 kampjun li ma jistgħux jitħaddmu fuq l-infrastruttura interna tagħna.

** Meta tattiva browsing, il-mudell jista’ xi kultant isib tweġibiet eżatti online, pereżempju billi jaqra blog posts b’problemi kampjun minn dataset. Innaqqsu t-tħassib dwar il-qerq tal-mudell waqt il-browsing b’żewġ strateġiji:

  • Imblukkajna domini li osservajna li l-mudell iqerraq minnhom fil-passat.

  • Użajna mudell tar-raġunament bħala monitor biex jeżamina t-tokens kollha f’kull attentat, sabiex jidentifika mġiba suspettuża. Mġiba suspettuża hija definita bħala "paġna, fajl, jew snippet li l-għan prinċipali tagħha huwa li tipprovdi t-tweġiba eżatta għal din il-mistoqsija speċifika—eż., ċavetta uffiċjali tal-marki, gist ta’ “soluzzjonijiet” leaked, jew diskussjoni li tikkwota t-tweġiba finali kelma b’kelma." Mġiba beninna hija definita bħala "Kwalunkwe riżorsa awtorevoli li bniedem diliġenti jista’ jikkonsulta (dokumentazzjoni, manwali, karti akkademiċi, artikli ta’ reputazzjoni) anke jekk b’mod inċidentali jkun fiha t-tweġiba korretta." Kull attentat fejn il-monitor qies ir-rollout bħala suspettuż jingħadd bħala żbaljat. Il-biċċa l-kbira tal-kampjuni li fallew minn dan il-kontroll kienu problemi li s-soluzzjoni eżatta tagħhom kienet disponibbli fuq diversi sorsi tal-internet mhux relatati mal-HLE.

Fl-aħħarnett, l-evalwazzjonijiet tagħna bil-browsing jistgħu ma jkunux perfettament riproduċibbli fl-API ta’ OpenAI minħabba differenza fil-backends tal-magni tat-tiftix bejn ChatGPT u l-API ta’ OpenAI. Dawn ir-riżultati huma maħsuba biex jirrappreżentaw l-esperjenza tal-utent ta’ ChatGPT, iżda skont id-domanda, il-konfigurazzjoni tat-tiftix tista’ tinbidel maż-żmien.

Kontributuri

Aaditya Singh, Aaron Schlesinger, Adam Fry, Adam Lerer, Adam Perelman, Adam Walker, Ahmed El-Kishky, Aidan Clark, Aidan McLaughlin, Aiden Low, Akila Welihinda, Akshay Nathan, Aleksander Madry, Aleksandra Spyra, Alex Karpenko, Alex Neitz, Alex Tachard Passos, Alex Wei, Alexander Prokofiev, Alexander Zielenski, Alexandra Barr, Alexey Ivanov, Alexi Christakis, Alfred Xue, Allison Tam, Ally Bennett, Ally Bennett , Amelia Liu, Amy McDonald Sandjideh, Ananya Kumar, Andre Saraiva, Andrea Vallone, Andrew Chen, Andrew Duberstein, Andrew Gibiansky, Andrew Kondrich, Andrew Tulloch, Andrey Mishchenko, Andy Applebaum, Andy Wang, Angela Baek, Annie Wei, Anting Shen, Antoine Pelisse, Anuj Saharan, Arun Vijayvergiya, Ashley Tyra, Ashvin Nair, Avi Nayak, Avital Oliver, Behrooz Ghorbani, Belinda Truong, Ben Sokolowsky, Beth Hoover, Bo Xu, Boaz Barak, Bohan Zhang, Borys Minaiev, Botao Hao, Bowen Baker, Bowen Cheng, Brandon McKinzie, Brandon Wang, Brian Hsu, Brian Yang, Brian Yu, Brian Zhang, Camillo Lugaresi, Carolina Paz, Carpus Chang, Cary Bassin , Cary Hudson, Casey Chu, Chak Li, Charles Zhao, Charlie Jatt, Charlotte Cole, Chelsea Voss, Chen Shen, Chengxu Zhuang, Chris Colby, Chris Hallacy , Chris Koch, Christina Kaplan, Christina Kim, Colin Reid, Colin Wei, Cristina Scheau, D. Sculley, Damien Deville, Dan Roberts, Dana Palmie, Dane Stuckey, Daniel Levine, David Hu, David Martin, David Robinson, David Sasaki, Davis Wu, Derek Chen, Dibya Bhattacharjee, Dimitris Tsipras, Dinghua Li, DJ Strouse, dmed Medina, Drew Hintz, Eddie Zhang, Edmund Wong, Elaine Ya Le, Eli Yani , Elizabeth Proehl, Emily Sokolova, Enoch Cheung, Eri Schwartz, Eric Mitchell, Eric Ning, Eric Sigler, Eric Wallace, Eugenio Panero, Evan Mays, Evgenii Nikishin, Fan Wang, Fangyuan Li, Filippo Raso, Foivos Tsimpourlas, Fouad Matin, Francis Song, Francis Zhang, Gary Yang, Gene Oden, Giambattista Parascandolo, Gildas Chabot, Grace Kim, Grace Zhao, Greg Brockman, Gregory Valiant, Guillaume Leclerc, Hadi Salman, Haitang Hu, Hannah Sheahan, Hao Sheng, Haoyu Wang, Henrique Ponde de Oliveira Pinto, Henry Aspegren, Heqing Yan, Hessam Bagherinezhad, Hongyu Ren, Hunter Lightman, Hyeonwoo Noh, Ian Kivlichan, Ian Sohl, Ignasi Clavera, Ikai Lan, Ilge Akkaya, Ilya Kostrikov, Irina Kofman, Isa Fulford, Jake Brill, Jakub Pachocki, James Betker, James Lee, James Qin, Jamie Kiros, Jason Ai, Jay Wang, Jean Harb, Jeff Mickey, Jeffrey Han, Jeffrey Wang, Jeremy Chen, Jerry Tworek, Jessica Liang, Jessica Shieh, Ji Lin, Jiahui Yu, Jianfeng Wang, Jie Tang, Jihan Yin, Jing Li, Joanne Jang, Joel Morris, Johannes Ferstad, Johannes Heidecke, John Fishbein, Jon Okun, Jonathan Gordon, Joost Huizinga, Jos Kraaijeveld, Joseph Mo, Josh Lawson , Josh Tobin, Junhua Mao, Kai Chen, Kai Hayashi, Karan Singhal, Karina Nguyen, Katy Shi, Kelly Stirman, Kenji Hata, Kenny Nguyen, Keren Gu-Lemberg, Kevin Gladstone, Kevin King, Kevin Liu, Kevin Lu, Kevin Park, Kevin Stone, Kevin Weil, Kevin Whinnery, Kevin Yu, Kote Mushegiani, Kristen Ying, Kristian Georgiev, Kshitij Gupta, Kyle Kosic, Lama Ahmad, Larry Lv, Lauren Itow, Lauren Yang, Lee Byron, Leo Chen, Leo Liu, Leon Maksin, Leyton Ho, Li Jing, Liang Xiong, Lin Yang, Linden Li, Lorenz Kuhn, Louis Feuvrier, Lu Zhang, Łukasz Kaiser, Mahmoud Eariby, Maja Trębacz, Manas Joglekar, Manoli Liodakis, Manuka Stratta, Mark Chen, Mark Hudnall, Mark Sun, Mark Wang, Martin Li, Marvin Zhang, Mateusz Litwin, Matt Jones, Matt Lim, Max Johnson, Max Schwarzer, Mayank Gupta, Meghan Shah, Mengqing Wang, Mengyuan Yan, Mia Glaese, Michael Bolin, Michael Lampe, Michael Malek, Michael Sharman, Michael Zhang, Michele Wang, Michelle Pokrass, Miguel Oom Temudo de Castro, Mihai Florian, Mike McClay, Mike Trpcic, Miki Habryn, Miles Wang, Ming Chen, Mingxuan Wang, Minnia Feng, Mitchell Gordon, Mo Bavarian, Mostafa Rohaninejad, Nacho Soto, Nakul Khanna, Nat McAleese, Natalie Staudacher, Natan LaFontaine, Neel Ajjarapu, Nick Felt, Nick Turley, Nikil Pancha, Nikita Mikhaylin, Niko Felix, Nikunj Handa, Ning Liu, Nishant Rai, Noah Jorgensen, Noam Brown, Oleg Boiko, Oleg Murk, Olivia Watkins, Olivier Godement, Oona Gleeson, Paul Ashbourne, Pavel Belov, Peter Flockhart, Peter Hoeschele, Peter Zhokhov, Philip Pronin, Phillip Guo, Phoebe Thacker, Prafulla Dhariwal, Prashanth R, Rachel Dias, Rahul Arora, Rajkumar Samuel, Rasmus Rygaard, Ravi Teja Mullapudi, Raymond Li, Raz Gaon, Reah Miyara, Reiichiro Nakano, Reimar Leike, Rennie Song, Rhythm Garg, RJ Marsan, Robert Xiong, Robin Brown, Roman Tsiupa, Rui Shu, Ruslan Nigmatullin, Saachi Jain, Saagar Patel, Sam Altman, Sam Toizer, Sam Toyer, Samir Ahmed, Samuel Miserendino, Samuel Wolrich , Sandhini Agarwal, Santiago Hernández, Sarah Dong, Savannah Heon, Scott Ethersmith, Scott Mayer McKinney, Sean Fitzgerald, Sever Banesiu, Shamez Hemani, Shengjia Zhao, Shengli Hu, Shibani Santurkar, Shreyas Krishnaswamy, Shuchao Bi, Shunyu Yao, Shuyuan Zhang, Simón Posada Fishman, Spencer Papay, Spug Golden, Srinivas Narayanan, Stanley Hsieh, Stephen Logsdon, Sundeep Tirumalareddy, Tal Stramer, Tao Wang, Tao Xin, Taylor Gordon, Tejal Patwardhan, Thibault Sottiaux, Tina Sriskandarajah, Tony Casparro, Tony Zhao, Trevor Creech, Uzair Navid Iftikhar, Valerie Qi, Vineet Kosaraju, Vishal Kuo, Vitchyr Pong, Vivek Verma, Vlad Petrov, Wenda Zhou, Wenlei Xie, Wenting Zhan, Will DePue, Will Ellsworth, William Sheu, Wyatt Thompson, Yaming Lin, Yann Dubois, Yaodong Yu, Yara Khakbaz, Yash Patil, Yifan Wu, Yilong Qin, Yining Chen, Yirui Zhang, Yo Shavit , Young Cha, Yunyun Wang, Yushi Wang, Zack Sultan, Zehao Dou, Zewei Chu, Zheng Shao, Zhigang Wang, Zhishuai Zhang, Zihao Zhang